Policy iteration for discrete-time systems with discounted costs: stability and near-optimality guarantees
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913288057520128 |
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| author | de Brusse, Jonathan Granzotto, Mathieu Postoyan, Romain Nešić, Dragan |
| author_facet | de Brusse, Jonathan Granzotto, Mathieu Postoyan, Romain Nešić, Dragan |
| contents | Given a discounted cost, we study deterministic discrete-time systems whose inputs are generated by policy iteration (PI). We provide novel near-optimality and stability properties, while allowing for non stabilizing initial policies. That is, we first give novel bounds on the mismatch between the value function generated by PI and the optimal value function, which are less conservative in general than those encountered in the dynamic programming literature for the considered class of systems. Then, we show that the system in closed-loop with policies generated by PI are stabilizing under mild conditions, after a finite (and known) number of iterations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Policy iteration for discrete-time systems with discounted costs: stability and near-optimality guarantees de Brusse, Jonathan Granzotto, Mathieu Postoyan, Romain Nešić, Dragan Optimization and Control Given a discounted cost, we study deterministic discrete-time systems whose inputs are generated by policy iteration (PI). We provide novel near-optimality and stability properties, while allowing for non stabilizing initial policies. That is, we first give novel bounds on the mismatch between the value function generated by PI and the optimal value function, which are less conservative in general than those encountered in the dynamic programming literature for the considered class of systems. Then, we show that the system in closed-loop with policies generated by PI are stabilizing under mild conditions, after a finite (and known) number of iterations. |
| title | Policy iteration for discrete-time systems with discounted costs: stability and near-optimality guarantees |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.19007 |