Sample Complexity of Partition Identification using Multi-armed Bandits with Applications to Nested Monte Carlo
Fri, Nov 02, 2018 @ 02:00 AM - 03:00 PM
Ming Hsieh Department of Electrical and Computer Engineering
Conferences, Lectures, & Seminars
Speaker: Prof. Sandeep Juneja, TIFR, Mumbai, India
Talk Title: Sample Complexity of Partition Identification using multi-armed Bandits with Applications to Nested Monte Carlo
Series: Special/Joint CPS/CommNetS Seminar
Abstract: Given a vector of probability distributions, or arms, each of which can be sampled independently, we consider the problem of identifying the partition to which this vector belongs from a finitely partitioned universe of such vector of distributions. We study this as a pure exploration problem in multi-armed bandit settings and develop sample complexity bounds on the total mean number of samples required for identifying the correct partition with high probability. This framework subsumes well-studied problems in the literature such as finding the best arm or the best few arms. We consider distributions belonging to the single parameter exponential family and primarily consider partitions where the vector of means of arms lie either in a given set or its complement. The sets considered correspond to distributions where there exists a mean above a specified threshold, where the set is a half space and where either the set or its complement is convex. In all these settings, we characterize the lower bounds on mean number of samples for each arm. Further, we propose algorithms that can match these bounds asymptotically with decreasing probability of error. Applications of this framework may be diverse. We briefly discuss a few associated with nested Monte Carlo and its applications to finance.
Biography: Sandeep is a Professor and Dean at the School of Technology and Computer Science in Tata Institute of Fundamental Research in Mumbai. His research interests lie in applied probability including in mathematical finance, Monte Carlo methods, multi-armed bandit based sequential decision making, and game theoretic analysis of queues. He is currently on the editorial board of Stochastic Systems. Earlier he has been on editorial boards of Mathematics of Operations Research, Management Science and ACM TOMACS.
Host: Rahul Jain
Location: Hughes Aircraft Electrical Engineering Center (EEB) - 248
Audiences: Everyone Is Invited
Contact: Talyia White