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 $\tau$-CMDP. We formulate the STL constrained optimal decision making problem as the $\tau$-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.

Exploration-exploitation dilemma has long been a crucial issue in reinforcement learning. In this paper, we propose a new approach to automatically balance between these two. Our method is built upon the Soft Actor-Critic (SAC) algorithm, which uses an "entropy temperature" that balances the original task reward and the policy entropy, and hence controls the trade-off between exploitation and exploration. It is empirically shown that SAC is very sensitive to this hyperparameter, and the follow-up work (SAC-v2), which uses constrained optimization for automatic adjustment, has some limitations. The core of our method, namely Meta-SAC, is to use metagradient along with a novel meta objective to automatically tune the entropy temperature in SAC. We show that Meta-SAC achieves promising performances on several of the Mujoco benchmarking tasks, and outperforms SAC-v2 over 10% in one of the most challenging tasks, humanoid-v2.