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On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

Chin Pang Ho (c.ho12***at***imperial.ac.uk)
Grani Hanasusanto (grani.hanasusanto***at***utexas.edu)

Abstract: We consider generic stochastic optimization problems in the presence of side information which enables a more insightful decision. The side information constitutes observable exogenous covariates that alter the conditional probability distribution of the random problem parameters. A decision maker who adapts her decisions according to the observed side information solves an optimization problem where the objective function is specified by the conditional expectation of the random cost. If the joint probability distribution is unknown then the conditional expectation can be approximated in a data-driven manner using the Nadaraya-Watson (NW) kernel regression. While the emerging approximation scheme has found successful applications in diverse decision problems under uncertainty, it is largely unknown whether the scheme can provide any reasonable out-of-sample performance guarantees. In this paper, we establish guarantees for the generic problems by leveraging techniques from moderate deviations theory. The new theoretical result motivates the design of an effective regularization scheme via empirical conditional standard deviation. We highlight the performance of the regularized NW approximation through an example in portfolio management.

Keywords: stochastic optimization; side information; Nadaraya-Watson estimator; moderate deviation principles; large deviation principles

Category 1: Stochastic Programming

Citation: Working paper

Download: [PDF]

Entry Submitted: 01/23/2019
Entry Accepted: 01/23/2019
Entry Last Modified: 03/24/2019

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