Function approximation is a powerful approach for structuring large decision problems that has facilitated great achievements in the areas of reinforcement learning and game playing. Regression counterfactual regret minimization (RCFR) is a simple algorithm for approximately solving imperfect information games with normalized rectified linear unit (ReLU) parameterized policies. In contrast, the more conventional softmax parameterization is standard in the field of reinforcement learning and yields a regret bound with a better dependence on the number of actions. We derive approximation error-aware regret bounds for $(\Phi, f)$-regret matching, which applies to a general class of link functions and regret objectives. These bounds recover a tighter bound for RCFR and provide a theoretical justification for RCFR implementations with alternative policy parameterizations ($f$-RCFR), including softmax. We provide exploitability bounds for $f$-RCFR with the polynomial and exponential link functions in zero-sum imperfect information games and examine empirically how the link function interacts with the severity of the approximation. We find that the previously studied ReLU parameterization performs better when the approximation error is small while the softmax parameterization can perform better when the approximation error is large.


Alternative Function Approximation Parameterizations for Solving Games: An Analysis of f-Regression Counterfactual Regret Minimization

Policy gradient and actor-critic algorithms form the basis of many commonly used training techniques in deep reinforcement learning. Using these algorithms in multiagent environments poses problems such as nonstationarity and instability. In this paper, we first demonstrate that standard softmax-based policy gradient can be prone to poor performance in the presence of even the most benign nonstationarity. By contrast, it is known that the replicator dynamics, a well-studied model from evolutionary game theory, eliminates dominated strategies and exhibits convergence of the time-averaged trajectories to interior Nash equilibria in zero-sum games. Thus, using the replicator dynamics as a foundation, we derive an elegant one-line change to policy gradient methods that simply bypasses the gradient step through the softmax, yielding a new algorithm titled Neural Replicator Dynamics (NeuRD). NeuRD reduces to the exponential weights/Hedge algorithm in the single-state all-actions case. Additionally, NeuRD has formal equivalence to softmax counterfactual regret minimization, which guarantees convergence in the sequential tabular case. Importantly, our algorithm provides a straightforward way of extending the replicator dynamics to the function approximation setting. Empirical results show that NeuRD quickly adapts to nonstationarities, outperforming policy gradient significantly in both tabular and function approximation settings, when evaluated on the standard imperfect information benchmarks of Kuhn Poker, Leduc Poker, and Goofspiel.

Neural Replicator Dynamics: Multiagent Learning via Hedging Policy Gradients

Learning and Adaptation

technical paper

AAMAS is the leading scientific conference for research in autonomous agents and multi-agent systems. The AAMAS conference series was initiated in 2002 as the merging of three respected scientific meetings: the International Conference on Multi-Agent Systems (ICMAS), the International Workshop on Agent Theories, Architectures, and Languages (ATAL), and the International Conference on Autonomous Agents (AA). The aim of the joint conference is to provide a single, high-profile, internationally-respected archival forum for scientific research in the theory and practice of autonomous agents and multi-agent systems.

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AAMAS 2020

AAMAS is the leading scientific conference for research in autonomous agents and multi-agent systems. The AAMAS conference series was initiated in 2002 as the merging of three respected scientific meetings: the International Conference on Multi-Agent Systems (ICMAS), the International Workshop on Agent Theories, Architectures, and Languages (ATAL), and the International Conference on Autonomous Agents (AA). 

Dustin Morrill

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Alternative Function Approximation Parameterizations for Solving Games: An Analysis of f-Regression Counterfactual Regret Minimization

Neural Replicator Dynamics: Multiagent Learning via Hedging Policy Gradients

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