Thompson Sampling Algorithm for Stochastic Games
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908795675869184 |
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| author | Cohen, Asaf He, Ruolan Wang, Yuqiong |
| author_facet | Cohen, Asaf He, Ruolan Wang, Yuqiong |
| contents | We study a stochastic differential game with $N$ competitive players in a linear-quadratic framework with ergodic cost, where $d$-dimensional diffusion processes govern the state dynamics with an unknown common drift (matrix). Assuming a Gaussian prior on the drift, we use filtering techniques to update its posterior estimates. Based on these estimates, we propose a Thompson-sampling-based algorithm with dynamic episode lengths to approximate strategies. We show that the Bayesian regret for each player has an error bound of order $O(\sqrt{T\log(T)})$, where $T$ is the time-horizon, independent of the number of players. This implies that average regret per unit time goes to zero. Finally, we prove that the algorithm results in a Nash equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20973 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thompson Sampling Algorithm for Stochastic Games Cohen, Asaf He, Ruolan Wang, Yuqiong Optimization and Control We study a stochastic differential game with $N$ competitive players in a linear-quadratic framework with ergodic cost, where $d$-dimensional diffusion processes govern the state dynamics with an unknown common drift (matrix). Assuming a Gaussian prior on the drift, we use filtering techniques to update its posterior estimates. Based on these estimates, we propose a Thompson-sampling-based algorithm with dynamic episode lengths to approximate strategies. We show that the Bayesian regret for each player has an error bound of order $O(\sqrt{T\log(T)})$, where $T$ is the time-horizon, independent of the number of players. This implies that average regret per unit time goes to zero. Finally, we prove that the algorithm results in a Nash equilibrium. |
| title | Thompson Sampling Algorithm for Stochastic Games |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.20973 |