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We consider the problem of making AI agents that collaborate well with humans in partially observable fully cooperative environments given datasets of human behavior. Inspired by piKL, a human-data-regularized search method that improves upon a behavioral cloning policy without diverging far away from it, we develop a three-step algorithm that achieve strong performance in coordinating with real humans in the Hanabi benchmark. We first use a regularized search algorithm and behavioral cloning to produce a better human model that captures diverse skill levels. Then, we integrate the policy regularization idea into reinforcement learning to train a human-like best response to the human model. Finally, we apply regularized search on top of the best response policy at test time to handle out-of-distribution challenges when playing with humans. We evaluate our method in two large scale experiments with humans. First, we show that our method outperforms experts when playing with a group of diverse human players in ad-hoc teams. Second, we show that our method beats a vanilla best response to behavioral cloning baseline by having experts play repeatedly with the two agents.