Differentially Private Reinforcement Learning with Self-Play

We study the problem of multi-agent reinforcement learning (multi-agent RL) with differential privacy (DP) constraints. This is well-motivated by various real-world applications involving sensitive data, where it is critical to protect users' private information. We first extend the definitions of Joint DP (JDP) and Local DP (LDP) to two-player zero-sum episodic Markov Games, where both definitions ensure trajectory-wise privacy protection. Then we design a provably efficient algorithm based on optimistic Nash value iteration and privatization of Bernstein-type bonuses. The algorithm is able to satisfy JDP and LDP requirements when instantiated with appropriate privacy mechanisms. Furthermore, for both notions of DP, our regret bound generalizes the best known result under the single-agent RL case, while our regret could also reduce to the best known result for multi-agent RL without privacy constraints. To the best of our knowledge, these are the first line of results towards understanding trajectory-wise privacy protection in multi-agent RL.

Paper

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Peer review

Reviewer f4t27/10 · confidence 4/52024-07-08

Summary

The paper studied two-player zero-sum episodic Markov Games under JDP and LDP. The authors designed DP-Nash-VI algorithm for the problems and derives both upper bounds and lower bounds.

Strengths

1. The paper investigated interesting problem of two-player zero-sum episodic Markov Games under JDP and LDP. 2. It is good to derive the the best known regret for non-private multi-agent RL as byproduct. 3. The authors give algorithms design and solid proofs of upper bounds and lower bounds for the problems.

Weaknesses

There is no experimental result to verify their theoretical findings.

Questions

1. In this paper, you consider bounded reward case. Can your method extend to heavy-tailed reward case in [1]? 2. Is it possible to further improve the gaps between your upper bounds and lower bounds? [1] Yulian Wu, Xingyu Zhou, Sayak Ray Chowdhury, and Di Wang. Differentially private episodic reinforcement learning with heavy-tailed rewards. arXiv preprint arXiv:2306.01121, 2023b

Rating

7

Confidence

4

Soundness

4

Presentation

3

Contribution

3

Limitations

There is no experiment but I understand the main contributions of paper is on theoretical side.

Reviewer 3xco5/10 · confidence 2/52024-07-11

Summary

The authors address multi-agent self-play reinforcement learning (RL) with differential privacy (DP) constraints to protect sensitive data. They propose an efficient algorithm that meets JDP and LDP requirements, and its regret bounds generalize the best-known results for single-agent RL, marking the first study of trajectory-wise privacy in multi-agent RL.

Strengths

1. The proposed algorithm demonstrates a statistically tight regret bound, supported by the authors' derived lower bound. 2. The differential privacy analysis is comprehensive, encompassing both Joint Differential Privacy (JDP) and Local Differential Privacy (LDP). 3. The writing is generally clear and concise.

Weaknesses

1. The overall technical contribution seems limited. Could the authors emphasize their primary technical contributions? Specifically, is it feasible to address the problem setting using existing algorithms augmented with the Laplacian mechanism? 2. The absence of an experimental study, even a simple one, is noticeable. Conducting experiments is crucial to validate the efficacy of the proposed algorithm, especially given the authors' claims of its efficiency.

Questions

1. The technical convenience of using Definition 2.2 instead of Definition 2.1 is not clear. Can the authors confirm if their proposed algorithm also satisfies the differential privacy requirements of Definition 2.1? If it does not, could you provide an intuitive explanation? 2. Given that the reward value is known and determined, why does the agent still require reward feedback from the user (as mentioned in line 135)?

Rating

5

Confidence

2

Soundness

3

Presentation

3

Contribution

3

Limitations

N/A

Reviewer vYkZ6/10 · confidence 3/52024-07-13

Summary

This paper explores multi-agent reinforcement learning (RL) with differential privacy (DP) constraints. The authors extend the concepts of Joint DP (JDP) and Local DP (LDP) to two-player zero-sum episodic Markov Games. They develop a provably efficient algorithm that combines optimistic Nash value iteration with the privatization of Bernstein-type bonuses, ensuring satisfaction of JDP and LDP requirements with appropriate privacy mechanisms. The algorithm achieves a regret bound that generalizes the best-known results in single-agent RL and could reduce to the best-known results in multi-agent RL without privacy constraints.

