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Volume 10 Issue 11
Nov.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Z. Chen and  N. Li,  “An optimal control-based distributed reinforcement learning framework for a class of non-convex objective functionals of the multi-agent network,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 11, pp. 2081–2093, Nov. 2023. doi: 10.1109/JAS.2022.105992
Citation: Z. Chen and  N. Li,  “An optimal control-based distributed reinforcement learning framework for a class of non-convex objective functionals of the multi-agent network,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 11, pp. 2081–2093, Nov. 2023. doi: 10.1109/JAS.2022.105992

An Optimal Control-Based Distributed Reinforcement Learning Framework for A Class of Non-Convex Objective Functionals of the Multi-Agent Network

doi: 10.1109/JAS.2022.105992
Funds:  This work was supported in part by the National Natural Science Foundation of China (NSFC) (61773260) and the Ministry of Science and Technology (2018YFB130590)
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  • This paper studies a novel distributed optimization problem that aims to minimize the sum of the non-convex objective functionals of the multi-agent network under privacy protection, which means that the local objective of each agent is unknown to others. The above problem involves complexity simultaneously in the time and space aspects. Yet existing works about distributed optimization mainly consider privacy protection in the space aspect where the decision variable is a vector with finite dimensions. In contrast, when the time aspect is considered in this paper, the decision variable is a continuous function concerning time. Hence, the minimization of the overall functional belongs to the calculus of variations. Traditional works usually aim to seek the optimal decision function. Due to privacy protection and non-convexity, the Euler-Lagrange equation of the proposed problem is a complicated partial differential equation. Hence, we seek the optimal decision derivative function rather than the decision function. This manner can be regarded as seeking the control input for an optimal control problem, for which we propose a centralized reinforcement learning (RL) framework. In the space aspect, we further present a distributed reinforcement learning framework to deal with the impact of privacy protection. Finally, rigorous theoretical analysis and simulation validate the effectiveness of our framework.

     

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    Highlights

    • This paper considers a novel distributed optimization problem, where the decision variable is a time-varying continuous function and the objective functional is the integration of a non-convex function over a continuous time interval. The existing distributed optimization method cannot deal with such a problem
    • For the proposed problem, this paper converts the optimization of the functional into an optimal control problem. This manner builds the relationship between distributed optimal control and distributed optimization. Moreover, a centralized reinforcement learning framework is proposed to solve the transformed problem
    • This paper also considers the privacy protection in distributed optimization. To eliminate its influence, a distributed reinforcement learning framework is further puts forward .Moreover, the convergence analysis is also provided

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