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Preference-based experience sharing scheme for multi-agent reinforcement learning in multi-target environments

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Abstract

Multi-agent reinforcement learning is a varied and highly active field of research. The idea of parameter sharing or experience sharing has recently been introduced into multi-agent reinforcement learning to accelerate the training of multiple neural networks and enhance the final returns. However, implementing the parameter or experience sharing methods in multi-agent environments could introduce additional constraint or computation cost. This work presents a preference-based experience sharing scheme, which allows for different policies in environments with weakly homogeneous agents and requires barely any additional computational power. In this scheme, the experience replay buffer is augmented by adding a choice vector which indicates the preferred target of the agent, and each agent can learn various policies from the experience data collected by other agents who choose the same target. PSE-MADDPG, an off-policy algorithm with the preference-based experience sharing scheme, is proposed and benchmarked on a multi-target assignment and cooperative navigation mission. Experimental results show that PSE-MADDPG can successfully solve the problem of multiple targets assignment and outperform two classical deep reinforcement learning algorithms by learning in fewer steps and converging to higher episode rewards. Meanwhile, PSE-MADDPG relaxes the constraint of the strongly homogeneous agents assumption and requires little additional computation cost.

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Data availability

The data and materials that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The code is accessible on a GitHub repository named 'PSE-MADDPG', visit:  https://github.com/guanzhongzx/PSE-MADDPG.

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Funding

The first and second author are supported by the National Natural Science Foundation of China (No. 61790552).

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Authors and Affiliations

  1. School of Automation, Northwestern Polytechnical University, West Youyi Road, Xi’an, 710072, Shaanxi, China

    Xuan Zuo, Pu Zhang & Zhun-Ga Liu

  2. School of Automation and Information Engineering, Xi’an University of Technology, Jinhua Road, Xi’an, 710048, Shaanxi, China

    Pu Zhang

  3. China Aerospace Academy of Systems Science and Engineering, Fucheng Road, Haidian, Beijing, 100048, China

    Hui-Yan Li

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  1. Xuan Zuo
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XZ contributed to designing the method, running the experiments and writing all sections. ZL contributed to providing feedback and guidance. PZ contributed to the conceptualisation and formal analysis. HL contribute to the methodology. All authors contributed on the results analysis and the manuscript revision.

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Correspondence to Xuan Zuo.

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Appendices

Appendix A: Compatible function approximation

We consider off-policy MARL methods that learn a deterministic target policy \(\mu _{\theta }(s)\) from trajectories generated by an arbitrary stochastic behaviour policy \(\pi (s, a)\). Similar to the stochastic case, we find a critic \(Q^{w}(s, a)\) such that the gradient \(\nabla _a Q^{\mu }(s, a)\) can be replaced by \(\nabla _a Q^w(s, a)\), without affecting the deterministic policy gradient. The following theorem applies to both on-policy, \({\mathbb {E}}[\cdot ]={\mathbb {E}}_{s \sim \rho ^{\mu }}[\cdot ]\), and off-policy, \({\mathbb {E}}[\cdot ]={\mathbb {E}}_{s \sim \rho ^{\beta }}[\cdot ]\).

Theorem 1

A function approximator \(Q^{w}(s, a)\) is compatible with a deterministic policy \(\mu _{\theta }(s)\), \(\nabla _\theta J_{\beta }(\theta ) = {\mathbb {E}}\left[ \left. \nabla _\theta \mu _\theta (s) \nabla _a Q^w(s, a)\right| _{a=\mu _\theta (s)}\right]\), if:

  1. (i)

    \(\left. \nabla _a Q^w(s, a)\right| _{a=\mu _\theta (s)}=\nabla _\theta \mu _\theta (s)^{\top } w\) and

  2. (ii)

    w minimises the mean-squared error, \(\text {MSE}(\theta , w)= {\mathbb {E}}\left[ \epsilon (s; \theta , w)^{\top } \epsilon (s; \theta , w)\right]\) where \(\epsilon (s; \theta , w) = \left. \nabla _a Q^w(s, a)\right| _{a=\mu _\theta (s)}-\left. \nabla _a Q^\mu (s, a)\right| _{a=\mu _\theta (s)}\).

Proof

If w minimises the MSE then the gradient of \({\epsilon }^2\) with respect to w must be zero. We then use the fact that, by condition (i), \(\nabla _w \epsilon (s; \theta , w)=\nabla _\theta \mu _\theta (s)\)

$$\begin{aligned} \begin{aligned} \nabla _w \text {MSE}(\theta , w)&= 0 \\ {\mathbb {E}}\left[ \nabla _\theta \mu _\theta (s) \epsilon (s ; \theta , w)\right]&= 0 \\ {\mathbb {E}}\left[ \left. \nabla _\theta \mu _\theta (s) \nabla _a Q^w(s, a)\right| _{a=\mu _\theta (s)}\right]&= {\mathbb {E}}\left[ \left. \nabla _\theta \mu _\theta (s) \nabla _a Q^\mu (s, a)\right| _{a=\mu _\theta (s)}\right] \\&= \nabla _\theta J_\beta \left( \mu _\theta \right) \text{ or } \nabla _\theta J\left( \mu _\theta \right) \end{aligned} \end{aligned}$$

For any deterministic policy \(\mu _{\theta }(s)\), there always exists a compatible function approximator of the form \(Q^w(s, a) = \left( a-\mu _\theta (s)\right) ^{\top } \nabla _\theta \mu _\theta (s)^{\top } w + V^v(s)\), where \(V^v(s)\) may be any differentiable baseline function that is independent of the action a. For example, a linear combination of state features \(\phi (s)\) and parameters v, \(V^v(s) = v^{\top }\phi (s)\) for parameters v. We note that a linear function approximator is not very useful for predicting action-values globally, since the action value diverges to \(\pm \infty\) for large actions. As a result, a linear function approximator is sufficient to select the direction in which the actor should adjust its policy parameters. \(\square\)

Appendix B: The pseudocode of RSE-MADDPG

The RSE-MADDPG algorithm is used as baseline for the proposed method.

figure b

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Zuo, X., Zhang, P., Li, HY. et al. Preference-based experience sharing scheme for multi-agent reinforcement learning in multi-target environments. Evolving Systems 15, 1681–1699 (2024). https://doi.org/10.1007/s12530-024-09587-4

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