Reoptimization Nearly Solves Weakly Coupled Markov Decision Processes
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917658613514240 |
|---|---|
| author | Gast, Nicolas Gaujal, Bruno Yan, Chen |
| author_facet | Gast, Nicolas Gaujal, Bruno Yan, Chen |
| contents | We propose a new policy, called the LP-update policy, to solve finite horizon weakly-coupled Markov decision processes. The latter can be seen as multi-constraint multi-action bandits, and generalize the classical restless bandit problems. Our solution is based on re-solving periodically a relaxed version of the original problem, that can be cast as a linear program (LP). When the problem is made of $N$ statistically identical sub-components, we show that the LP-update policy becomes asymptotically optimal at rate $O(T^2/\sqrt{N})$. This rate can be improved to $O(T/\sqrt{N})$ if the problem satisfies some ergodicity property and to $O(1/N)$ if the problem is non-degenerate. The definition of non-degeneracy extends the same notion for restless bandits. By using this property, we also improve the computational efficiency of the LP-update policy. We illustrate the performance of our policy on randomly generated examples, as well as a generalized applicant screening problem, and show that it outperforms existing heuristics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01961 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Reoptimization Nearly Solves Weakly Coupled Markov Decision Processes Gast, Nicolas Gaujal, Bruno Yan, Chen Optimization and Control Probability We propose a new policy, called the LP-update policy, to solve finite horizon weakly-coupled Markov decision processes. The latter can be seen as multi-constraint multi-action bandits, and generalize the classical restless bandit problems. Our solution is based on re-solving periodically a relaxed version of the original problem, that can be cast as a linear program (LP). When the problem is made of $N$ statistically identical sub-components, we show that the LP-update policy becomes asymptotically optimal at rate $O(T^2/\sqrt{N})$. This rate can be improved to $O(T/\sqrt{N})$ if the problem satisfies some ergodicity property and to $O(1/N)$ if the problem is non-degenerate. The definition of non-degeneracy extends the same notion for restless bandits. By using this property, we also improve the computational efficiency of the LP-update policy. We illustrate the performance of our policy on randomly generated examples, as well as a generalized applicant screening problem, and show that it outperforms existing heuristics. |
| title | Reoptimization Nearly Solves Weakly Coupled Markov Decision Processes |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2211.01961 |