Model-free Neural Counterfactual Regret Minimization with Bootstrap Learning
This work provides a more efficient and stable method for training neural CFR algorithms, which is beneficial for researchers and practitioners working on solving large-scale imperfect information games.
This paper introduces Recursive CFR (ReCFR), a new variant of Counterfactual Regret Minimization that learns Recursive Substitute Values (RSVs) instead of cumulative regrets. Based on ReCFR, Neural ReCFR-B is proposed, which achieves competitive performance with state-of-the-art neural CFR algorithms at a significantly lower training cost.
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.