arXiv subjects

Vivek F. Farias

Publications and source records attributed to Vivek F. Farias.

21 records · Page 2Linked to original sources

arXiv2011

A Nonparametric Approach to Modeling Choice with Limited Data

A central push in operations models over the last decade has been the incorporation of models of customer choice. Real world implementations of many of these models face the formidable stumbling block of simply identifying the `right' model of choice to use. Thus motivated, we visit the following problem: For a `generic' model of consumer choice (namely, distributions over preference lists) and a limited amount of data on how consumers actually make decisions (such as marginal information about these distributions), how may one predict revenues from offering a particular assortment of choices? We present a framework to answer such questions and design a number of tractable algorithms from a data and computational standpoint for the same. This paper thus takes a significant step towards `automating' the crucial task of choice model selection in the context of operational decision problems.

stat.AP↗

arXiv2009

Universal Reinforcement Learning

We consider an agent interacting with an unmodeled environment. At each time, the agent makes an observation, takes an action, and incurs a cost. Its actions can influence future observations and costs. The goal is to minimize the long-term average cost. We propose a novel algorithm, known as the active LZ algorithm, for optimal control based on ideas from the Lempel-Ziv scheme for universal data compression and prediction. We establish that, under the active LZ algorithm, if there exists an integer $K$ such that the future is conditionally independent of the past given a window of $K$ consecutive actions and observations, then the average cost converges to the optimum. Experimental results involving the game of Rock-Paper-Scissors illustrate merits of the algorithm.

cs.IT↗

arXiv2008

Stochastic Depletion Problems: Effective Myopic Policies for a class of Dynamic Optimization Problems

This paper presents a general class of dynamic stochastic optimization problems we refer to as Stochastic Depletion Problems. A number of challenging dynamic optimization problems of practical interest are stochastic depletion problems. Optimal solutions for such problems are difficult to obtain, both from a pragmatic computational perspective as also from a theoretical perspective. As such, simple heuristics are highly desirable. We isolate two simple properties that, if satisfied by a problem within this class, guarantee that a myopic policy incurs a performance loss of at most 50 % relative to the optimal adaptive control policy for that problem. We are able to verify that these two properties are satisfied for several interesting families of stochastic depletion problems and as a consequence identify efficient near-optimal control policies for a number of interesting dynamic stochastic optimization problems.

math.OC↗