Efficient End-to-End Learning for Decision-Making: A Meta-Optimization Approach

TL;DR

This paper introduces a meta-optimization approach that trains neural networks to efficiently approximate complex optimization problems, significantly reducing computational costs in end-to-end decision-making models across various applications.

Contribution

The paper presents a novel neural network architecture with theoretical guarantees that accelerates optimization in end-to-end learning, applicable to diverse large-scale problems.

Findings

Achieves exponential convergence and approximation guarantees.

Provides faster, scalable solutions compared to existing methods.

Demonstrates effectiveness on real-world and synthetic optimization tasks.

Abstract

End-to-end learning has become a widely applicable and studied problem in training predictive ML models to be aware of their impact on downstream decision-making tasks. These end-to-end models often outperform traditional methods that separate training from the optimization and only myopically focus on prediction error. However, the computational complexity of end-to-end frameworks poses a significant challenge, particularly for large-scale problems. While training an ML model using gradient descent, each time we need to compute a gradient we must solve an expensive optimization problem. We present a meta-optimization method that learns efficient algorithms to approximate optimization problems, dramatically reducing computational overhead of solving the decision problem in general, an aspect we leverage in the training within the end-to-end framework. Our approach introduces a neural network architecture that near-optimally solves optimization problems while ensuring feasibility constraints through alternate projections. We prove exponential convergence, approximation guarantees, and generalization bounds for our learning method. This method offers superior computational efficiency, producing high-quality approximations faster and scaling better with problem size compared to existing techniques. Our approach applies to a wide range of optimization problems including deterministic, single-stage as well as two-stage stochastic optimization problems. We illustrate how our proposed method applies to (1) an electricity generation problem using real data from an electricity routing company coordinating the movement of electricity throughout 13 states, (2) a shortest path problem with a computer vision task of predicting edge costs from terrain maps, (3) a two-stage multi-warehouse cross-fulfillment newsvendor problem, as well as a variety of other newsvendor-like problems.