C-MCTS: Safe Planning with Monte Carlo Tree Search

Many real-world decision-making tasks, such as safety-critical scenarios, cannot be fully described in a single-objective setting using the Markov Decision Process (MDP) framework, as they include hard constraints. These can instead be modeled with additional cost functions within the Constrained Markov Decision Process (CMDP) framework. Even though CMDPs have been extensively studied in the Reinforcement Learning literature, little attention has been given to sampling-based planning algorithms such as MCTS for solving them. Previous approaches use Monte Carlo cost estimates to avoid constraint violations. However, these suffer from high variance which results in conservative performance with respect to costs. We propose Constrained MCTS (C-MCTS), an algorithm that estimates cost using a safety critic. The safety critic training is based on Temporal Difference learning in an offline phase prior to agent deployment. This critic limits the exploration of the search tree and removes unsafe trajectories within MCTS during deployment. C-MCTS satisfies cost constraints but operates closer to the constraint boundary, achieving higher rewards compared to previous work. As a nice byproduct, the planner is more efficient requiring fewer planning steps. Most importantly, we show that under model mismatch between the planner and the real world, our approach is less susceptible to cost violations than previous work.