ISR Seminar: "A Wasserstein Distance Approach for Concentration of Empirical Risk Estimates"

Thursday, February 9, 2023
1:00 p.m.
1146 A. V. Williams Bldg

ISR Seminar

A Wasserstein Distance Approach for Concentration of Empirical Risk Estimates

Speaker: Prashanth L.A.
Associate Professor, Department of Computer Science and Engineering
Indian Institute of Technology Madras

Hosts: Michael Fu (mfu@umd.edu) and Steve Marcus

Abstract
This talk presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper referenced below. The classes of risk measures introduced include as special cases well known risk measures from the finance literature such as conditional value at risk (CVaR), optimized certainty equivalent risk, spectral risk measures, utility-based shortfall risk, cumulative prospect theory (CPT) value, rank dependent expected utility and distorted risk measures.

Two estimation schemes are considered, one for each class of risk measures. One estimation scheme involves applying the risk measure to the empirical distribution function formed from a collection of i.i.d. samples of the random variable (r.v.), while the second scheme involves applying the same procedure to a truncated sample. The bounds provided apply to three popular classes of distributions, namely sub-Gaussian, sub-exponential and heavy-tailed distributions. The bounds are derived by first relating the estimation error to the Wasserstein distance between the true and empirical distributions, and then using recent concentration bounds for the latter. Previous concentration bounds are available only for specific risk measures such as CVaR and CPT-value.

The bounds derived are shown to either match or improve upon previous bounds in cases where they are available. The usefulness of the bounds is illustrated through an algorithm and the corresponding regret bound for a stochastic bandit problem involving a general risk measure from each of the two classes introduced in the paper referenced below.

Reference
Prashanth L.A. and Sanjay P. Bhat, A Wasserstein distance approach for concentration of empirical risk estimates, Journal of Machine Learning Research, vol. 23, no. 238, pp. 1-61, 2022.

Biography
Prashanth L.A. is an Associate Professor in the Department of Computer Science and Engineering at Indian Institute of Technology Madras. Prior to this, he was a postdoctoral researcher at the Institute for Systems Research, University of Maryland - College Park from 2015 to 2017 and at INRIA Lille - Team SequeL from 2012 to 2014. From 2002 to 2009, he was with Texas Instruments (India) Pvt Ltd, Bangalore, India.

He received his Masters and Ph.D degrees in Computer Science and Automation from Indian Institute of Science, in 2008 and 2013, respectively.  He was awarded the third prize for his Ph.D. dissertation, by the IEEE Intelligent Transportation Systems Society (ITSS). He is the coauthor of a book entitled `Stochastic Recursive Algorithms for Optimization: Simultaneous Perturbation Methods', published by Springer in 2013. His research interests are in reinforcement learning, simulation optimization and multi-armed bandits, with applications in transportation systems, wireless networks and recommendation systems.

Prashanth also is a former ISR postdoctoral researcher who worked with Steve Marcus and Michael Fu.

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