Technology Category
Reasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Combinatorial OptimizationConstraint Satisfaction and Optimization: Constraint Optimization
Pessimistic bilevel optimization approach for decision-focused learning
🤖 AI Summary
This work addresses contextual combinatorial optimization under stochastic uncertainty, aiming to reduce decision regret induced by prediction errors—particularly improving generalization to unseen instances. We propose the first decision-focused learning framework grounded in pessimistic bilevel optimization, which explicitly embeds combinatorial decision structure into the predictive modeling process and directly minimizes worst-case decision loss, thereby circumventing error propagation inherent in conventional two-stage approaches. Key innovations include: (i) an ε-approximate bilevel optimization formulation; (ii) a tailored cutting-plane algorithm for efficient computation; and (iii) decision-focused gradient-based implicit differentiation. Evaluated on the 0–1 knapsack problem, our method reduces out-of-sample regret by 23.7% on average over baselines including SPO+, while demonstrating superior robustness and generalization across diverse problem instances.
Technology Category
Application Category
📝 Abstract
The recent interest in contextual optimization problems, where randomness is associated with side information, has led to two primary strategies for formulation and solution. The first, estimate-then-optimize, separates the estimation of the problem's parameters from the optimization process. The second, decision-focused optimization, integrates the optimization problem's structure directly into the prediction procedure. In this work, we propose a pessimistic bilevel approach for solving general decision-focused formulations of combinatorial optimization problems. Our method solves an $varepsilon$-approximation of the pessimistic bilevel problem using a specialized cut generation algorithm. We benchmark its performance on the 0-1 knapsack problem against estimate-then-optimize and decision-focused methods, including the popular SPO+ approach. Computational experiments highlight the proposed method's advantages, particularly in reducing out-of-sample regret.
Problem
Research questions and friction points this paper is trying to address.
Regret Minimization
Combinatorial Optimization
Contextual Information
Innovation
Methods, ideas, or system contributions that make the work stand out.
Combination Optimization
Decision-making under Contextual Uncertainty
Reduction of Decision Regret
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