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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence / EAAI-20

Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines

February 1, 2023

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Authors

Martin Schmid

DeepMind


Neil Burch

DeepMind


Marc Lanctot

Deepmind


Matej Moravcik

DeepMInd


Rudolf Kadlec

Google DeepMind


Michael Bowling

DeepMind


DOI:

10.1609/aaai.v33i01.33012157


Abstract:

Learning strategies for imperfect information games from samples of interaction is a challenging problem. A common method for this setting, Monte Carlo Counterfactual Regret Minimization (MCCFR), can have slow long-term convergence rates due to high variance. In this paper, we introduce a variance reduction technique (VR-MCCFR) that applies to any sampling variant of MCCFR. Using this technique, periteration estimated values and updates are reformulated as a function of sampled values and state-action baselines, similar to their use in policy gradient reinforcement learning. The new formulation allows estimates to be bootstrapped from other estimates within the same episode, propagating the benefits of baselines along the sampled trajectory; the estimates remain unbiased even when bootstrapping from other estimates. Finally, we show that given a perfect baseline, the variance of the value estimates can be reduced to zero. Experimental evaluation shows that VR-MCCFR brings an order of magnitude speedup, while the empirical variance decreases by three orders of magnitude. The decreased variance allows for the first time CFR+ to be used with sampling, increasing the speedup to two orders of magnitude.

Topics: AAAI

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HOW TO CITE:

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines Proceedings of the AAAI Conference on Artificial Intelligence (2019) 2157-2164.

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines AAAI 2019, 2157-2164.

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling (2019). Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines. Proceedings of the AAAI Conference on Artificial Intelligence, 2157-2164.

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling. Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines. Proceedings of the AAAI Conference on Artificial Intelligence 2019 p.2157-2164.

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling. 2019. Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines. "Proceedings of the AAAI Conference on Artificial Intelligence". 2157-2164.

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling. (2019) "Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines", Proceedings of the AAAI Conference on Artificial Intelligence, p.2157-2164

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling, "Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines", AAAI, p.2157-2164, 2019.

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling. "Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines". Proceedings of the AAAI Conference on Artificial Intelligence, 2019, p.2157-2164.

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling. "Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines". Proceedings of the AAAI Conference on Artificial Intelligence, (2019): 2157-2164.

Martin Schmid||Neil Burch||Marc Lanctot||Matej Moravcik||Rudolf Kadlec||Michael Bowling. Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games Using Baselines. AAAI[Internet]. 2019[cited 2023]; 2157-2164.


ISSN: 2374-3468


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