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  4. A learning-based approach to stochastic optimal control under reach-avoid constraint
 
conference paper

A learning-based approach to stochastic optimal control under reach-avoid constraint

Ni, Tingting  
•
Kamgarpour, Maryam  
May 6, 2025
HSCC '25: Proceedings of the 28th ACM International Conference on Hybrid Systems: Computation and Control
28th ACM International Conference on Hybrid Systems: Computation and Control (HSCC 2025).

We develop a model-free approach to optimally control stochastic, Markovian systems subject to a reach-avoid constraint. Specifically, the state trajectory must remain within a safe set while reaching a target set within a finite time horizon. Due to the time-dependent nature of these constraints, we show that, in general, the optimal policy for this constrained stochastic control problem is non-Markovian, which increases the computational complexity. To address this challenge, we apply the state-augmentation technique from [23], reformulating the problem as a constrained Markov decision process (CMDP) on an extended state space. This transformation allows us to search for a Markovian policy, avoiding the complexity of non-Markovian policies. To learn the optimal policy without a system model, and using only trajectory data, we develop a log-barrier policy gradient approach. We prove that under suitable assumptions, the policy parameters converge to the optimal parameters, while ensuring that the system trajectories satisfy the stochastic reach-avoid constraint with high probability.

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