# Uncoupled and Convergent Learning in Monotone Games under Bandit Feedback

arXiv: https://arxiv.org/abs/2408.08395 · HTML: https://mlsanity.com/paper/2408.08395/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2024.

## Built on by (most cited first, 6 of 6)

- [From Average-Iterate to Last-Iterate Convergence in Games: A Reduction and Its Applications](https://mlsanity.com/paper/2506.03464/) (2025)
- [The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback](https://mlsanity.com/paper/2604.16087/) (2026)
- [Efficient Uncoupled Learning Dynamics with tildeO!left(T-1/4right) Last-Iterate Convergence in Bilinear Saddle-Point Problems over Convex Sets under Bandit Feedback](https://mlsanity.com/paper/2602.21436/) (2026)
- [Minimax Last-Iterate Convergence in Matrix Games with Observed Actions](https://mlsanity.com/paper/2609.34656/) (2026)
- [Polylogarithmic Nash Regret in Matrix Games with Bandit Feedback](https://mlsanity.com/paper/2609.34812/) (2026)
- [Fast Last-Iterate Convergence in Zero-Sum Markov Games with Bandit Feedback](https://mlsanity.com/paper/2610.05968/) (2026)

## Abstract (arXiv)

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.