Uncoupled and Convergent Learning in Monotone Games under Bandit Feedback
<|reference_start|>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.<|reference_end|>
@article{dong2024uncoupled,
    title={Uncoupled and Convergent Learning in Monotone Games under Bandit
  Feedback},
    author={Jing Dong, Baoxiang Wang, Yaoliang Yu},
    journal={arXiv preprint arXiv:2408.08395},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.08395},
    primaryClass={cs.GT}
}