Self-adapting Robustness in Demand Learning

40 Pages Posted: 17 Dec 2020

See all articles by Boxiao Chen

Boxiao Chen

University of Illinois at Chicago - College of Business Administration

Selvaprabu Nadarajah

University of Illinois at Chicago - College of Business Administration

Parshan Pakiman

University of Illinois at Chicago - College of Business Administration

Stefanus Jasin

University of Michigan, Stephen M. Ross School of Business

Date Written: November 20, 2020

Abstract

We study dynamic pricing over a finite number of periods in the presence of demand model ambiguity. Departing from the typical no-regret learning environment, where price changes are allowed at any time, pricing decisions are made at pre-specified points in time and each price can be applied to a large number of arrivals. In this environment, which arises in retailing, a pricing decision based on an incorrect demand model can significantly impact cumulative revenue. We develop an adaptively-robust-learning (ARL) pricing policy that learns the true model parameters from the data while actively managing demand model ambiguity. It optimizes an objective that is robust with respect to a self-adapting set of demand models, where a given model is included in this set only if the sales data revealed from prior pricing decisions makes it ``probable''. As a result, it gracefully transitions from being robust when demand model ambiguity is high to minimizing regret when this ambiguity diminishes upon receiving more data. We characterize the stochastic behavior of ARL's self-adapting ambiguity sets and derive a regret bound that highlights the link between the scale of revenue loss and the customer arrival pattern. We also show that ARL, by being conscious of both model ambiguity and revenue, bridges the gap between a distributionally robust policy and a follow-the-leader policy, which focus on model ambiguity and revenue, respectively. We numerically find that the ARL policy, or its extension thereof, exhibits superior performance compared to distributionally robust, follow-the-leader, and upper-confidence-bound policies in terms of expected revenue and/or value at risk.

Keywords: dynamic pricing, demand learning, self-adapting algorithm, robust optimization, risk management, regret minimization

JEL Classification: C18, M37, C44

Suggested Citation

Chen, Boxiao and Nadarajah, Selvaprabu and Pakiman, Parshan and Jasin, Stefanus, Self-adapting Robustness in Demand Learning (November 20, 2020). Available at SSRN: https://ssrn.com/abstract=3734591 or http://dx.doi.org/10.2139/ssrn.3734591

Boxiao Chen

University of Illinois at Chicago - College of Business Administration ( email )

601 S Morgan St
Chicago, IL 60607
United States

Selvaprabu Nadarajah (Contact Author)

University of Illinois at Chicago - College of Business Administration ( email )

601 South Morgan Street
Chicago, IL 60607
United States

Parshan Pakiman

University of Illinois at Chicago - College of Business Administration ( email )

1200 W Harrison St
Chicago, IL 60607
United States

HOME PAGE: http://parshanpakiman.github.io/homepage/

Stefanus Jasin

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

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