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AI.R

Not Even the EPA Can Say What's Polluting the Air

The HackerNoon Newsletter: Lumoz Unveils esMOZ Airdrop Details (11/17/2024)

We're thrilled to announce the forthcoming Lumoz’s esMOZ airdrop, distributed to all sorts of contributors! This milestone wouldn't have been possible without the dedication and contributions of our vibrant community. Over the last two years, our community has supported Lumoz through key phases: the Pre-Alpha testnet engaged 87,567 active participants, the Alpha testnet attracted 286,179 followers, and participation in the Quidditch testnet exceeded one million. These numbers underscore the community’s strong support and trust in Lumoz. Your contributions have driven invaluable feedback, strengthening Lumoz’s technical foundation and shaping our ecosystem's growth. This airdrop is our way of expressing gratitude for your continued support and is a significant step toward our journey into the next chapter. Airdrop Rules Airdrop Inquiry Link: https://lumoz.org/airdrop Lumoz Tokens have a total supply of 10 billion, with 10% (1 billion esMOZ tokens) dedicated to this airdrop. Based on our recent valuation, this represents a value of approximately $30 million. The exchange rate for esMOZ to MOZ will be 1:1, and the exchange will follow an unlocking schedule as detailed in our official documentation (https://docs.lumoz.org/). As the largest airdrop in Lumoz's history, it will target early adopters, Lumoz PoW & node holders, ecosystem contributors, and active participants from ecosystems like ETH, Celestia, and the Move Ecosystem. Detailed Eligibility Criteria: Early Lumoz Participants:  Lumoz Point holders will receive esMOZ on a 1:1 basis for points held. Users with over 500 points will also receive bonus esMOZ airdrops.


Lumoz PoW Testnet Participants: From November 5 to December 5, Lumoz will host ZK mining on the testnet. Participants will earn esMOZ airdrops proportional to MOZ test tokens mined during this period. Updated rewards will be available on the airdrop page.


Lumoz zkVerifier Node Holders:  Holders of the Lumoz zkVerifier License, as captured in the October 26 snapshot, are eligible for airdrops.


Lumoz Ecosystem Users: This includes users of Lumoz RaaS services in projects like Merlin Chain, ZKFair, Ultiverse, and Matr1x. Active users in these ecosystems will receive direct airdrops, visible on the official airdrop page starting November 5. This portion of the airdrop will consist of two parts: The first part will be directly airdropped to active addresses in the ecosystem, which can be checked on the Lumoz official airdrop page starting November 5. The second part will be airdropped to users participating in ecosystem-related activities. After the events conclude, the esMOZ earned through participation will be updated on the Lumoz official airdrop page. Please follow official updates from each ecosystem for specific activity times. Active Users in Ecosystems like ETH, Celestia, and Move: Eligible users include: Participants interacting with major DeFi projects in ETH, including Ethereum, Polygon, and Arbitrum over the past six months.


