Extensive-Form Game Solving via Blackwell Approachability on Treeplexes
Keywords: Extensive-form games, Blackwell approachability, counterfactual regret minimization
Abstract: We introduce the first algorithmic framework for Blackwell approachability on the sequence-form polytope, the class of convex polytopes capturing the strategies of players in extensive-form games (EFGs).
This leads to a new class of regret-minimization algorithms that are stepsize-invariant, in the same sense as the Regret Matching and Regret Matching$^+$ algorithms for the simplex.
Our modular framework can be combined with any existing regret minimizer over cones to compute a Nash equilibrium in two-player zero-sum EFGs with perfect recall, through the self-play framework. Leveraging predictive online mirror descent, we introduce *Predictive Treeplex Blackwell$^+$* (PTB$^+$), and show a $O(1/\sqrt{T})$ convergence rate to Nash equilibrium in self-play. We then show how to stabilize PTB$^+$ with a stepsize, resulting in an algorithm with a state-of-the-art $O(1/T)$ convergence rate.
We provide an extensive set of experiments to compare our framework with several algorithmic benchmarks, including CFR$^+$ and its predictive variant, and we highlight interesting connections between practical performance and the stepsize-dependence or stepsize-invariance properties of classical algorithms.
Primary Area: Algorithmic game theory
Submission Number: 5213
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