Accelerating Nash Equilibrium Convergence in Monte Carlo Settings Through Counterfactual Value Based Fictitious Play

Summary

The paper introduces a novel algorithm, Monte Carlo Counterfactual Value-Based Fictitious Play (MCCFVFP). This algorithm aims to accelerate the convergence of Nash Equilibria in extensive-form imperfect information games. MCCFVFP combines the counterfactual value calculations from Counterfactual Regret Minimization (CFR) with the best response strategy from Fictitious Play (FP). The authors claim that MCCFVFP achieves up to three times faster convergence compared to advanced MCCFR variants and significantly outperforms them in large-scale games with a high proportion of dominated strategies.

Strengths

- The paper introduces a unique and novel combination of counterfactual value calculations with fictitious play, leveraging strengths from both methods. - The theoretical analysis proving the convergence of MCCFVFP adds a strong foundation to the empirical results. - MCCFVFP is shown to achieve significantly faster convergence rates in extensive-form games, particularly in scenarios with a high proportion of dominated strategies.

Weaknesses

The paper could provide a more detailed comparison with a broader range of existing algorithms beyond MCCFR variants to establish a more comprehensive performance baseline.

Questions

Can the authors describe a bit about the comparison between MCCFVFP with reinforcement learning approaches for extensive form imperfect information games?

Rating

7

Confidence

2

Soundness

3

Presentation

3

Contribution

3

Limitations

yes

Summary

The paper proposes a new algorithm for solving extensive-form imperfect information games that relies on Monte Carlo (MC) simulations. The method abbreviated MCCFVFP combines MC settings with Counterfactual Regret Minimization (CFR) and the best response strategy of fictious play. Experimental evaluation demonstrate its speed advantage over the state-of-the-art competitors, in particular in clear games (i.e. games in which the vast majority of strategies are dominated ones).

Strengths

The method clearly outperforms competitive approaches in terms of convergence speed. The method is particularly well suited for clear games, i.e. the ones with over 90% of dominated strategies, as reported by the authors.

Weaknesses

1. The paper has not been carefully revised before submission and there are certain issues that hinder is smooth reading and understanding. For instance, $u^i$ is not explicitly defined in the paper (I assume it is the payoff of player $i$) and in some cases is a one-argument function, in other case a two-argument one (cf. eq. 2). Similarly, $R_{T}^{i,+}$ in eq. 5. 2. A discussion in section 5.2.1. is rather accidental. Some plots in Fig. 2 are addressed while the other are not mentioned (e.g. Princess and Monster plots). 3. RM is not explicitly defined in the paper – it is only defined in the appendix

Questions

-- See points 1 and 2 in weaknesses -- The results for tangeled games are not so strong as for the clear games. At the same time tangeled games are intuitively much more complex than clear games, which shows certain limitations of the proposed method. Please comment on that. -- Random games with 21845 nodes do not seem to be challenging. Would the conclusions hold for much larger random games? -- In section 5.3. the numbers of stored information sets of both methods are equal. Is it really the case or there is a mistake there?

Rating

6

Confidence

3

Soundness

3

Presentation

2

Contribution

3

Limitations

The limitations are not explicitly specified.

Summary

The paper introduces a new algorithm called Monte Carlo Counterfactual Value-Based Fictitious Play (MCCFVFP) for solving extensive-form imperfect information games. This algorithm combines the counterfactual value calculations of Counterfactual Regret Minimization (CFR) with the best response strategy of Fictitious Play (FP). The authors demonstrate that MCCFVFP accelerates convergence to Nash Equilibrium (NE) significantly faster than existing Monte Carlo CFR (MCCFR) variants, especially in games with a high proportion of dominated strategies. They highlight its superior performance in large-scale settings, such as two-player limit short deck Texas Hold’em poker, where the blueprint strategy developed by MCCFVFP outperforms that developed by MCCFR.

Strengths

The paper introduces an interesting integration of CFR's counterfactual value calculations with FP’s best response strategy, creating an approach to accelerating convergence in Monte Carlo settings. This combination provides a new perspective on solving extensive-form games. The theoretical proofs and experimental results are robust, showing evidence of MCCFVFP’s good performance in both convergence speed and practical application to large-scale games. The proposed algorithm has implications for the field of game theory and artificial intelligence, particularly in developing efficient strategies for large-scale, imperfect information games. This can have practical applications in various domains, including poker and other strategic games.

Weaknesses

I believe the biggest drawback of this paper is its writing. Only readers with a deep understanding of CFR can comprehend the content of the article relatively smoothly. I think the author needs to include more background information in the main text, especially since it is currently only 8 pages long, and NeurIPS allows up to 9 pages. The article contains numerous undefined symbols and typos, which greatly hinder the reader's understanding. It gives the impression that it was written in haste and requires thorough proofreading. Line 58: **** Line 72: u^i has never been defined. Line 107: L has never been defined. Line 157: R_i^i Line 175: The same sentence appears twice. Line 192: 6x−Ittakes2 Line 279: Table 1 liner ...

Questions

1）In Figure 2, the author only compared CFR+. I believe DCFR and PCFR should also be compared. 2）How sensitive is MCCFVFP to the proportion of dominated strategies in a game? Is there a clear threshold where it starts to outperform MCCFR? 3）Have you investigated how MCCFVFP performs in multi-player games beyond two players?

Rating

5

Confidence

4

Soundness

3

Presentation

1

Contribution

3

Limitations

Yes