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The predict+optimize problem combines machine learning ofproblem coefficientswith a combinatorial optimization prob-lem that uses the predictedcoefficients. While this problemcan be solved in two separate stages, it isbetter to directlyminimize the optimization loss. However, this requiresdif-ferentiating through a discrete, non-differentiable combina-torialfunction. Most existing approaches use some form ofsurrogate gradient.Demirovicet alshowed how to directlyexpress the loss of the optimizationproblem in terms of thepredicted coefficients as a piece-wise linear function.How-ever, their approach is restricted to optimization problemswith a dynamicprogramming formulation. In this work wepropose a novel divide and conqueralgorithm to tackle op-timization problems without this restriction and predictitscoefficients using the optimization loss. We also introduce agreedy versionof this approach, which achieves similar re-sults with less computation. Wecompare our approach withother approaches to the predict+optimize problem andshowwe can successfully tackle some hard combinatorial problemsbetter thanother predict+optimize methods.

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