Computing Approximate Equilibria in Sequential Adversarial Games by Exploitability Descent
This provides a new algorithmic approach for solving sequential adversarial games, which is incremental but shows potential improvements with function approximation in some cases.
The paper tackles the problem of computing approximate equilibria in two-player zero-sum extensive-form games with imperfect information by introducing exploitability descent, a direct policy optimization algorithm against worst-case opponents, which converges to Nash equilibrium with rates comparable to existing methods like XFP and CFR in benchmark games.
In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove that when following this optimization, the exploitability of a player's strategy converges asymptotically to zero, and hence when both players employ this optimization, the joint policies converge to a Nash equilibrium. Unlike fictitious play (XFP) and counterfactual regret minimization (CFR), our convergence result pertains to the policies being optimized rather than the average policies. Our experiments demonstrate convergence rates comparable to XFP and CFR in four benchmark games in the tabular case. Using function approximation, we find that our algorithm outperforms the tabular version in two of the games, which, to the best of our knowledge, is the first such result in imperfect information games among this class of algorithms.