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Recent techniques for approximating Nash equilibria in very large gamesleverage neural networks to learn approximately optimal policies (strategies).One promising line of research uses neural networks to approximatecounterfactual regret minimization (CFR) or its modern variants. DREAM, theonly current CFR-based neural method that is model free and therefore scalableto very large games, trains a neural network on an estimated regret target thatcan have extremely high variance due to an importance sampling term inheritedfrom Monte Carlo CFR (MCCFR). In this paper we propose an unbiased model-freemethod that does not require any importance sampling. Our method, ESCHER, isprincipled and is guaranteed to converge to an approximate Nash equilibriumwith high probability. We show that the variance of the estimated regret ofESCHER is orders of magnitude lower than DREAM and other baselines. We thenshow that ESCHER outperforms the prior state of the art -- DREAM and neuralfictitious self play (NFSP) -- on a number of games and the difference becomesdramatic as game size increases. In the very large game of dark chess, ESCHERis able to beat DREAM and NFSP in a head-to-head competition over $90\%$ of thetime.

ESCHER: Eschewing Importance Sampling in Games by Computing a History Value Function to Estimate Regret