期刊
MATHEMATICAL PROGRAMMING
卷 173, 期 1-2, 页码 465-507出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-018-1254-8
关键词
Continuous games; Dual averaging; Variational stability; Fenchel coupling; Nash equilibrium
类别
资金
- French National Research Agency (ANR) project ORACLESS [ANR-GAGA-13-JS01-0004-01]
- Huawei Innovation Research Program ULTRON
This paper examines the convergence of no-regret learning in games with continuous action sets. For concreteness, we focus on learning via dual averaging, a widely used class of no-regret learning schemes where players take small steps along their individual payoff gradients and then mirror the output back to their action sets. In terms of feedback, we assume that players can only estimate their payoff gradients up to a zero-mean error with bounded variance. To study the convergence of the induced sequence of play, we introduce the notion of variational stability, and we show that stable equilibria are locally attracting with high probability whereas globally stable equilibria are globally attracting with probability 1. We also discuss some applications to mixed-strategy learning in finite games, and we provide explicit estimates of the method's convergence speed.
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