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In this paper, a deep reinforcement learning based method is proposed toobtain optimal policies for optimal infinite-horizon control of probabilisticBoolean control networks (PBCNs). Compared with the existing literatures, theproposed method is model-free, namely, the system model and the initial statesneedn't to be known. Meanwhile, it is suitable for large-scale PBCNs. First, weestablish the connection between deep reinforcement learning and optimalinfinite-horizon control, and structure the problem into the framework of theMarkov decision process. Then, PBCNs are defined as large-scale or small-scale,depending on whether the memory of the action-values exceeds the RAM of thecomputer. Based on the newly introduced definition, Q-learning (QL) and doubledeep Q-network (DDQN) are applied to the optimal infinite-horizon control ofsmall-scale and large-scale PBCNs, respectively. Meanwhile, the optimal statefeedback controllers are designed. Finally, two examples are presented, whichare a small-scale PBCN with 3 nodes, and a large-scale one with 28 nodes. Toverify the convergence of QL and DDQN, the optimal control policy and theoptimal action-values, which are obtained from both the algorithms, arecompared with the ones based on a model-based method named policy iteration.Meanwhile, the performance of QL is compared with DDQN in the small-scale PBCN.

Deep Reinforcement Learning Based Optimal Infinite-Horizon Control of Probabilistic Boolean Control Networks