No-Regret Learning for Fair Multi-Agent Social Welfare Optimization

• URL: http://arxiv.org/abs/2405.20678v1
• Date: Fri, 31 May 2024 08:21:11 GMT
• Title: No-Regret Learning for Fair Multi-Agent Social Welfare Optimization
• Authors: Mengxiao Zhang, Ramiro Deo-Campo Vuong, Haipeng Luo,
• Abstract summary: We consider the problem of online multi-agent Nash social welfare (NSW) We show that no algorithm can achieve sublinear regret. We also show that logarithmic regret is possible whenever there exists one agent who is indifferent about different arms.
• Score: 35.44934658941197
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of online multi-agent Nash social welfare (NSW) maximization. While previous works of Hossain et al. [2021], Jones et al. [2023] study similar problems in stochastic multi-agent multi-armed bandits and show that $\sqrt{T}$-regret is possible after $T$ rounds, their fairness measure is the product of all agents' rewards, instead of their NSW (that is, their geometric mean). Given the fundamental role of NSW in the fairness literature, it is more than natural to ask whether no-regret fair learning with NSW as the objective is possible. In this work, we provide a complete answer to this question in various settings. Specifically, in stochastic $N$-agent $K$-armed bandits, we develop an algorithm with $\widetilde{\mathcal{O}}\left(K^{\frac{2}{N}}T^{\frac{N-1}{N}}\right)$ regret and prove that the dependence on $T$ is tight, making it a sharp contrast to the $\sqrt{T}$-regret bounds of Hossain et al. [2021], Jones et al. [2023]. We then consider a more challenging version of the problem with adversarial rewards. Somewhat surprisingly, despite NSW being a concave function, we prove that no algorithm can achieve sublinear regret. To circumvent such negative results, we further consider a setting with full-information feedback and design two algorithms with $\sqrt{T}$-regret: the first one has no dependence on $N$ at all and is applicable to not just NSW but a broad class of welfare functions, while the second one has better dependence on $K$ and is preferable when $N$ is small. Finally, we also show that logarithmic regret is possible whenever there exists one agent who is indifferent about different arms.

Related papers

• p-Mean Regret for Stochastic Bandits [52.828710025519996]
  We introduce a simple, unified UCB-based algorithm that achieves novel $p$-mean regret bounds. Our framework encompasses both average cumulative regret and Nash regret as special cases.
  arXiv  Detail & Related papers  (2024-12-14T08:38:26Z)
• No-Regret M${}^{\natural}$-Concave Function Maximization: Stochastic Bandit Algorithms and NP-Hardness of Adversarial Full-Information Setting [23.188831772813103]
  We study online M$natural$-concave function problems, which are interactive versions of the problem studied by Murota and Shioura (1999). For the bandit setting, we present $O(T-1/2)$-simple regret and $O(T2/3)$-regret algorithms under $T$ times access to noisy value oracles of M$natural$-concave functions. We prove that even with full-information feedback, no algorithms that run in time per round can achieve $O(T1-c)$ regret for any constant $c
  arXiv  Detail & Related papers  (2024-05-21T01:31:44Z)
• Horizon-free Reinforcement Learning in Adversarial Linear Mixture MDPs [72.40181882916089]
  We show that our algorithm achieves an $tildeObig((d+log (|mathcalS|2 |mathcalA|))sqrtKbig)$ regret with full-information feedback, where $d$ is the dimension of a known feature mapping linearly parametrizing the unknown transition kernel of the MDP, $K$ is the number of episodes, $|mathcalS|$ and $|mathcalA|$ are the cardinalities of the state and action spaces
  arXiv  Detail & Related papers  (2023-05-15T05:37:32Z)
• An Efficient Algorithm for Fair Multi-Agent Multi-Armed Bandit with Low Regret [7.059472280274009]
  We propose a new efficient algorithm with lower regret than even previous inefficient ones. For $N$ agents, $K$ arms, and $T$ rounds, our approach has a regret bound of $tildeO(sqrtNKT + NK)$. We also complement our efficient algorithm with an inefficient approach with $tildeO(sqrtKT + N2K)$ regret.
  arXiv  Detail & Related papers  (2022-09-23T19:15:43Z)
• Fairness and Welfare Quantification for Regret in Multi-Armed Bandits [13.094997642327371]
  We extend the notion of regret with a welfarist perspective. We study Nash regret, defined as the difference between the -- a priori unknown -- optimal mean (among the arms) and the algorithm's performance.
  arXiv  Detail & Related papers  (2022-05-27T12:12:56Z)
• Corralling a Larger Band of Bandits: A Case Study on Switching Regret for Linear Bandits [99.86860277006318]
  We consider the problem of combining and learning over a set of adversarial algorithms with the goal of adaptively tracking the best one on the fly. The CORRAL of Agarwal et al. achieves this goal with a regret overhead of order $widetildeO(sqrtd S T)$ where $M$ is the number of base algorithms and $T$ is the time horizon. Motivated by this issue, we propose a new recipe to corral a larger band of bandit algorithms whose regret overhead has only emphlogarithmic dependence on $M$ as long
  arXiv  Detail & Related papers  (2022-02-12T21:55:44Z)
• Doubly Optimal No-Regret Online Learning in Strongly Monotone Games with Bandit Feedback [29.553652241608997]
  We study the class of textitsmooth and strongly monotone games and study optimal no-regret learning therein. We first construct a new bandit learning algorithm and show that it achieves the single-agent optimal regret of $tildeTheta(nsqrtT)$. Our results thus settle this open problem and contribute to the broad landscape of bandit game-theoretical learning.
  arXiv  Detail & Related papers  (2021-12-06T08:27:54Z)
• Near-Optimal Regret Bounds for Contextual Combinatorial Semi-Bandits with Linear Payoff Functions [53.77572276969548]
  We show that the C$2$UCB algorithm has the optimal regret bound $tildeO(dsqrtkT + dk)$ for the partition matroid constraints. For general constraints, we propose an algorithm that modifies the reward estimates of arms in the C$2$UCB algorithm.
  arXiv  Detail & Related papers  (2021-01-20T04:29:18Z)
• Impact of Representation Learning in Linear Bandits [83.17684841392754]
  We study how representation learning can improve the efficiency of bandit problems. We present a new algorithm which achieves $widetildeO(TsqrtkN + sqrtdkNT)$ regret, where $N$ is the number of rounds we play for each bandit.
  arXiv  Detail & Related papers  (2020-10-13T16:35:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.