Divide and Learn: A Divide and Conquer Approach for Predict+Optimize
This work provides a new method for researchers and practitioners working on predict+optimize problems, especially for combinatorial optimization problems that lack dynamic programming formulations.
This paper addresses the predict+optimize problem, where machine learning predicts coefficients for a combinatorial optimization problem. The authors propose a novel divide and conquer algorithm, along with a greedy variant, to minimize the optimization loss directly, outperforming other predict+optimize methods on hard combinatorial problems.
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.