Abstract:  We consider the classical stochastic multi-armed bandit problem with constraints on the total switching cost and total inventory consumption. We prove matching upper and lower bounds on regret and provide near-optimal algorithms for this problem. Surprisingly, we discover phase transitions and cyclic phenomena of the optimal regret. That is, we show that associated with the inventory constrained multi-armed bandit problem, there are phases defined by the number of arms and switching costs, where the regret upper and lower bounds in each phase remains the same and drop significantly between phases. The results enable us to fully characterize the trade-off between regret and incurred switching cost in the stochastic inventory constrained multi-armed bandit problem, contributing new insights to this fundamental problem. Finally, we discover similar phenomena in a classical revenue management problem, the dynamic pricing model, where pre-existing offline data is applied to improve the online learning process.

Bio:  David Simchi-Levi is a Professor of Engineering Systems at MIT.  He is considered one of the premier thought leaders in supply chain management and business analytics.

His research focuses on developing and implementing robust and efficient techniques for operations management. He has published widely in professional journals on both practical and theoretical aspects of supply chain and revenue management.

His Ph.D. students have accepted faculty positions in leading academic institutes including U. of California Berkeley, Carnegie Mellon U., Columbia U., Cornell U., Duke U., Georgia Tech, Harvard U., U. of Illinois Urbana-Champaign, U. of Michigan, Purdue U. and Virginia Tech.

Professor Simchi-Levi co-authored the books Managing the Supply Chain (McGraw-Hill, 2004), the award winning Designing and Managing the Supply Chain (McGraw-Hill, 2007) and The Logic of Logistics (3^rd edition, Springer 2013). He also published Operations Rules: Delivering Customer Value through Flexible Operations (MIT Press, 2011).

Professor Simchi-Levi is the current Editor-in-Chief of Management Science, one of the two flagship journals of INFORMS. He served as the Editor-in-Chief for Operations Research (2006-2012), the other flagship journal of INFORMS and for Naval Research Logistics (2003-2005). He is an INFORMS Fellow, MSOM Distinguished Fellow and the recipient of the 2014 INFORMS Daniel H. Wagner Prize for Excellence in Operations Research Practice; 2014 INFORMS Revenue Management and Pricing Section Practice Award; 2009 INFORMS Revenue Management and Pricing Section Prize and Ford 2015 Engineering Excellence Award.

Professor Simchi-Levi has consulted and collaborated extensively with private and public organizations. He was the founder of LogicTools which provided software solutions and professional services for supply chain optimization. LogicTools became part of IBM in 2009. In 2012 he co-founded OPS Rules, an operations analytics consulting company. The company became part of Accenture in 2016.

In 2014, he co-founded Opalytics, a cloud analytics platform company focusing on operations and supply chain intelligence. The company became part of the Accenture Applied Intelligence in 2018.