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Uncoupled and Convergent Learning in Monotone Games under Bandit Feedback

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arxiv 2408.08395 v1 pith:FNQWPOHY submitted 2024-08-15 cs.GT

Uncoupled and Convergent Learning in Monotone Games under Bandit Feedback

classification cs.GT
keywords gamesmonotonealgorithmbanditconvergencefeedbackimprovedlearning
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Near-Optimal Last-Iterate Convergence for Zero-Sum Games with Bandit Feedback and Opponent Actions

    cs.LG 2026-05 unverdicted novelty 8.0

    With opponent-action feedback in zero-sum games, an efficient algorithm achieves near-optimal t^{-1/2} last-iterate convergence in duality gap with high probability.

  2. The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback

    cs.LG 2026-04 unverdicted novelty 7.0

    In bandit-feedback zero-sum games, uncoupled algorithms achieve last-iterate Nash convergence at the optimal rate of O(T^{-1/4}).