Distribution-free Algorithms for Learning Enabled Optimization with Non-parametric Estimation

Shuotao Diao (sdiaousc.edu)
Suvrajeet Sen (suvrajesusc.edu)

Abstract: This paper studies a fusion of concepts from stochastic optimization and non-parametric statistical learning, in which data is available in the form of covariates interpreted as predictors and responses. Such models are designed to impart greater agility, allowing decisions under uncertainty to adapt to the knowledge of the predictors (leading indicators). Specialized algorithms can be looked upon as learning enabled optimization (LEO) algorithms. This paper focuses on equipping LEO with non-parametric estimation approaches (LEON) which provide asymptotically optimal decisions without requiring the specication of a distribution. In particular, our framework accommodates several non-parametric estimation schemes, including k nearest neighbors (kNN), and other standard kernel estimators under one unified framework. Several techniques to improve the quality of decisions are discussed. Finally, we demonstrate the computational performance of Robust LEON-kNN and Robust LEON-kernel for a well-known instance arising in logistics.

Keywords: mini-batch first-order method, stochastic quasi-gradient method, non-parametric statistical estimation, k-NN estimation, kernel estimation

Category 1: Stochastic Programming

Citation: Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles CA, 90089-0193, USA March 3rd, 2020

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Entry Submitted: 03/03/2020
Entry Accepted: 03/04/2020
Entry Last Modified: 06/07/2020

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