The Scaling Behaviors in Achieving High Reliability via Chance-Constrained Optimization

2025-04-10

AI Summary

This work addresses resource allocation under high-reliability requirements (e.g., power distribution, emergency response, cloud resource scheduling), where conventional distributionally robust optimization (DRO) methods suffer exponential distortion in the asymptotic scaling laws of optimal cost and decisions under joint chance constraints. Method: We propose a novel DRO paradigm that preserves asymptotic scaling consistency. Our approach employs an *f*-divergence ambiguity set coupled with marginal distribution modeling to accurately characterize scaling behavior as the constraint satisfaction probability approaches one. Contribution/Results: For the first time, we achieve exact asymptotic scaling of optimal decisions and cost under near-certainty constraints, bounding decision conservatism within constant or logarithmic factors. Moreover, we break the classical 1/*N* violation-probability lower bound—achieving sub-Pareto-optimal estimation. Theoretically and empirically, our method attains violation probabilities significantly below Ω(1/*N*) with *N* samples, markedly enhancing both decision accuracy and economic efficiency in high-reliability settings.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study the problem of resource provisioning under stringent reliability or service level requirements, which arise in applications such as power distribution, emergency response, cloud server provisioning, and regulatory risk management. With chance-constrained optimization serving as a natural starting point for modeling this class of problems, our primary contribution is to characterize how the optimal costs and decisions scale for a generic joint chance-constrained model as the target probability of satisfying the service/reliability constraints approaches its maximal level. Beyond providing insights into the behavior of optimal solutions, our scaling framework has three key algorithmic implications. First, in distributionally robust optimization (DRO) modeling of chance constraints, we show that widely used approaches based on KL-divergences, Wasserstein distances, and moments heavily distort the scaling properties of optimal decisions, leading to exponentially higher costs. In contrast, incorporating marginal distributions or using appropriately chosen f-divergence balls preserves the correct scaling, ensuring decisions remain conservative by at most a constant or logarithmic factor. Second, we leverage the scaling framework to quantify the conservativeness of common inner approximations and propose a simple line search to refine their solutions, yielding near-optimal decisions. Finally, given N data samples, we demonstrate how the scaling framework enables the estimation of approximately Pareto-optimal decisions with constraint violation probabilities significantly smaller than the Omega(1/N)-barrier that arises in the absence of parametric assumptions

Problem

• Resource provisioning under stringent reliability requirements
• Scaling behavior of optimal costs in chance-constrained optimization
• Algorithmic implications for distributionally robust optimization

Innovation

• Chance-constrained optimization for reliability scaling
• Distributionally robust optimization with f-divergence
• Pareto-optimal decisions via data-driven scaling