Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.02479 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912361283059712 |
|---|---|
| author | Li, Yanyun Guo, Xianping |
| author_facet | Li, Yanyun Guo, Xianping |
| contents | We consider the maximal reach-avoid probability to a target in finite horizon for semi-Markov decision processes with time-varying obstacles. Since the variance of the obstacle set, the model \eqref{Model} is non-homogeneous. To overcome such difficulty, we construct a related two-dimensional model \eqref{newModel}, and then prove the equivalence between such reach-avoid probability of the original model and that of the related two-dimensional one. For the related two-dimensional model, we analyze some special characteristics of the equivalent reach-avoid probability. On this basis, we provide a special improved value-type algorithm to obtain the equivalent maximal reach-avoid probability and its $ε$-optimal policy. Then, at the last step of the algorithm, by the equivalence between these two models, we obtain the original maximal reach-avoid probability and its $ε$-optimal policy for the original model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reach-avoid semi-Markov decision processes with time-varying obstacles Li, Yanyun Guo, Xianping Probability We consider the maximal reach-avoid probability to a target in finite horizon for semi-Markov decision processes with time-varying obstacles. Since the variance of the obstacle set, the model \eqref{Model} is non-homogeneous. To overcome such difficulty, we construct a related two-dimensional model \eqref{newModel}, and then prove the equivalence between such reach-avoid probability of the original model and that of the related two-dimensional one. For the related two-dimensional model, we analyze some special characteristics of the equivalent reach-avoid probability. On this basis, we provide a special improved value-type algorithm to obtain the equivalent maximal reach-avoid probability and its $ε$-optimal policy. Then, at the last step of the algorithm, by the equivalence between these two models, we obtain the original maximal reach-avoid probability and its $ε$-optimal policy for the original model. |
| title | Reach-avoid semi-Markov decision processes with time-varying obstacles |
| topic | Probability |
| url | https://arxiv.org/abs/2505.02479 |