Significant stakers in the Celestia network. Active users engaging with leading DeFi projects in Move, primarily Aptos and Sui, within the past six months. Please note that the airdrop inquiry period will last one month, during which, specific claim details will be announced. NFT Activity Coming Soon After obtaining esMOZ, users are naturally most concerned about the exchange rules. Lumoz's official documentation has previously stated that the exchange ratio between esMOZ and MOZ is 1:1, although there will be a certain unlocking period. While this setup is designed for Lumoz's long-term development, there have been voices in the community expressing a desire for an earlier unlocking. We value the feedback from every community user, which is why we have introduced an NFT section that will allow users to directly exchange a certain amount of esMOZ for MOZ. NFTs will be set at different levels, with each level offering varying esMOZ exchange limits. In the future, NFTs will also support free circulation, allowing users to exchange according to their needs for flexible asset management. We will announce the rules for obtaining NFTs shortly, so stay tuned! This airdrop marks just the beginning for Lumoz. Follow our official Twitter for updates and stay informed on our journey forward. About Lumoz Lumoz is a leading modular computing layer and ZK-RaaS platform, delivering computation for Rollups, ZK-ML, and ZKP verification through its PoW mining system. Earlier this year, Lumoz completed its Pre-A funding round, raising $14 million with backing from prominent investors like OKX Ventures, HashKey Capital, KuCoin Ventures, Polygon, and IDG Blockchain. With over 1.5 million users, 200+ projects, 28,137 validators, and 145 PoW miners engaged, Lumoz’s mainnet is set to launch by year’s end. We're thrilled to announce the forthcoming Lumoz’s esMOZ airdrop, distributed to all sorts of contributors! This milestone wouldn't have been possible without the dedication and contributions of our vibrant community. Over the last two years, our community has supported Lumoz through key phases: the Pre-Alpha testnet engaged 87,567 active participants, the Alpha testnet attracted 286,179 followers, and participation in the Quidditch testnet exceeded one million. These numbers underscore the community’s strong support and trust in Lumoz. Your contributions have driven invaluable feedback, strengthening Lumoz’s technical foundation and shaping our ecosystem's growth. This airdrop is our way of expressing gratitude for your continued support and is a significant step toward our journey into the next chapter. Airdrop Rules Airdrop Inquiry Link: https://lumoz.org/airdrop https://lumoz.org/airdrop https://lumoz.org/airdrop Lumoz Tokens have a total supply of 10 billion, with 10% (1 billion esMOZ tokens) dedicated to this airdrop. Based on our recent valuation, this represents a value of approximately $30 million. The exchange rate for esMOZ to MOZ will be 1:1, and the exchange will follow an unlocking schedule as detailed in our official documentation ( https://docs.lumoz.org/ ). https://docs.lumoz.org/ As the largest airdrop in Lumoz's history, it will target early adopters, Lumoz PoW & node holders, ecosystem contributors, and active participants from ecosystems like ETH, Celestia, and the Move Ecosystem. Detailed Eligibility Criteria: Detailed Eligibility Criteria: Early Lumoz Participants:  Lumoz Point holders will receive esMOZ on a 1:1 basis for points held. Users with over 500 points will also receive bonus esMOZ airdrops. Lumoz PoW Testnet Participants: From November 5 to December 5, Lumoz will host ZK mining on the testnet. Participants will earn esMOZ airdrops proportional to MOZ test tokens mined during this period. Updated rewards will be available on the airdrop page. Lumoz zkVerifier Node Holders:  Holders of the Lumoz zkVerifier License, as captured in the October 26 snapshot, are eligible for airdrops. Lumoz Ecosystem Users: This includes users of Lumoz RaaS services in projects like Merlin Chain, ZKFair, Ultiverse, and Matr1x. Active users in these ecosystems will receive direct airdrops, visible on the official airdrop page starting November 5. This portion of the airdrop will consist of two parts: Early Lumoz Participants:  Lumoz Point holders will receive esMOZ on a 1:1 basis for points held. Users with over 500 points will also receive bonus esMOZ airdrops. Early Lumoz Participants:  Lumoz Point holders will receive esMOZ on a 1:1 basis for points held. Users with over 500 points will also receive bonus esMOZ airdrops. Lumoz PoW Testnet Participants: From November 5 to December 5, Lumoz will host ZK mining on the testnet. Participants will earn esMOZ airdrops proportional to MOZ test tokens mined during this period. Updated rewards will be available on the airdrop page. Lumoz PoW Testnet Participants: From November 5 to December 5, Lumoz will host ZK mining on the testnet. Participants will earn esMOZ airdrops proportional to MOZ test tokens mined during this period. Updated rewards will be available on the airdrop page. Lumoz zkVerifier Node Holders:  Holders of the Lumoz zkVerifier License, as captured in the October 26 snapshot, are eligible for airdrops. Lumoz zkVerifier Node Holders:  Holders of the Lumoz zkVerifier License, as captured in the October 26 snapshot, are eligible for airdrops. Lumoz Ecosystem Users: This includes users of Lumoz RaaS services in projects like Merlin Chain, ZKFair, Ultiverse, and Matr1x. Active users in these ecosystems will receive direct airdrops, visible on the official airdrop page starting November 5. This portion of the airdrop will consist of two parts: Lumoz Ecosystem Users: This includes users of Lumoz RaaS services in projects like Merlin Chain, ZKFair, Ultiverse, and Matr1x. Active users in these ecosystems will receive direct airdrops, visible on the official airdrop page starting November 5. This portion of the airdrop will consist of two parts: The first part will be directly airdropped to active addresses in the ecosystem, which can be checked on the Lumoz official airdrop page starting November 5. The first part will be directly airdropped to active addresses in the ecosystem, which can be checked on the Lumoz official airdrop page starting November 5. The second part will be airdropped to users participating in ecosystem-related activities. After the events conclude, the esMOZ earned through participation will be updated on the Lumoz official airdrop page. Please follow official updates from each ecosystem for specific activity times. The second part will be airdropped to users participating in ecosystem-related activities. After the events conclude, the esMOZ earned through participation will be updated on the Lumoz official airdrop page. Please follow official updates from each ecosystem for specific activity times. Active Users in Ecosystems like ETH, Celestia, and Move: Eligible users include: Active Users in Ecosystems like ETH, Celestia, and Move: Eligible users include: Participants interacting with major DeFi projects in ETH, including Ethereum, Polygon, and Arbitrum over the past six months. Significant stakers in the Celestia network. Participants interacting with major DeFi projects in ETH, including Ethereum, Polygon, and Arbitrum over the past six months. Participants interacting with major DeFi projects in ETH, including Ethereum, Polygon, and Arbitrum over the past six months. Significant stakers in the Celestia network. Significant stakers in the Celestia network. Active users engaging with leading DeFi projects in Move, primarily Aptos and Sui, within the past six months. Please note that the airdrop inquiry period will last one month, during which, specific claim details will be announced. Active users engaging with leading DeFi projects in Move, primarily Aptos and Sui, within the past six months. Please note that the airdrop inquiry period will last one month, during which, specific claim details will be announced. NFT Activity Coming Soon NFT Activity Coming Soon After obtaining esMOZ, users are naturally most concerned about the exchange rules. Lumoz's official documentation has previously stated that the exchange ratio between esMOZ and MOZ is 1:1, although there will be a certain unlocking period. While this setup is designed for Lumoz's long-term development, there have been voices in the community expressing a desire for an earlier unlocking. We value the feedback from every community user, which is why we have introduced an NFT section that will allow users to directly exchange a certain amount of esMOZ for MOZ. NFTs will be set at different levels, with each level offering varying esMOZ exchange limits. In the future, NFTs will also support free circulation, allowing users to exchange according to their needs for flexible asset management. We will announce the rules for obtaining NFTs shortly, so stay tuned! This airdrop marks just the beginning for Lumoz. Follow our official Twitter for updates and stay informed on our journey forward. About Lumoz About Lumoz Lumoz is a leading modular computing layer and ZK-RaaS platform, delivering computation for Rollups, ZK-ML, and ZKP verification through its PoW mining system. Earlier this year, Lumoz completed its Pre-A funding round, raising $14 million with backing from prominent investors like OKX Ventures, HashKey Capital, KuCoin Ventures, Polygon, and IDG Blockchain. With over 1.5 million users, 200+ projects, 28,137 validators, and 145 PoW miners engaged, Lumoz’s mainnet is set to launch by year’s end.

