Approximating n-player behavioural strategy nash equilibria using coevolution

Coevolutionary algorithms are plagued with a set of problems related to intransitivity that make it questionable what the end product of a coevolutionary run can achieve. With the introduction of solution concepts into coevolution, part of the issue was alleviated, however efficiently representing and achieving game theoretic solution concepts is still not a trivial task. In this paper we propose a coevolutionary algorithm that approximates behavioural strategy Nash equilibria in n-player zero sum games, by exploiting the minimax solution concept. In order to support our case we provide a set of experiments in both games of known and unknown equilibria. In the case of known equilibria, we can confirm our algorithm converges to the known solution, while in the case of unknown equilibria we can see a steady progress towards Nash. Copyright 2011 ACM

Deep Reinforcement Learning from Self-Play in Imperfect-Information Games

Many real-world applications can be described as large-scale games of imperfect information. To deal with these challenging domains, prior work has focused on computing Nash equilibria in a handcrafted abstraction of the domain. In this paper we introduce the first scalable end-to-end approach to learning approximate Nash equilibria without prior domain knowledge. Our method combines fictitious self-play with deep reinforcement learning. When applied to Leduc poker, Neural Fictitious Self-Play (NFSP) approached a Nash equilibrium, whereas common reinforcement learning methods diverged. In Limit Texas Holdem, a poker game of real-world scale, NFSP learnt a strategy that approached the performance of state-of-the-art, superhuman algorithms based on significant domain expertise.Comment: updated version, incorporating conference feedbac

Solving Games with Functional Regret Estimation

We propose a novel online learning method for minimizing regret in large extensive-form games. The approach learns a function approximator online to estimate the regret for choosing a particular action. A no-regret algorithm uses these estimates in place of the true regrets to define a sequence of policies. We prove the approach sound by providing a bound relating the quality of the function approximation and regret of the algorithm. A corollary being that the method is guaranteed to converge to a Nash equilibrium in self-play so long as the regrets are ultimately realizable by the function approximator. Our technique can be understood as a principled generalization of existing work on abstraction in large games; in our work, both the abstraction as well as the equilibrium are learned during self-play. We demonstrate empirically the method achieves higher quality strategies than state-of-the-art abstraction techniques given the same resources.Comment: AAAI Conference on Artificial Intelligence 201