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Dynamic Data-Driven Estimation of Non-Parametric Choice Models

Nam Ho-Nguyen (hnh***at***andrew.cmu.edu)
Fatma Kilinc-Karzan (fkilinc***at***andrew.cmu.edu)

Abstract: We study non-parametric estimation of consumer choice models, which were introduced to alleviate unreasonable assumptions and issues of suboptimal model fit/selection present in traditional parametric models, and are prevalent in several application areas. Existing literature focuses only on the static observational setting where all of the observations are given upfront, and lacks both convergence guarantees and guarantees on model sparsity. As opposed to this, in this paper we focus on estimating a non-parametric choice model from observational data in a dynamic setting, where observations are obtained over time. We first describe a general convex-concave saddle-point (SP) joint estimation and optimization (JEO) problem, and provide a primal-dual framework for deriving algorithms to solve this problem based on online convex optimization. Our general framework allows us to suggest a variety of algorithms and examine their convergence guarantees in a unified way. We then describe how the choice model estimation problem can be cast as an SPJEO problem, which allows us to utilize our algorithms to solve these problems. In particular, by tailoring our JEO algorithms carefully to the choice model estimation problem, we can obtain provable convergence guarantees and explicit bounds on the sparsity of the estimated model. Our numerical experiments confirm the effectiveness of the algorithms derived from our framework.

Keywords: non-parametric choice, first-order methods, dynamic data, saddle point

Category 1: Applications -- OR and Management Sciences (Marketing )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation:

Download: [PDF]

Entry Submitted: 02/18/2017
Entry Accepted: 02/19/2017
Entry Last Modified: 07/28/2019

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