CAM Colloquium - José Luis Montiel Olea, Department of Economics, Cornell University

Description

Title: ϵ-Minimax Solutions of Statistical Decision Problems via the Hedge Algorithm

joint with Andres Aradillas Fernandez (Cornell), José Blanchet (Stanford), Chen Qiu (Cornell), Jorg Stoye (Cornell), Lezhi Tan (Stanford).

Abstract: We present an algorithm for obtaining ϵ-minimax solutions of statistical decision problems. We are interested in problems where i) the statistician is allowed to choose randomly among I decision rules, and ii) the statistical model may have a parameter space with infinitely many elements. The minimax solution of these problems admits a convex programming representation over the (I − 1)-simplex, and the algorithm suggested herein to obtain an ϵ-approximation of the minimax solution is a version of mirror subgradient descent, initialized with uniform weights and stopped after a finite number of iterations. The resulting iterative procedure is known in the computer science literature as the Hedge algorithm (a particular case of the Multiplicative Weights update method) and it is used in algorithmic game theory as a practical tool to find approximate solutions of two-person zero-sum games. We apply the suggested algorithm to different minimax problems in the econometrics literature. An empirical application to the problem of optimally selecting sites to maximize the external validity of an experimental policy evaluation illustrates the usefulness of the suggested procedure.

Bio: José Luis Montiel Olea is an Associate Professor at Cornell University's Department of Economics and the Louis Salvatore '92 Faculty Leadership Fellow in the College of Arts and Sciences. His research interests lie broadly in Econometrics (theoretical and applied), Machine Learning, Time Series, and Statistical Decision Theory. He received a Ph.D. in Economics from Harvard University in 2013. His advisers were Gary Chamberlain, Tomasz Strzalecki, and Matias Cattaneo. After graduation, he spent three years (2013-2016) as Assistant Professor at New York University's Department of Economics. Before moving to Cornell, he was an Assistant Professor at Columbia University's Department of Economics for six years (2016-2022).

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