Lumoz Unveils esMOZ Airdrop Details

Lumoz revela detalles del lanzamiento aéreo de esMOZ

Lumoz Devwale Detay Airdrop esMOZ

A Lumoz bemutatja az esMOZ Airdrop részleteit

Lumoz svela i dettagli dell'airdrop esMOZ

LumozがesMOZエアドロップの詳細を発表

Lumoz បង្ហាញព័ត៌មានលម្អិត esMOZ Airdrop

Lumoz onthult esMOZ Airdrop-details

Lumoz ujawnia szczegóły zrzutu esMOZ

Lumoz Desvela esMOZ Airdrop Detalles

Lumoz zbulon detajet e esMOZ Airdrop

Lumoz тафсилоти esMOZ Airdrop-ро ошкор мекунад

Lumoz esMOZ Airdrop tafsilotlarini ochib beradi

If free money sounds suspicious to you, then you’re doing a good job of taking care of your funds. But fear not, because, in this case, crypto airdrops are a totally legit marketing tool. They’ve been around for years, and they keep coming. Many cryptocurrency projects actually give away a portion of their coins to gain adoption and recognition among users. That’s exactly what an airdrop is, indeed: a method used by cryptocurrency projects to distribute free tokens to a group of users, often as part of a marketing or community-building strategy. It typically works by sending tokens directly to users’ wallets based on certain criteria, such as holding a specific coin or completing tasks like social media engagement. Airdrop’s Purpose & Types Crypto airdrops are used to distribute tokens widely and quickly, helping projects build an initial ownership base. When tokens are owned by many people, the project becomes more stable, as its value isn’t concentrated in the hands of a few. Airdrops also serve as a strong marketing tool, drawing attention to the project as people are often eager to receive free tokens. This excitement helps increase awareness and brings new users into the ecosystem. Airdrops can also be used to reward loyal community members. By offering tokens to existing supporters, development teams foster a sense of appreciation, encouraging these users to stay engaged with the project and reducing the likelihood of them selling off their holdings. This approach helps maintain the token's price and strengthens community loyalty over time. Not all airdrops are the same, though, and their intended effectiveness could vary. There are several types of airdrops, each serving a different purpose. Standard airdrops require users to sign up, offering a straightforward way to receive tokens. Bounty airdrops, on the other hand, require users to perform specific tasks like promoting the project or contributing to its development. Lastly, holder airdrops reward existing supporters who already own a certain cryptocurrency, often without needing them to take any further action. Some Downsides Airdrops can be a great way to boost awareness and attract users to a crypto project, but they come with several challenges --especially for the team behind the projects and its loyal community. One significant downside is the sell pressure they create. Since recipients get tokens for free, many are quick to sell them off rather than hold them for the long term. This sudden increase in sell pressure can drive down the token’s price, hindering the project’s market stability and long-term value. Another issue is the potential for users to exploit the airdrop process. Some participants may create multiple accounts or fake activities to maximize their rewards while contributing little to the project. This not only skews the token distribution but also wastes resources that could have been better spent on genuine supporters. Additionally, airdrop hunters often have no loyalty to the project. Their goal could be only to collect tokens and sell them immediately, rather than becoming active members of the community. This can make it difficult to build a dedicated user base and achieve sustainable growth. As we can see, the effectiveness of airdrops is debatable, as they often attract short-term users. However, they remain a useful complementary tool for generating initial interest and bringing attention to new crypto projects. How to Participate in a Crypto Airdrop To participate in a crypto airdrop, the first step is to meet the eligibility criteria set by the project. These requirements can vary and may include, as we’ve mentioned, simple actions like signing up or more involved tasks such as promoting the project on social media. Regardless of the specific conditions, you’ll always need a crypto wallet compatible with that specific platform to receive the tokens. In most cases, when an airdrop is announced, pay attention to two important dates: the snapshot and the distribution. The snapshot is when the project team records the list of wallets that qualify for the airdrop, so you’ll need to ensure you meet all requirements by that time. The distribution date is when the tokens will be sent to your wallet, marking the completion of the airdrop process. Staying up to date with your favorite networks on social media could help you to discover new airdrops. However, it’s important to always stay cautious. Only follow official instructions (from official accounts) to avoid potential scams, and keep in mind that you may have tax obligations on any tokens you receive. Even if the token’s value drops, taxes may still apply, so it’s wise to plan ahead. Additionally, remember that cryptocurrencies can be volatile, so airdropped tokens may fluctuate in value significantly. Obyte Distribution Over the years, Obyte has had several types of airdrops trying to help with the distribution and adoption of its native currency GBYTE and the private coin Blackbytes (GBB). Instead of an Initial Coin Offering (ICO) or a similar crowd sale, GBYTEs started their journey by being distributed for free to Bitcoin (BTC) holders who chose to participate between 2016 and 2017. Around 645,341 GBYTEs (more than 64% of the total supply) were distributed this way to foster adoption. In the following years, other “bounty airdrop” programs were added to welcome more users, and some of them are still available. Currently, you can earn free GBYTEs in Obyte by verifying your personal information through attestations. This process allows you to confirm details like your real name, email, or GitHub account using chatbots in the Obyte wallet. Depending on the type of attestation you complete, you can earn between $8 and $79 in GBYTEs as a reward. These attestations also provide access to various applications within the Obyte ecosystem. Another way to earn some free GBYTEs is by participating in our Telegram quiz. By answering multiple-choice questions about Obyte correctly, you can earn at least $0.02 in GBYTEs, paid as a textcoin. It’s an easy way to learn about Obyte while gaining small rewards. Now, if you’re interested in doing a bit more work, we also have a Grants Program available for open-source projects that enhance our ecosystem. Everyone is welcome to participate! Featured Vector Image by Freepik If free money sounds suspicious to you, then you’re doing a good job of taking care of your funds. But fear not, because, in this case, crypto airdrops are a totally legit marketing tool. They’ve been around