# Computing Approximate Equilibria in Sequential Adversarial Games by Exploitability Descent

## TL;DR

This paper introduces exploitability descent, a novel algorithm for approximating equilibria in two-player zero-sum extensive-form games with imperfect information, demonstrating convergence to Nash equilibrium through direct policy optimization.

## Contribution

The paper proposes exploitability descent, a new algorithm with proven convergence to Nash equilibrium, outperforming existing methods in certain imperfect information games with function approximation.

## Key findings

- Converges asymptotically to zero exploitability.
- Outperforms tabular algorithms in some games with function approximation.
- First to show such results in imperfect information games among this class.

## Abstract

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.