Model-free Neural Counterfactual Regret Minimization with Bootstrap Learning

TL;DR

This paper introduces Neural ReCFR-B, a model-free neural CFR algorithm with bootstrap learning that uses recursive substitute values to improve convergence and reduce training costs in large-scale imperfect information games.

Contribution

The paper proposes Recursive CFR and Neural ReCFR-B, novel variants that replace cumulative regrets with recursive substitute values, enhancing efficiency and convergence in neural CFR methods.

Findings

Neural ReCFR-B converges at a rate of O(1/√T).

Neural ReCFR-B achieves competitive performance with lower training costs.

Recursive substitute values reduce variance in training targets.

Abstract

Counterfactual Regret Minimization (CFR) has achieved many fascinating results in solving large-scale Imperfect Information Games (IIGs). Neural network approximation CFR (neural CFR) is one of the promising techniques that can reduce computation and memory consumption by generalizing decision information between similar states. Current neural CFR algorithms have to approximate cumulative regrets. However, efficient and accurate approximation in a large-scale IIG is still a tough challenge. In this paper, a new CFR variant, Recursive CFR (ReCFR), is proposed. In ReCFR, Recursive Substitute Values (RSVs) are learned and used to replace cumulative regrets. It is proven that ReCFR can converge to a Nash equilibrium at a rate of $O({1}/{\sqrt{T}})$. Based on ReCFR, a new model-free neural CFR with bootstrap learning, Neural ReCFR-B, is proposed. Due to the recursive and non-cumulative nature of RSVs, Neural ReCFR-B has lower-variance training targets than other neural CFRs. Experimental results show that Neural ReCFR-B is competitive with the state-of-the-art neural CFR algorithms at a much lower training cost.