for years, and they keep coming. Many cryptocurrency projects actually give away a portion of their coins to gain adoption and recognition among users. That’s exactly what an airdrop is, indeed: a method used by cryptocurrency projects to distribute free tokens to a group of users, often as part of a marketing or community-building strategy . It typically works by sending tokens directly to users’ wallets based on certain criteria, such as holding a specific coin or completing tasks like social media engagement. That’s exactly what an airdrop is, indeed: a method used by cryptocurrency projects to distribute free tokens to a group of users, often as part of a marketing or community-building strategy Airdrop’s Purpose & Types Crypto airdrops are used to distribute tokens widely and quickly, helping projects build an initial ownership base. When tokens are owned by many people, the project becomes more stable, as its value isn’t concentrated in the hands of a few. Airdrops also serve as a strong marketing tool, drawing attention to the project as people are often eager to receive free tokens. This excitement helps increase awareness and brings new users into the ecosystem. Airdrops can also be used to reward loyal community members. By offering tokens to existing supporters, development teams foster a sense of appreciation, encouraging these users to stay engaged with the project and reducing the likelihood of them selling off their holdings. This approach helps maintain the token's price and strengthens community loyalty over time. Not all airdrops are the same, though, and their intended effectiveness could vary. There are several types of airdrops , each serving a different purpose. Standard airdrops require users to sign up, offering a straightforward way to receive tokens. Bounty airdrops, on the other hand, require users to perform specific tasks like promoting the project or contributing to its development. Lastly, holder airdrops reward existing supporters who already own a certain cryptocurrency, often without needing them to take any further action. Not all airdrops are the same, though, and their intended effectiveness could vary. several types of airdrops several types of airdrops Some Downsides Airdrops can be a great way to boost awareness and attract users to a crypto project, but they come with several challenges --especially for the team behind the projects and its loyal community. One significant downside is the sell pressure they create. Since recipients get tokens for free, many are quick to sell them off rather than hold them for the long term. This sudden increase in sell pressure can drive down the token’s price, hindering the project’s market stability and long-term value. Another issue is the potential for users to exploit the airdrop process. Some participants may create multiple accounts or fake activities to maximize their rewards while contributing little to the project. This not only skews the token distribution but also wastes resources that could have been better spent on genuine supporters. This not only skews the token distribution but also wastes resources that could have been better spent on genuine supporters. Additionally, airdrop hunters often have no loyalty to the project. Their goal could be only to collect tokens and sell them immediately, rather than becoming active members of the community. This can make it difficult to build a dedicated user base and achieve sustainable growth. As we can see, the effectiveness of airdrops is debatable, as they often attract short-term users. However, they remain a useful complementary tool for generating initial interest and bringing attention to new crypto projects. How to Participate in a Crypto Airdrop To participate in a crypto airdrop, the first step is to meet the eligibility criteria set by the project. These requirements can vary and may include, as we’ve mentioned, simple actions like signing up or more involved tasks such as promoting the project on social media. Regardless of the specific conditions, you’ll always need a crypto wallet compatible with that specific platform to receive the tokens. In most cases, when an airdrop is announced, pay attention to two important dates: the snapshot and the distribution . In most cases, when an airdrop is announced, pay attention to two important dates: the snapshot and the distribution The snapshot is when the project team records the list of wallets that qualify for the airdrop, so you’ll need to ensure you meet all requirements by that time. The distribution date is when the tokens will be sent to your wallet, marking the completion of the airdrop process. Staying up to date with your favorite networks on social media could help you to discover new airdrops. However, it’s important to always stay cautious. Only follow official instructions (from official accounts) to avoid potential scams , and keep in mind that you may have tax obligations on any tokens you receive. Even if the token’s value drops, taxes may still apply, so it’s wise to plan ahead. Additionally, remember that cryptocurrencies can be volatile, so airdropped tokens may fluctuate in value significantly. potential scams potential scams Obyte Distribution Over the years, Obyte has had several types of airdrops trying to help with the distribution and adoption of its native currency GBYTE and the private coin Blackbytes (GBB) . Instead of an Initial Coin Offering (ICO) or a similar crowd sale, GBYTEs started their journey by being distributed for free to Bitcoin (BTC) holders who chose to participate between 2016 and 2017. Blackbytes (GBB) Blackbytes (GBB) Around 645,341 GBYTEs (more than 64% of the total supply) were distributed this way to foster adoption. In the following years , other “bounty airdrop” programs were added to welcome more users, and some of them are still available. Currently, you can earn free GBYTEs in Obyte by verifying your personal information through attestations. This process allows you to confirm details like your real name, email, or GitHub account using chatbots in the Obyte wallet. In the following years In the following years Currently, you can earn free GBYTEs in Obyte by verifying your personal information through attestations . through attestations through attestations Depending on the type of attestation you complete, you can earn between $8 and $79 in GBYTEs as a reward. These attestations also provide access to various applications within the Obyte ecosystem. Another way to earn some free GBYTEs is by participating in our Telegram quiz . By answering multiple-choice questions about Obyte correctly, you can earn at least $0.02 in GBYTEs, paid as a textcoin. It’s an easy way to learn about Obyte while gaining small rewards. Now, if you’re interested in doing a bit more work, we also have a Grants Program available for open-source projects that enhance our ecosystem. Everyone is welcome to participate! Telegram quiz Telegram quiz Grants Program Grants Program Featured Vector Image by Freepik Featured Vector Image by Freepik Freepik Freepik

