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

• URL: http://arxiv.org/abs/2412.16561v1
• Date: Sat, 21 Dec 2024 10:07:40 GMT
• Title: A learning-based approach to stochastic optimal control under reach-avoid constraint
• Authors: Tingting Ni, Maryam Kamgarpour,
• Abstract summary: We develop a model-free approach to optimally control, Markovian systems subject to a reach-avoid constraint. We prove that under suitable assumptions, the policy parameters converge to the optimal parameters, while ensuring that the system trajectories satisfy the reach-avoid constraint with high probability.
• Score: 7.036452261968767
• License:
• Abstract: 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 arXiv:2402.19360, 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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