Divide and Learn: A Divide and Conquer Approach for Predict+Optimize

TL;DR

This paper introduces a divide and conquer algorithm for the predict+optimize problem, enabling direct optimization of combinatorial problems without dynamic programming restrictions, improving performance on complex tasks.

Contribution

It presents a novel divide and conquer method for differentiable optimization in predict+optimize, extending beyond previous dynamic programming limitations.

Findings

Outperforms existing predict+optimize methods on complex problems

The greedy version achieves similar results with less computation

Successfully tackles hard combinatorial problems

Abstract

The predict+optimize problem combines machine learning ofproblem coefficients with a combinatorial optimization prob-lem that uses the predicted coefficients. While this problemcan be solved in two separate stages, it is better to directlyminimize the optimization loss. However, this requires dif-ferentiating through a discrete, non-differentiable combina-torial function. Most existing approaches use some form ofsurrogate gradient. Demirovicet alshowed how to directlyexpress the loss of the optimization problem in terms of thepredicted coefficients as a piece-wise linear function. How-ever, their approach is restricted to optimization problemswith a dynamic programming formulation. In this work wepropose a novel divide and conquer algorithm to tackle op-timization problems without this restriction and predict itscoefficients using the optimization loss. We also introduce agreedy version of this approach, which achieves similar re-sults with less computation. We compare our approach withother approaches to the predict+optimize problem and showwe can successfully tackle some hard combinatorial problemsbetter than other predict+optimize methods.