Educational Byte: What Is a Crypto Airdrop or How to Earn Free Money

بايت تعليمي: ما هو Airdrop للعملات المشفرة أو كيفية كسب أموال مجانية

Навучальны байт: Што такое Crypto Airdrop або Як зарабіць бясплатныя грошы

শিক্ষাগত বাইট: একটি ক্রিপ্টো এয়ারড্রপ কী বা কীভাবে বিনামূল্যে অর্থ উপার্জন করা যায়

Εκπαιδευτικό Byte: Τι είναι το Crypto Airdrop ή πώς να κερδίσετε δωρεάν χρήματα

Byte educativo: ¿Qué es un airdrop de criptomonedas o cómo ganar dinero gratis?

教育バイト: 暗号通貨エアドロップとは何か、または無料でお金を稼ぐ方法

Билим берүү байт: Crypto Airdrop деген эмне же кантип бекер акча табуу керек

Educational Byte: Inona ny Crypto Airdrop na ny fomba hahazoana vola maimaim-poana

Боловсролын байт: Crypto Airdrop гэж юу вэ эсвэл яаж үнэгүй мөнгө олох вэ

تعلیمي بایټ: کریپټو ایرډراپ څه شی دی یا څنګه وړیا پیسې وګټئ

Byte Educativo: Imataq Crypto Airdrop utaq Imaynatataq Gratis Qullqita Ganana

I-Byte yeMfundo: Yintoni i-Crypto Airdrop okanye Uyifumana njani imali yasimahla

Authors:
(1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany;
(2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany;
(3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany;
(4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Numerical Example Conclusion and References VI. CONCLUSION In this paper, we have introduced the FedFAir algorithm which uses Over-the-Air Computation to carry out efficient decentralized learning while providing fairness and improved performance. We have shown that the FedFAir algorithm converges to an optimal solution of the minimax problem. Furthermore, we have also illustrated our theoretical findings with a numerical example. Future research will include the development of resilient federated learning algorithms when there are malicious agents in the system. REFERENCES [1] B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, “Communication-efficient learning of deep networks from decentralized data,” in Artificial intelligence and statistics. PMLR, 2017, pp. 1273–1282. [2] V. Smith, C.-K. Chiang, M. Sanjabi, and A. S. Talwalkar, “Federated multi-task learning,” Advances in neural information processing systems, vol. 30, 2017. [3] K. Bonawitz, H. Eichner, W. Grieskamp, D. Huba, A. Ingerman, V. Ivanov, C. Kiddon, J. Konecny, S. Mazzocchi, B. McMahan et al., “Towards federated learning at scale: System design,” Proceedings of Machine Learning and Systems, vol. 1, pp. 374–388, 2019. [4] Q. Yang, Y. Liu, T. Chen, and Y. Tong, “Federated machine learning: Concept and applications,” ACM Transactions on Intelligent Systems and Technology (TIST), vol. 10, no. 2, pp. 1–19, 2019. [5] A. Nedic, “Distributed gradient methods for convex machine learning problems in networks: Distributed optimization,” IEEE Signal Processing Magazine, vol. 37, no. 3, pp. 92–101, 2020. [6] V. P. Chellapandi, A. Upadhyay, A. Hashemi, and S. H. Zak, “On ˙ the convergence of decentralized federated learning under imperfect information sharing,” IEEE Control Systems Letters, 2023. [7] T. Omori and K. Kashima, “Combinatorial optimization approach to client scheduling for federated learning,” IEEE Control Systems Letters, 2023. [8] T. Sery, N. Shlezinger, K. Cohen, and Y. C. Eldar, “Over-the-air federated learning from heterogeneous data,” IEEE Transactions on Signal Processing, vol. 69, pp. 3796–3811, 2021. [9] T. Gafni, N. Shlezinger, K. Cohen, Y. C. Eldar, and H. V. Poor, “Federated learning: A signal processing perspective,” IEEE Signal Processing Magazine, vol. 39, no. 3, pp. 14–41, 2022. [10] M. Ye, X. Fang, B. Du, P. C. Yuen, and D. Tao, “Heterogeneous federated learning: State-of-the-art and research challenges,” ACM Computing Surveys, vol. 56, no. 3, pp. 1–44, 2023. [11] J. Koneˇcn `y, H. B. McMahan, F. X. Yu, P. Richt´arik, A. T. Suresh, and D. Bacon, “Federated learning: Strategies for improving communication efficiency,” arXiv preprint arXiv:1610.05492, 2016. [12] T. Li, A. K. Sahu, A. Talwalkar, and V. Smith, “Federated learning: Challenges, methods, and future directions,” IEEE Signal Processing Magazine, vol. 37, no. 3, pp. 50–60, 2020. [13] P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis, A. N. Bhagoji, K. Bonawitz, Z. Charles, G. Cormode, R. Cummings et al., “Advances and open problems in federated learning,” Foundations and Trends® in Machine Learning, vol. 14, no. 1–2, pp. 1–210, 2021. [14] H. Y. Oksuz, F. Molinari, H. Sprekeler, and J. Raisch, “Federated learning in wireless networks via over-the-air computations,” in 2023 62nd IEEE Conference on Decision and Control (CDC), 2023, pp. 4379–4386. [15] F. Molinari, N. Agrawal, S. Sta´nczak, and J. Raisch, “Max-consensus over fading wireless channels,” IEEE Transactions on Control of Network Systems, vol. 8, no. 2, pp. 791–802, 2021. [16] M. Frey, I. Bjelakovi´c, and S. Sta´nczak, “Over-the-air computation in correlated channels,” IEEE Transactions on Signal Processing, vol. 69, pp. 5739–5755, 2021. [17] K. Yang, T. Jiang, Y. Shi, and Z. Ding, “Federated learning via overthe-air computation,” IEEE Transactions on Wireless Communications, vol. 19, no. 3, pp. 2022–2035, 2020. [18] F. Molinari and J. Raisch, “Exploiting wireless interference for distributively solving linear equations,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 2999–3006, 2020. [19] D. Bertsekas, A. Nedic, and A. Ozdaglar, Convex analysis and optimization. Athena Scientific, 2003, vol. 1. [20] M. Mohri, G. Sivek, and A. T. Suresh, “Agnostic federated learning,” in International Conference on Machine Learning. PMLR, 2019, pp. 4615–4625. [21] Z. Hu, K. Shaloudegi, G. Zhang, and Y. Yu, “Federated learning meets multi-objective optimization,” IEEE Transactions on Network Science and Engineering, vol. 9, no. 4, pp. 2039–2051, 2022. [22] D. P. Bertsekas, “Necessary and sufficient conditions for a penalty method to be exact,” Mathematical programming, vol. 9, no. 1, pp. 87–99, 1975. [23] K. Srivastava, A. Nedi´c, and D. Stipanovi´c, “Distributed min-max optimization in networks,” in 2011 17th International Conference on Digital Signal Processing (DSP). IEEE, 2011, pp. 1–8. [24] R. Ahlswede, “Multi-way communication channels,” in Second International Symposium on Information Theory: Tsahkadsor, Armenia, USSR, Sept. 2-8, 1971, 1973. [25] A. Giridhar and P. Kumar, “Toward a theory of in-network computation in wireless sensor networks,” IEEE Communications Magazine, vol. 44, no. 4, pp. 98–107, apr 2006. [26] F. Molinari, N. Agrawal, S. Sta´nczak, and J. Raisch, “Over-the-air max-consensus in clustered networks adopting half-duplex communication technology,” IEEE Transactions on Control of Network Systems, 2022. [27] W. Rudin et al., Principles of mathematical analysis. McGraw-hill New York, 1976, vol. 3. [28] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University Press, 2012. [29] A. F. Molisch, Wireless communications. John Wiley & Sons, 2012. [30] B. Sklar, “Rayleigh fading channels in mobile digital communication systems. i. characterization,” IEEE Communications magazine, vol. 35, no. 7, pp. 90–100, 1997. [31] R. G. Bartle and D. R. Sherbert, Introduction to real analysis. Wiley New York, 2000. [32] B. T. Polyak, Introduction to optimization. optimization software. Inc., Publications Division, New York, 1987. [33] Y. I. Alber, A. N. Iusem, and M. V. Solodov, “On the projected subgradient method for nonsmooth convex optimization in a hilbert space,” Mathematical Programming, vol. 81, pp. 23–35, 1998. