Uncoupled and Convergent Learning in Monotone Games under Bandit Feedback

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.