Learning to Optimize Contextually Constrained Problems for Real-Time Decision-Generation

TL;DR

This paper introduces a novel generative modeling framework that combines interior point methods and adversarial learning to produce decision solutions for context-dependent continuous optimization problems, ensuring optimality guarantees.

Contribution

It presents a new approach integrating optimization techniques with adversarial learning to generate decisions with theoretical optimality guarantees for variable feasible sets.

Findings

Outperforms predict-then-optimize methods in portfolio optimization.

Achieves better personalized treatment design compared to supervised deep learning.

Provides in-sample and out-of-sample optimality guarantees.

Abstract

The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this work, we combine techniques from both fields to address the problem of learning to generate decisions to instances of continuous optimization problems where the feasible set varies with contextual features. We propose a novel framework for training a generative model to estimate optimal decisions by combining interior point methods and adversarial learning, which we further embed within an data generation algorithm. Decisions generated by our model satisfy in-sample and out-of-sample optimality guarantees. Finally, we investigate case studies in portfolio optimization and personalized treatment design, demonstrating that our approach yields advantages over predict-then-optimize and supervised deep learning techniques, respectively.