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Authors: Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Abstract and Introduction Problem Setup Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Convergence Properties Numerical Example Numerical Example Conclusion and References Conclusion and References VI. CONCLUSION In this paper, we have introduced the FedFAir algorithm which uses Over-the-Air Computation to carry out efficient decentralized learning while providing fairness and improved performance. We have shown that the FedFAir algorithm converges to an optimal solution of the minimax problem. Furthermore, we have also illustrated our theoretical findings with a numerical example. Future research will include the development of resilient federated learning algorithms when there are malicious agents in the system. REFERENCES [1] B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, “Communication-efficient learning of deep networks from decentralized data,” in Artificial intelligence and statistics. PMLR, 2017, pp. 1273–1282. [2] V. Smith, C.-K. Chiang, M. Sanjabi, and A. S. Talwalkar, “Federated multi-task learning,” Advances in neural information processing systems, vol. 30, 2017. [3] K. Bonawitz, H. Eichner, W. Grieskamp, D. Huba, A. Ingerman, V. Ivanov, C. Kiddon, J. Konecny, S. Mazzocchi, B. McMahan et al., “Towards federated learning at scale: System design,” Proceedings of Machine Learning and Systems, vol. 1, pp. 374–388, 2019. [4] Q. Yang, Y. Liu, T. Chen, and Y. Tong, “Federated machine learning: Concept and applications,” ACM Transactions on Intelligent Systems and Technology (TIST), vol. 10, no. 2, pp. 1–19, 2019. [5] A. Nedic, “Distributed gradient methods for convex machine learning problems in networks: Distributed optimization,” IEEE Signal Processing Magazine, vol. 37, no. 3, pp. 92–101, 2020. [6] V. P. Chellapandi, A. Upadhyay, A. Hashemi, and S. H. Zak, “On ˙ the convergence of decentralized federated learning under imperfect information sharing,” IEEE Control Systems Letters, 2023. [7] T. Omori and K. Kashima, “Combinatorial optimization approach to client scheduling for federated learning,” IEEE Control Systems Letters, 2023. [8] T. Sery, N. Shlezinger, K. Cohen, and Y. C. Eldar, “Over-the-air federated learning from heterogeneous data,” IEEE Transactions on Signal Processing, vol. 69, pp. 3796–3811, 2021. [9] T. Gafni, N. Shlezinger, K. Cohen, Y. C. Eldar, and H. V. Poor, “Federated learning: A signal processing perspective,” IEEE Signal Processing Magazine, vol. 39, no. 3, pp. 14–41, 2022. [10] M. Ye, X. Fang, B. Du, P. C. Yuen, and D. Tao, “Heterogeneous federated learning: State-of-the-art and research challenges,” ACM Computing Surveys, vol. 56, no. 3, pp. 1–44, 2023. [11] J. Koneˇcn `y, H. B. McMahan, F. X. Yu, P. Richt´arik, A. T. Suresh, and D. Bacon, “Federated learning: Strategies for improving communication efficiency,” arXiv preprint arXiv:1610.05492, 2016. [12] T. Li, A. K. Sahu, A. Talwalkar, and V. Smith, “Federated learning: Challenges, methods, and future directions,” IEEE Signal Processing Magazine, vol. 37, no. 3, pp. 50–60, 2020. [13] P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis, A. N. Bhagoji, K. Bonawitz, Z. Charles, G. Cormode, R. Cummings et al., “Advances and open problems in federated learning,” Foundations and Trends® in Machine Learning, vol. 14, no. 1–2, pp. 1–210, 2021. [14] H. Y. Oksuz, F. Molinari, H. Sprekeler, and J. Raisch, “Federated learning in wireless networks via over-the-air computations,” in 2023 62nd IEEE Conference on Decision and Control (CDC), 2023, pp. 4379–4386. [15] F. Molinari, N. Agrawal, S. Sta´nczak, and J. Raisch, “Max-consensus over fading wireless channels,” IEEE Transactions on Control of Network Systems, vol. 8, no. 2, pp. 791–802, 2021. [16] M. Frey, I. Bjelakovi´c, and S. Sta´nczak, “Over-the-air computation in correlated channels,” IEEE Transactions on Signal Processing, vol. 69, pp. 5739–5755, 2021. [17] K. Yang, T. Jiang, Y. Shi, and Z. Ding, “Federated learning via overthe-air computation,” IEEE Transactions on Wireless Communications, vol. 19, no. 3, pp. 2022–2035, 2020. [18] F. Molinari and J. Raisch, “Exploiting wireless interference for distributively solving linear equations,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 2999–3006, 2020. [19] D. Bertsekas, A. Nedic, and A. Ozdaglar, Convex analysis and optimization. Athena Scientific, 2003, vol. 1. [20] M. Mohri, G. Sivek, and A. T. Suresh, “Agnostic federated learning,” in International Conference on Machine Learning. PMLR, 2019, pp. 4615–4625. [21] Z. Hu, K. Shaloudegi, G. Zhang, and Y. Yu, “Federated learning meets multi-objective optimization,” IEEE Transactions on Network Science and Engineering, vol. 9, no. 4, pp. 2039–2051, 2022. [22] D. P. Bertsekas, “Necessary and sufficient conditions for a penalty method to be exact,” Mathematical programming, vol. 9, no. 1, pp. 87–99, 1975. [23] K. Srivastava, A. Nedi´c, and D. Stipanovi´c, “Distributed min-max optimization in networks,” in 2011 17th International Conference on Digital Signal Processing (DSP). IEEE, 2011, pp. 1–8. [24] R. Ahlswede, “Multi-way communication channels,” in Second International Symposium on Information Theory: Tsahkadsor, Armenia, USSR, Sept. 2-8, 1971, 1973. [25] A. Giridhar and P. Kumar, “Toward a theory of in-network computation in wireless sensor networks,” IEEE Communications Magazine, vol. 44, no. 4, pp. 98–107, apr 2006. [26] F. Molinari, N. Agrawal, S. Sta´nczak, and J. Raisch, “Over-the-air max-consensus in clustered networks adopting half-duplex communication technology,” IEEE Transactions on Control of Network Systems, 2022. [27] W. Rudin et al., Principles of mathematical analysis. McGraw-hill New York, 1976, vol. 3. [28] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University Press, 2012. [29] A. F. Molisch, Wireless communications. John Wiley & Sons, 2012. [30] B. Sklar, “Rayleigh fading channels in mobile digital communication systems. i. characterization,” IEEE Communications magazine, vol. 35, no. 7, pp. 90–100, 1997. [31] R. G. Bartle and D. R. Sherbert, Introduction to real analysis. Wiley New York, 2000. [32] B. T. Polyak, Introduction to optimization. optimization software. Inc., Publications Division, New York, 1987. [33] Y. I. Alber, A. N. Iusem, and M. V. Solodov, “On the projected subgradient method for nonsmooth convex optimization in a hilbert space,” Mathematical Programming, vol. 81, pp. 23–35, 1998. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Boosting Fairness and Robustness in Over-the-Air Federated Learning: Conclusion and References

