We develop a unified stochastic approximation framework for analyzing the long-run behavior of multi-agent online learning in games. Our framework is based on a "primal-dual", mirrored Robbins-Monro (MRM) template which encompasses a wide array of popular game-theoretic learning algorithms (gradient methods, their optimistic variants, the EXP3 algorithm for learning with payoff-based feedback in finite games, etc.). In addition to providing an integrated view of these algorithms, the proposed MRM blueprint allows us to obtain a broad range of new convergence results, both asymptotic and in finite time, in both continuous and finite games.

@article{mertikopoulos2022learning,
	author = {Mertikopoulos, Panayotis and Hsieh, Ya-Ping and Cevher, Volkan},
	journal = {arXiv preprint arXiv:2206.03922},
	month = {June},
	title = {Learning in games from a stochastic approximation viewpoint},
	year = {2022}}