Reach-Avoid Control of Stochastic Discrete-Time Systems via Reinforcement Learning and SOS-Based Safety Verification

Reinforcement learning (RL) has emerged as a powerful tool for control in stochastic systems. In this paper, we propose a hybrid RL-based approach for reach-avoid control in discrete-time stochastic systems. Specifically, we employ Proximal Policy Optimization (PPO) for pretraining a policy, followed by fine-tuning using Deep Deterministic Policy Gradient (DDPG) to improve performance in continuous action spaces. To ensure safety and stability, we leverage Sum-of-Squares (SOS) optimization to compute stochastic Lyapunov functions and stochastic barrier functions, providing formal guarantees on system reachability and avoidance constraints. Experimental results demonstrate the effectiveness of our approach in synthesizing safe and optimal controllers, with significant improvements in both sample efficiency and policy robustness.