Gray-Box Optimization using Optimism in the Face of Uncertainty

Mathematics > Optimization and Control [Submitted on 16 Jun 2026] Title:Gray-Box Optimization using Optimism in the Face of Uncertainty View PDF HTML (experimental)Abstract:This paper considers sequential gray-box optimization where the objective function is given as the composition of a loss function and a parametric model. Crucially, the parameters of the model are unknown and need to be iteratively estimated from noisy observations of the model outputs. This problem setup generalizes the parametric black-box optimization problem known as (contextual) stochastic linear bandit. To address the sequential gray-box optimization problem, we propose a structure-exploiting method that leverages known problem structure given in terms of the loss function and an a priori set of admissible parameters. The method is based on the principle of optimism in the face of uncertainty and trades off exploration and exploitation by minimizing a lower confidence bound on the true objective function. We provide a detailed regret analysis of the novel method, improving on state-of-the-art results for the special case of linear stochastic bandits due to the use of a recently published bound for the parameter confidence sets arising in multi-output linear least-squares estimation. Numerical examples illustrate the superior performance of structure-exploiting methods compared to structure-agnostic approaches. Submission history From: Katrin Baumgärtner [view email][v1] Tue, 16 Jun 2026 09:41:41 UTC (691 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.