Authors:
(1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany;
(2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany;
(3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany;
(4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Numerical Example Conclusion and References V. NUMERICAL EXAMPLE Notice that the FedAVG algorithm achieves approximately 70 − 75% of classification accuracy after 100000 iterations as it can also be seen in Fig. 1. However, due to the heterogeneity in distribution of the data, we observe that the FedAVG algorithm cannot properly identify the samples of data with labels 0. This can be seen from the confusion matrices in Fig. 2, where the FedAVG model cannot successfully recognize the data labeled as 0, whereas the FedFAir algorithm performs much better by recognizing a large percentage of data, both labelled 0 and 1. nd 1. Additionally, we compare the FedFAir algorithm and the standard FedAVG [1] algorithm in terms of communication efficiency. For the latter, the TDMA scheme is used for communication between agents and the central unit. In this case, individual time slots are allocated for each agent to transmit its parameter vector at each communication round. After receiving parameter vectors, the central unit computes the average of them and sends it back to the agents. Since we consider a system with N = 12 agents, it takes N = 12 time slots per communication round for each agent to transmit its updated parameter vector while only 3 are needed for the FedFAir algorithm (see (13)), independent of the value of N. This makes the execution of one iteration of the FedFAir algorithm N/3 = 4 times faster than the execution of an iteration of the FedAVG algorithm. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Authors: Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Abstract and Introduction Problem Setup Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Convergence Properties Numerical Example Numerical Example Conclusion and References Conclusion and References V. NUMERICAL EXAMPLE Notice that the FedAVG algorithm achieves approximately 70 − 75% of classification accuracy after 100000 iterations as it can also be seen in Fig. 1. However, due to the heterogeneity in distribution of the data, we observe that the FedAVG algorithm cannot properly identify the samples of data with labels 0. This can be seen from the confusion matrices in Fig. 2, where the FedAVG model cannot successfully recognize the data labeled as 0, whereas the FedFAir algorithm performs much better by recognizing a large percentage of data, both labelled 0 and 1. nd 1. Additionally, we compare the FedFAir algorithm and the standard FedAVG [1] algorithm in terms of communication efficiency. For the latter, the TDMA scheme is used for communication between agents and the central unit. In this case, individual time slots are allocated for each agent to transmit its parameter vector at each communication round. After receiving parameter vectors, the central unit computes the average of them and sends it back to the agents. Since we consider a system with N = 12 agents, it takes N = 12 time slots per communication round for each agent to transmit its updated parameter vector while only 3 are needed for the FedFAir algorithm (see (13)), independent of the value of N. This makes the execution of one iteration of the FedFAir algorithm N/3 = 4 times faster than the execution of an iteration of the FedAVG algorithm. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Boosting Fairness and Robustness in Over-the-Air Federated Learning: Numerical Example

Authors:
(1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany;
(2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany;
(3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany;
(4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Numerical Example Conclusion and References IV. CONVERGENCE PROPERTIES We start with the following lemmas that are essential for the proofs presented in the paper. For the first term on the right-hand side of (21), we have which can then be used to obtain This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Authors: Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Abstract and Introduction Problem Setup Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Convergence Properties Numerical Example Numerical Example Conclusion and References Conclusion and References IV. CONVERGENCE PROPERTIES We start with the following lemmas that are essential for the proofs presented in the paper. For the first term on the right-hand side of (21), we have which can then be used to obtain This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Boosting Fairness and Robustness in Over-the-Air Federated Learning: Convergence Properties

Authors:
(1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany;
(2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany;
(3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany;
(4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Numerical Example Conclusion and References III. FEDERATED FAIR OVER-THE-AIR LEARNING (FEDFAIR) ALGORITHM Next, we state our assumptions on individual objective functions and the step size as follows: We refer here to [28, Ch 2.3, Ch 2.4] and [29, Ch 5.4], thus considering channel coefficients independent realizations (see [30]). This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Authors: Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Abstract and Introduction Problem Setup Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Convergence Properties Numerical Example Numerical Example Conclusion and References Conclusion and References III. FEDERATED FAIR OVER-THE-AIR LEARNING (FEDFAIR) ALGORITHM Next, we state our assumptions on individual objective functions and the step size as follows: We refer here to [28, Ch 2.3, Ch 2.4] and [29, Ch 5.4], thus considering channel coefficients independent realizations (see [30]). This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Boosting Fairness and Robustness in Over-the-Air Federated Learning: FedAir Algorithm

