Lazy-CFR: fast and near-optimal regret minimization for extensive games with imperfect information

Counterfactual regret minimization (CFR) methods are effective for solving two-player zero-sum extensive games with imperfect information with state-of-the-art results. However, the vanilla CFR has to traverse the whole game tree in each round, which is time-consuming in large-scale games. In this paper, we present Lazy-CFR, a CFR algorithm that adopts a lazy update strategy to avoid traversing the whole game tree in each round. We prove that the regret of Lazy-CFR is almost the same to the regret of the vanilla CFR and only needs to visit a small portion of the game tree. Thus, Lazy-CFR is provably faster than CFR. Empirical results consistently show that Lazy-CFR is significantly faster than the vanilla CFR.