Contrastive Losses and Solution Caching for Predict-and-Optimize

TL;DR

This paper introduces a novel surrogate loss function based on Noise Contrastive Estimation and a solution caching scheme to improve the efficiency of predict-and-optimize methods for combinatorial decision problems under uncertainty.

Contribution

It proposes a Noise Contrastive-based surrogate loss and a solver-agnostic solution caching approach to reduce training time while maintaining accuracy in predict-and-optimize tasks.

Findings

The caching scheme significantly reduces training time.

The surrogate loss matches state-of-the-art accuracy.

The method is solver-agnostic and scalable.

Abstract

Many decision-making processes involve solving a combinatorial optimization problem with uncertain input that can be estimated from historic data. Recently, problems in this class have been successfully addressed via end-to-end learning approaches, which rely on solving one optimization problem for each training instance at every epoch. In this context, we provide two distinct contributions. First, we use a Noise Contrastive approach to motivate a family of surrogate loss functions, based on viewing non-optimal solutions as negative examples. Second, we address a major bottleneck of all predict-and-optimize approaches, i.e. the need to frequently recompute optimal solutions at training time. This is done via a solver-agnostic solution caching scheme, and by replacing optimization calls with a lookup in the solution cache. The method is formally based on an inner approximation of the feasible space and, combined with a cache lookup strategy, provides a controllable trade-off between training time and accuracy of the loss approximation. We empirically show that even a very slow growth rate is enough to match the quality of state-of-the-art methods, at a fraction of the computational cost.