Authors:
(1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany;
(2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany;
(3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany;
(4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Numerical Example Conclusion and References II. PROBLEM SETUP A. Minmax Reformulation In a federated learning setting with N agents, where V = {1,2,··· ,N} denotes the index set, we are interested in improving the performance of the worst-performing agent by solving the following optimization problem: We aim to compute a parameter vector estimate minimizing the worst-case loss observed among all agents, thus providing some form of fairness [20], [21]. However, it is difficult and inefficient to use (3) directly for federated learning purposes. Instead, we can consider an alternative (epigraph) form: B. Over-the-Air Communication Mode This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Authors: Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Abstract and Introduction Problem Setup Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Convergence Properties Numerical Example Numerical Example Conclusion and References Conclusion and References II. PROBLEM SETUP A. Minmax Reformulation A. Minmax Reformulation In a federated learning setting with N agents, where V = {1,2,··· ,N} denotes the index set, we are interested in improving the performance of the worst-performing agent by solving the following optimization problem: We aim to compute a parameter vector estimate minimizing the worst-case loss observed among all agents, thus providing some form of fairness [20], [21]. However, it is difficult and inefficient to use (3) directly for federated learning purposes. Instead, we can consider an alternative (epigraph) form: B. Over-the-Air Communication Mode B. Over-the-Air Communication Mode This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Boosting Fairness and Robustness in Over-the-Air Federated Learning: Problem Setup

Authors:
(1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany;
(2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany;
(3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany;
(4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Numerical Example Conclusion and References Abstract Over-the-Air Computation is a beyond-5G communication strategy that has recently been shown to be useful for the decentralized training of machine learning models due to its efficiency. In this paper, we propose an Over-the-Air federated learning algorithm that aims to provide fairness and robustness through minmax optimization. By using the epigraph form of the problem at hand, we show that the proposed algorithm converges to the optimal solution of the minmax problem. Moreover, the proposed approach does not require reconstructing channel coefficients by complex encoding decoding schemes as opposed to state-of-the-art approaches. This improves both efficiency and privacy. I. INTRODUCTION For large-scale systems, where information exchange and cooperation are vital, one critical challenge for the averaging based federated learning algorithms is heterogeneity [8]– [10]. When the data is heterogeneous, i.e., the fact that agents observe data from different distributions, the parameter vectors minimizing the local cost functions will in general vary significantly between different agents, and minimizing the cost function (2) may not be desirable. Instead, using a worst-case optimization problem may reflect practical requirements more accurately. Another problem that we encounter in large-scale networks is that the communication load on the overall system increases with the number of agents [11]–[14]. When multiple agents transmit information at the same time and in the same frequency band, signals are affected by the physical phenomenon of interference. Standard communication protocols[1] prevent interference by transmitting signals orthogonally. However, these techniques are not resource-efficient in the sense that they increase the need for bandwidth or the number of communication rounds, which in general leads to a decrease in total throughput and efficiency [15], [16]. In this paper, we present a federated learning algorithm that aims to improve the performance of the worst performing agent in the system, thus providing fairness and robustness against heterogeneity. We leverage a beyond-5G communication strategy, called Over-the-Air Computation, which is more efficient as the number of agents grows [16]. Unlike the existing literature on Over-the-Air computation, e.g, [8], [17], the proposed algorithm can operate despite the inherently unknown nature of channel coefficients. We do not assume any knowledge of (nor the capability to reconstruct) channel coefficients, and therefore we will not need extra preprocessing efforts to reconstruct the channel, which makes the proposed scheme more time and resource efficient. Moreover, since the channel coefficients are completely unknown, privacy is inherently guaranteed, as discussed in [18]. The remainder of this paper is organized as follows: we present the problem setup in Section II. In Section III, we introduce the proposed algorithm, whose convergence analysis is presented in Section IV. A numerical example is presented in Section V. Concluding remarks are given in Section VI. This paper is available on arxiv under CC BY 4.0 DEED license. [1] In TDMA (Time Division Multiple Access), agents are assigned different time slots when they can transmit, whereas in FDMA (Frequency Division Multiple Access), different frequency bands are allocated to different users. Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Authors: Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Abstract and Introduction Problem Setup Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Convergence Properties Numerical Example Numerical Example Conclusion and References Conclusion and References Abstract Over-the-Air Computation is a beyond-5G communication strategy that has recently been shown to be useful for the decentralized training of machine learning models due to its efficiency. In this paper, we propose an Over-the-Air federated learning algorithm that aims to provide fairness and robustness through minmax optimization. By using the epigraph form of the problem at hand, we show that the proposed algorithm converges to the optimal solution of the minmax problem. Moreover, the proposed approach does not require reconstructing channel coefficients by complex encoding decoding schemes as opposed to state-of-the-art approaches. This improves both efficiency and privacy. I. INTRODUCTION For large-scale systems, where information exchange and cooperation are vital, one critical challenge for the averaging based federated learning algorithms is heterogeneity [8]– [10]. When the data is heterogeneous, i.e., the fact that agents observe data from different distributions, the parameter vectors minimizing the local cost functions will in general vary significantly between different agents, and minimizing the cost function (2) may not be desirable. Instead, using a worst-case optimization problem may reflect practical requirements more accurately. Another problem that we encounter in large-scale networks is that the communication load on the overall system increases with the number of agents [11]–[14]. When multiple agents transmit information at the same time and in the same frequency band, signals are affected by the physical phenomenon of interference. Standard communication protocols[1] prevent interference by transmitting signals orthogonally. However, these techniques are not resource-efficient in the sense that they increase the need for bandwidth or the number of communication rounds, which in general leads to a decrease in total throughput and efficiency [15], [16]. In this paper, we present a federated learning algorithm that aims to improve the performance of the worst performing agent in the system, thus providing fairness and robustness against heterogeneity. We leverage a beyond-5G communication strategy, called Over-the-Air Computation, which is more efficient as the number of agents grows [16]. Unlike the existing literature on Over-the-Air computation, e.g, [8], [17], the proposed algorithm can operate despite the inherently unknown nature of channel coefficients. We do not assume any knowledge of (nor the capability to reconstruct) channel coefficients, and therefore we will not need extra preprocessing efforts to reconstruct the channel, which makes the proposed scheme more time and resource efficient. Moreover, since the channel coefficients are completely unknown, privacy is inherently guaranteed, as discussed in [18]. The remainder of this paper is organized as follows: we present the problem setup in Section II. In Section III, we introduce the proposed algorithm, whose convergence analysis is presented in Section IV. A numerical example is presented in Section V. Concluding remarks are given in Section VI. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv [1] In TDMA (Time Division Multiple Access), agents are assigned different time slots when they can transmit, whereas in FDMA (Frequency Division Multiple Access), different frequency bands are allocated to different users.

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