Prof. Ningyuan Chen
University of Toronto
Talk:
Allocating Divisible Resources on Arms with Unknown and Random Rewards
Abstract:
We consider a decision maker allocating one unit of renewable and divisible resource in each period on a number of arms. The arms have unknown and random rewards whose means are proportional to the allocated resource and whose variances are proportional to an order b of the allocated resource. In particular, if the decision maker allocates resource $A_i$ to arm $i$ in a period, then the reward $Y_i$ is $Yi(Ai)=A_i\mu_i+A_i^b \xi_i$, where $\mu_i$ is the unknown mean and the noise $\xi_i$ is independent and sub-Gaussian. When the order $b$ ranges from 0 to 1, the framework smoothly bridges the standard stochastic multi-armed bandit and online learning with full feedback. We design two algorithms that attain the optimal gap-dependent and gap-independent regret bounds for $b\in [0,1]$, and demonstrate a phase transition at $b=1/2$. The theoretical results hinge on a novel concentration inequality we have developed that bounds a linear combination of sub-Gaussian random variables whose weights are fractional, adapted to the filtration, and monotonic.
Biography:
Dr. Ningyuan Chen is currently an associate professor at the Department of Management at the University of Toronto, Mississauga and at the Rotman School of Management, University of Toronto. Before joining the University of Toronto, he was an assistant professor at the Hong Kong University of Science and Technology. Prior to that, he was a postdoctoral fellow at the Yale School of Management. He received his Ph.D. from the Industrial Engineering and Operations Research (IEOR) department at Columbia University in 2015. He is interested in various approaches to making data-driven decisions in business applications such as revenue management. His studies have been published in Management Science, Operations Research, Annals of Statistics, NeurIPS and other journals and proceedings. His research is supported by the UGC of Hong Kong and the Discovery Grants Program of Canada. He is the recipient of the Roger Martin Award for Excellence in Research and the IMI Research Award.
