Abstract: More than 50 years of development have made mixed integer programming (MIP) an extremely successful tool. MIP’s modeling flexibility allows it describe a wide range of business, engineering and scientific problems, and, while MIP is NP-hard, many of these problems are routinely solved in practice thanks to state-of-the-art solvers that nearly double their machine-independent speeds every year. In this talk we show how a careful application of MIP modeling techniques can lead to extremely effective MIP-based methods for three problems in machine learning and statistics.

The first problem concerns causal inference of treatment effects in observational studies [1]. For this problem we introduce a MIP-based matching method that directly balances covariates for multi-variate treatments and produces samples that are representative of a target population. We show how using the right MIP formulation for the problem is critical for large data sets, and illustrate the effectiveness of the resulting approach by estimating the effect that the different intensities of the 2010 Chilean earthquake had on educational outcomes. The second problem concerns the design of adaptive questionnaires for consumer preference elicitation [2]. For this problem we introduce an approximate Bayesian method for the design of the questionnaires, which can significantly reduce the variance of the estimates obtained for certain consumer preference parameters. We show how carefully modeling the associated question selection using MIP is crucial to achieving the required near-realtime selection of the next question asked to the consumer. The third problem concerns certifying that a trained neural network is robust to adversarial attacks [3]. For this problem we introduce strong MIP formulations that can significantly reduce the computational time needed to achieve the certification.

[1] Building Representative Matched Samples with Multi-valued Treatments in Large Observational Studies. M. Bennett, J. P. Vielma and J. R. Zubizarreta. Submitted for publication, 2019. arXiv:1810.06707

[2] Ellipsoidal methods for adaptive choice-based conjoint analysis. D. Saure and J. P. Vielma. Operations Research 67, 2019. pp. 295-597.

[3] Strong mixed-integer programming formulations for trained neural networks. R. Anderson, J. Huchette, C. Tjandraatmadja and J. P. Vielma. In A. Lodi and V. Nagarajan, editors, Proceedings of the 20th Conference on Integer Programming and Combinatorial Optimization (IPCO 2019), Lecture Notes in Computer Science 11480, 2019. pp. 27-42.

Bio:  Juan Pablo Vielma is the Richard S. Leghorn (1939) Career Development Associate Professor at MIT Sloan School of Management and is affiliated to MIT’s Operations Research Center. Dr. Vielma has a B.S. in Mathematical Engineering from University of Chile and a Ph.D. in Industrial Engineering from the Georgia Institute of Technology. His current research interests include the theory and practice of mixed-integer mathematical optimization and applications in energy, natural resource management, marketing and statistics. In January of 2017 he was named by President Obama as one of the recipients of the Presidential Early Career Award for Scientists and Engineers (PECASE). Some of his other recognitions include the NSF CAREER Award and the INFORMS Computing Society Prize. He is currently an associate editor for Operations Research and Operations Research Letters, a member of the board of directors of the INFORMS Computing Society, and a member of the NumFocus steering committee for JuMP.