aiqbench analysis
This research introduces ACCESS, a novel framework that decouples optimization from feasibility evaluation in chance-constrained stochastic programs, addressing the computational bottlenecks of standard methods like Sample Average Approximation. By generating candidates via single-scenario subproblems and assessing them through GPU-accelerated batched simulations, the approach significantly improves solution quality while maintaining rigorous feasibility guarantees. The method demonstrates superior performance across diverse benchmarks, offering a scalable path forward for complex stochastic optimization problems in AI-driven decision systems.
Optimization for One, Feasibility for Most: Decoupling Optimization from Feasibility in Chance-Constrained Programs
arXiv:2610.19027v1 Announce Type: cross Abstract: Chance-constrained stochastic programs (CCSPs) require solutions that satisfy uncertain constraints with high probability. Standard approaches either embed scenarios directly into optimization by considering sample average approximation (SAA)-based reformulations, growing prohibitively expensive and often failing to find feasible solutions; or employ conservative reformulations that guarantee feasibility but sacrifice objective quality by design. We propose ACCESS (Adaptive Chance-Constrained Exploration via Structured Sampling), a structured sampling framework that decouples optimization from feasibility evaluation. First, high-quality candidate solutions are generated by solving many inexpensive single-scenario subproblems, avoiding sampling directly in the constrained high-dimensional solution space. Second, feasibility is assessed separately via large-scale batched simulation over a massive number of scenarios, which is naturally amenable to GPU parallelism. That reduces the search from a high-dimensional solution space to a two-dimensional parameter space controlling conservatism and scenario diversity; while concentrating on candidates near the feasibility boundary, where high-quality feasible solutions lie. We also introduce a variant, ACCESS($\delta$), which provides certified feasibility guarantees with probability $1-\delta$. Experiments across three benchmark classes and five scenario distributions show that ACCESS matches or exceeds the best objective found by any method in nearly every setting, while ACCESS($\delta$) is empirically feasible on every instance. The conservative reformulations remain several percent worse in objective, and SAA is frequently infeasible while taking an order of magnitude longer on the harder benchmarks.
Abstract:Chance-constrained stochastic programs (CCSPs) require solutions that satisfy uncertain constraints with high probability. Standard approaches either embed scenarios directly into optimization by considering sample average approximation (SAA)-based reformulations, growing prohibitively expensive and often failing to find feasible solutions; or employ conservative reformulations that guarantee feasibility but sacrifice objective quality by design. We propose ACCESS (Adaptive Chance-Constrained Exploration via Structured Sampling), a structured sampling framework that decouples optimization from feasibility evaluation. First, high-quality candidate solutions are generated by solving many inexpensive single-scenario subproblems, avoiding sampling directly in the constrained high-dimensional solution space. Second, feasibility is assessed separately via large-scale batched simulation over a massive number of scenarios, which is naturally amenable to GPU parallelism. That reduces the search from a high-dimensional solution space to a two-dimensional parameter space controlling conservatism and scenario diversity; while concentrating on candidates near the feasibility boundary, where high-quality feasible solutions lie. We also introduce a variant, ACCESS($\delta$), which provides certified feasibility guarantees with probability $1-\delta$. Experiments across three benchmark classes and five scenario distributions show that ACCESS matches or exceeds the best objective found by any method in nearly every setting, while ACCESS($\delta$) is empirically feasible on every instance. The conservative reformulations remain several percent worse in objective, and SAA is frequently infeasible while taking an order of magnitude longer on the harder benchmarks.
Optimization and Control (math.OC); Machine Learning (cs.LG)
arXiv:2610.19027 [math.OC]
(or arXiv:2610.19027v1 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2610.19027 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 316 words
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