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The leading approach for solving large imperfect-information games is automated abstraction followed by running an equilibrium finding algorithm. We introduce a distributed version of the most commonly used equilibrium-finding algorithm , counterfactual regret minimization (CFR), which enables CFR to scale to dramatically larger abstractions and numbers of(More)
Regret matching is a widely-used algorithm for learning how to act. We begin by proving that regrets on actions in one setting (game) can be transferred to warm start the regrets for solving a different setting with same structure but different payoffs that can be written as a function of parameters. We prove how this can be done by carefully discounting(More)
Regret minimization is widely used in determining strategies for imperfect-information games and in online learning. In large games, computing the regrets associated with a single iteration can be slow. For this reason, pruning – in which parts of the decision tree are not traversed in every iteration – has emerged as an essential method for speeding up(More)
Imperfect-information games, where players have private information, pose a unique challenge in artificial intelligence. In recent years, Heads-Up No-Limit Texas Hold'em poker, a popular version of poker, has emerged as the primary benchmark for evaluating game-solving algorithms for imperfect-information games. We demonstrate a winning agent from the 2016(More)
Iterative algorithms such as Counterfactual Regret Minimization (CFR) are the most popular way to solve large zero-sum imperfect-information games. In this paper we introduce Best-Response Pruning (BRP), an improvement to iterative algorithms such as CFR that allows poorly-performing actions to be temporarily pruned. We prove that when using CFR in zero-sum(More)
Unlike perfect-information games, imperfect-information games cannot be solved by decomposing the game into subgames that are solved independently. Thus all decisions must consider the strategy of the game as a whole. While it is not possible to solve an imperfect-information game exactly through decomposition, it is possible to approximate solutions, or(More)