Off-Policy Conservative Distributional Reinforcement Learning With Safety Constraints

Safe exploration can be regarded as a constrained Markov decision problem (CMDP) where the expected long-term cost is constrained. Previous off-policy algorithms convert the constrained optimization problem into the corresponding unconstrained dual problem by introducing the Lagrangian relaxation technique. However, the cost function of the above algorithms provides inaccurate estimations and causes the instability of the Lagrange multiplier learning. In this article, we present a novel off-policy reinforcement learning (RL) algorithm called conservative distributional maximum a posteriori policy optimization (CDMPO). At first, to accurately judge whether the current situation satisfies the constraints, CDMPO adapts distributional RL method to estimate the Q-function and C-function. Then, CDMPO uses a conservative value function loss to reduce the number of violations of constraints during the exploration process. In addition, we utilize adaptive proportional integral derivative (APID) to update the Lagrange multiplier stably. In our experiments, we select eight representative constrained tasks from two well-known safe RL benchmarks (Safety Gym and Bullet Safety Gym), providing a comprehensive evaluation of our methods across diverse scenarios. Empirical results show that the proposed method has fewer violations of constraints in the early exploration process. The final test results also illustrate that our method has better-risk control capabilities.