Chance-constrained probability measure optimization

[2309.08231] Chance-constrained probability measure optimization Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2309.08231 (math) [Submitted on 15 Sep 2023 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Chance-constrained probability measure optimization Authors: Xun Shen , Ye Wang , Yuhu Wu , Satoshi Ito , Jun-ichi Imura View PDF HTML (experimental) Abstract: Stochastic optimization with chance constraints often relies on deterministic decision-making, where optimal decisions are fixed and may be applied to a system repeatedly. A critical question arises: Can probabilistic decision-making, where probability measures/distributions are considered as decision variables, outperform deterministic decision-making in terms of the expected performance when chance constraints are present? This paper addresses this question by introducing the \textit{Chance-Constrained Probability Measure Optimization} (CCPMO) framework, which formulates the problem of optimizing probabilistic decisions under chance constraints. We first establish the existence of the optimal solution to CCPMO. Crucially, we prove that the optimal probabilistic decisions can always be represented by a probability measure concentrated on only two points, thereby reducing the CCPMO problem to an equivalent, simplified form. To solve this reduced problem, we propose a sample-based smooth approximation method. This approach leverages samples of model uncertainties to construct an approximate problem with uniform convergence and probabilistic feasibility guarantees. The approximate problem can be efficiently solved using standard nonlinear programming techniques. Finally, we validate the proposed framework through a numerical example of a quadrotor control problem under turbulent conditions. The results demonstrate that probabilistic decision-making outperforms deterministic approaches in expected performance while satisfying safety-critical chance constraints. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2309.08231 [math.OC] (or arXiv:2309.08231v2 [math.OC] for this version) https://doi.org/10.48550/arXiv.2309.08231 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Xun Shen [ view email ] [v1] Fri, 15 Sep 2023 08:02:22 UTC (451 KB) [v2] Tue, 25 Aug 2026 05:16:57 UTC (854 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2023-09 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs 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 . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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