A machine learning approach to optimization

Abstract: Most applications in engineering, operations research and finance rely on solving the same optimization problem several times with varying parameters. This method generates a large amount of data that is usually discarded. In this talk, we describe how to use historical data to understand and solve optimization problems. We present a machine learning approach to predict the strategy behind the optimal solution of continuous and mixed-integer convex optimization problems. Using interpretable algorithms such as optimal classification trees we gain insights on the relationship between the problem data and the optimal solution. In this way, optimization is no longer a black-box and practitioners can understand it. Moreover, our method is able to compute the optimal solutions at very high speed. This applies also to non-interpretable machine learning predictors such as neural networks since they can be evaluated very efficiently. We benchmark our approach on several examples obtaining accuracy above 90% and computation times multiple orders of magnitude faster than state-of-the-art solvers. Therefore, our method provides on the one hand a novel insightful understanding of the optimal strategies to solve a broad class of continuous and mixed-integer optimization problems and on the other hand a powerful computational tool to solve online optimization at very high speed.

algebraic topologycombinatoricsinformation theorymetric geometrynumerical analysisoptimization and controlstatistics theory

Audience: researchers in the topic

Mathematics of Data and Decisions @ Davis

Series comments: Description: Mathematical aspects of data science and decision-making

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