Approximately optimal distributed controls for high-dimensional stochastic systems with pairwise interaction through controls
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914116472406016 |
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| author | Devey, Elise |
| author_facet | Devey, Elise |
| contents | This paper investigates large-population stochastic control problems in which agents share their state information and cooperate to minimize a convex cost functional. The latter is decomposed into individual and coupling costs, with the distinctive feature that the coupling term is a pairwise interaction function between the controls. To address this setting, we follow closely (Jackson & Lacker, 2025): we introduce a related problem where each agent observes only its own state. We then establish a quantitative bound on the difference between the value functions associated with these two problems. We obtain this result by reformulating the problems analytically as Hamilton-Jacobi type equations and comparing their associated Hamiltonians. The main difficulty of our approach lies in establishing a precise comparison between the distributions of the corresponding optimal controls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximately optimal distributed controls for high-dimensional stochastic systems with pairwise interaction through controls Devey, Elise Optimization and Control 93E20, 49N80 This paper investigates large-population stochastic control problems in which agents share their state information and cooperate to minimize a convex cost functional. The latter is decomposed into individual and coupling costs, with the distinctive feature that the coupling term is a pairwise interaction function between the controls. To address this setting, we follow closely (Jackson & Lacker, 2025): we introduce a related problem where each agent observes only its own state. We then establish a quantitative bound on the difference between the value functions associated with these two problems. We obtain this result by reformulating the problems analytically as Hamilton-Jacobi type equations and comparing their associated Hamiltonians. The main difficulty of our approach lies in establishing a precise comparison between the distributions of the corresponding optimal controls. |
| title | Approximately optimal distributed controls for high-dimensional stochastic systems with pairwise interaction through controls |
| topic | Optimization and Control 93E20, 49N80 |
| url | https://arxiv.org/abs/2510.23537 |