A unified stochastic approximation framework for learning in games
This work provides a general analysis tool for game theory researchers, but it is incremental as it unifies and extends existing methods rather than introducing a fundamentally new approach.
The authors tackled the problem of analyzing learning algorithms in games by developing a unified stochastic approximation framework that applies to both continuous and finite games, resulting in new convergence criteria for Nash equilibria and finite-time convergence under a property called coherence.
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms, including gradient-based methods, the exponential/multiplicative weights algorithm for learning in finite games, optimistic and bandit variants of the above, etc. In addition to providing an integrated view of these algorithms, our framework further allows us to obtain several new convergence results, both asymptotic and in finite time, in both continuous and finite games. Specifically, we provide a range of criteria for identifying classes of Nash equilibria and sets of action profiles that are attracting with high probability, and we also introduce the notion of coherence, a game-theoretic property that includes strict and sharp equilibria, and which leads to convergence in finite time. Importantly, our analysis applies to both oracle-based and bandit, payoff-based methods - that is, when players only observe their realized payoffs.