{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/optimal-adaptive-control-with-separable-drift","title":"Optimal adaptive control with separable drift uncertainty","arxiv_id":"2309.07091","date":"2023-09-13","proceeding":null,"authors":["Samuel N. Cohen","Christoph Knochenhauer","Alexander Merkel"],"abstract":"We consider a problem of stochastic optimal control with separable drift uncertainty in strong formulation on a finite horizon. The drift coefficient of the state $Y^{u}$ is multiplicatively influenced by an unknown random variable $\\lambda$, while admissible controls $u$ are required to be adapted to the observation filtration. Choosing a control actively influences the state and information acquisition simultaneously and comes with a learning effect. The problem, initially non-Markovian, is embedded into a higher-dimensional Markovian, full information control problem with control-dependent filtration and noise. To that problem, we apply the stochastic Perron method to characterize the value function as the unique viscosity solution to the HJB equation, explicitly construct $\\varepsilon$-optimal controls and show that the values of strong and weak formulations agree. Numerical illustrations show a significant difference between the adaptive control and the certainty equivalence control.","url_abs":"https://arxiv.org/abs/2309.07091v2","url_pdf":"https://arxiv.org/pdf/2309.07091v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"optimal-adaptive-control-with-separable-drift","repo_url":"https://github.com/alexandermerkel/optimal-adaptive-control-with-separable-drift-uncertainty","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}