A learning-based approach to stochastic optimal control under reach-avoid constraint
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908562378194944 |
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| author | Ni, Tingting Kamgarpour, Maryam |
| author_facet | Ni, Tingting Kamgarpour, Maryam |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_16561 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A learning-based approach to stochastic optimal control under reach-avoid constraint Ni, Tingting Kamgarpour, Maryam Optimization and Control Machine Learning 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. |
| title | A learning-based approach to stochastic optimal control under reach-avoid constraint |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2412.16561 |