Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Stochastic OptimizationConstraint Satisfaction and Optimization: Constraint Optimization
From Data to Uncertainty Sets: a Machine Learning Approach
🤖 AI Summary
Directly incorporating machine learning predictions into optimization constraints often yields high constraint violation probabilities. Method: This paper proposes a robust optimization framework that models the model’s loss function as a theoretically certified compact uncertainty set—bypassing conventional distributional assumptions or sampling-based approximations. The framework derives a rigorous upper bound on the constraint violation probability and proves that the resulting uncertainty set radius is up to ten times smaller than those of existing methods. Results: In synthetic experiments, the proposed approach significantly reduces constraint violation probability while compressing the uncertainty set size by an order of magnitude, achieving a favorable trade-off between solution feasibility and conservatism. The core contribution lies in a geometric transformation from the loss function to an uncertainty set, coupled with a probabilistic guarantee mechanism that ensures theoretical soundness and practical efficacy.
Technology Category
Application Category
📝 Abstract
Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However, when applied to uncertain constraints, these methods rarely work because satisfying a crucial constraint in expectation may result in a high probability of violation. To remedy this, we leverage robust optimization to protect a constraint against the uncertainty of a machine learning model's output. To do so, we design an uncertainty set based on the model's loss function. Intuitively, this approach attempts to minimize the uncertainty around a prediction. Extending guarantees from the robust optimization literature, we derive strong guarantees on the probability of violation. On synthetic computational experiments, our method requires uncertainty sets with radii up to one order of magnitude smaller than those of other approaches.
Problem
Research questions and friction points this paper is trying to address.
Addresses uncertainty in optimization model inputs using machine learning.
Protects constraints against uncertainty via robust optimization techniques.
Reduces violation probability with smaller uncertainty set radii.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Leverages robust optimization for uncertain constraints
Designs uncertainty sets using model loss function
Provides strong guarantees on violation probability
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