Deep reinforcement learning under signal temporal logic constraints using Lagrangian relaxation
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Deep reinforcement learning (DRL) has attracted much attention as an approach to solve sequential decision making problems without mathematical models of systems or environments. In general, a constraint may be imposed on the decision making. In this study, we consider the optimal decision making problems with constraints to complete temporal high-level tasks in the continuous state-action domain. We describe the constraints using signal temporal logic (STL), which is useful for time sensitive control tasks since it can specify continuous signals within a bounded time interval. To deal with the STL constraints, we introduce an extended constrained Markov decision process (CMDP), which is called a τ-CMDP. We formulate the STL constrained optimal decision making problem as the τ-CMDP and propose a two-phase constrained DRL algorithm using the Lagrangian relaxation method. Through simulations, we also demonstrate the learning performance of the proposed algorithm.
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