Recent literature on dynamic pricing has focused on models where the market value of a product is linear in its observed features up to perturbation by market noise with some distribution $F_0$. Products are sold one at a time, and only a binary response recording the success or failure of the sale is observed. The seller's goal is to post future prices in order to minimize their regret.  The pricing algorithms in the realistic case where $F_0$ is unknown have hitherto proposed the estimation strategies using smoothing techniques which require parameter choices like a kernel and its bandwidth. To obviate such tuning parameter choices, we estimate $ F_0$ using the nonparametric MLE (NPMLE) under the constraint that $1-F_0$ is log-concave, an assumption that arises naturally in the dynamic pricing problem and implement a policy that achieves an attractive regret bound. In the process, we determine the uniform convergence rate of the NPMLE under log-concavity of $1-F_0$: namely,  $\sup_u|F(u)-\widehat{F}^{NPMLE}(u)|= \mathcal{O}((\log(n)/n)^{2/5})$, which may be of independent interest. This is joint work with Daniele Bracale and Yuekai Sun. 

Bio:  Moulinath Banerjee completed his bachelor's and master's in statistics at the Indian Statistical Institute in 1995 and 1997, respectively,^[1] then authored a doctoral dissertation, Likelihood Ratio Inference in Regular and Nonregular Problems in 2000, advised by Jon A. Wellner of the University of Washington.^[2]  He remained in Washington as a lecturer until joining the University of Michigan faculty in 2001.^[1]    His research interests comprise non-standard statistical models, shape-constrained methods, empirical process theory, distributed computing, learning across environments, and more recently, applications of OT at the statistics and machine learning interface. Apart from his statistical pursuits, he takes an avid interest in classical music, fine dining, literature, and philosophy, and together with a co-author has published a new translation of the Rubaiyat of Omar Khayyam from the original Persian. He is an elected fellow of both the ASA and the IMS, an IMS medallion lecture awardee for 2024, and the current editor of IMS's review journal, Statistical Science.