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arXiv · 2408.08395

Uncoupled and Convergent Learning in Monotone Games under Bandit Feedback

Jing Dong·Baoxiang Wang·Yaoliang Yu
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Abstract

We study the problem of no-regret learning algorithms for general monotone and smooth games and their last-iterate convergence properties. Specifically, we investigate the problem under bandit feedback and strongly uncoupled dynamics, which allows modular development of the multi-player system that applies to a wide range of real applications. We propose a mirror-descent-based algorithm, which converges in $O(T^{-1/4})$ and is also no-regret. The result is achieved by a dedicated use of two regularizations and the analysis of the fixed point thereof. The convergence rate is further improved to $O(T^{-1/2})$ in the case of strongly monotone games. Motivated by practical tasks where the game evolves over time, the algorithm is extended to time-varying monotone games. We provide the first non-asymptotic result in converging monotone games and give improved results for equilibrium tracking games.

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Jing Dong, Baoxiang Wang, Yaoliang Yu. 2024-08-15. Uncoupled and Convergent Learning in Monotone Games under Bandit Feedback. https://arxiv.org/abs/2408.08395

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