Strengths

1. This paper extends the concepts of Joint DP (JDP) and Local DP (LDP) to two-player zero-sum episodic Markov Games, which is important and inspiring for future studies on differential privacy in multi-agent RL. 2. The proposed DP-Nash-VI algorithm could satisfy either Joint DP (JDP) and Local DP (LDP)constraints with corresponding regret guarantees. Their regret bounds strictly generalize the best-known results under DP single-agent RL, and their results could be reduced to the best-known results in multi-agent RL without privacy constraints.

Weaknesses

Though this is a purely theoretical paper, it may be better to include some simulation results to validate the theoretical results.

Questions

Could the authors highlight the key technical challenges involved in combining the techniques from Liu et al. [2021] and Qiao and Wang [2023]?

Rating

6

Confidence

3

Soundness

4

Presentation

4

Contribution

3

Limitations

No negative societal impact of this work.

Reviewer Bzin5/10 · confidence 3/52024-07-13

Summary

This paper gives an algorithm for differentially private reinforcement learning in two-player zero-sum games. The paper considers a standard model for differential privacy already established for single-agent RL. In this model, in each episode a unique user follows a policy $\pi$ recommended by the RL agent i.e. the user encounters states $s$, takes actions $a$ sampled from $\pi(s)$, and receives rewards $r$. The goal is for the RL agent to learn optimal policy recommendations, without revealing the private information of each user consisting of the trajectory of states, actions, and rewards. The paper considers two standard models for privacy in RL, joint differential privacy (JDP) and local differential privacy (LDP). The proposed algorithm achieves nearly optimal (in certain parameter regimes) regret in both of these privacy constrained settings.

Strengths

Differential privacy in multi-agent reinforcement learning is an important problem, and achieving this in two-player zero-sum games could be step towards the general multi-agent case.

Weaknesses

- The algorithm proposed is a straightforward combination of prior work [1] achieving privacy for single-agent RL and [2] achieving low-regret learning for self-play in zero-sum games. It is not clear from the paper what new ideas, if any, are needed, beyond directly applying the private counts and bonuses from [1] to compute the upper and lower confidence bounds used in [2]. - While privacy for multi-agent RL seems quite relevant and interesting, privacy for two-player zero-sum games seems much less well-motivated. For example, in the autonomous driving case, general multi-agent RL corresponds to learning in a setting where there are many autonomous vehicles on the road and one wants to keep the information of each one private. Two-player zero-sum markov games instead correspond to the setting where there are exactly two autonomous vehicles on the road in each episode, and somehow they are in direct zero-sum competition (e.g. a one-on-one race). In fact, the only reason differential privacy makes sense in this setting is that the paper assumes that a different pair of users competes in each episode, and it is privacy across these different pairs that is preserved. In general, it really seems to me that the most important questions regarding privacy in RL relate to a large number of interacting agents, and that the setting of this paper was chosen specifically so that the techniques of [1] and [2] could be directly applied, rather than because the problem itself seemed important to solve. Specific Issues: - The text in Table 1 is too small to read. [1] Qiao, Dan, and Yu-Xiang Wang. "Near-optimal differentially private reinforcement learning." International Conference on Artificial Intelligence and Statistics. PMLR, 2023. [2] Liu, Qinghua, et al. "A sharp analysis of model-based reinforcement learning with self-play." International Conference on Machine Learning. PMLR, 2021.

Questions

1. Are there any technical challenges to overcome when combining the known algorithm for private single-agent RL with the algorithm for self-play in zero-sum games? 2. Why is privacy across episodes of two-player zero-sum games an interesting problem? Is there some natural approach to generalize to mutli-agent RL? Are there natural examples where one would want to preserve privacy in a sequence of direct competitions between two players?

Rating

5

Confidence

3

Soundness

3

Presentation

3

Contribution

2

Limitations

Yes.

Area Chair 8A1p2024-08-13

Dear reviewer, Since the discussion deadline is approaching, please let the authors know if their rebuttal has addressed your concerns. If you still have concerns, you could first acknowledge that you have read the rebuttal and discuss them in the remaining time (with the authors) or the next phase (with other reviewers). Best, Your AC

Reviewer f4t22024-08-08

Thank you for the reply. I keep the score. Good luck!

Reviewer 3xco2024-08-09

Thank you very much for the response. I will keep my score.

Reviewer Bzin2024-08-13

Thanks for your response. I appreciate your points about having to modify the bonus, and about the obstructions regarding the use of model-based algorithms in multi-agent RL. After reviewing the discussion I will increase my score to 5.

Program Chairsdecision2024-09-25

Decision

Accept (poster)

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