Two-timescale Stochastic Approximation, Random Topology and their connections to Reinforcement Learning and Data Analysis

Location: ECE, Golden Jubilee Hall

Title: Two-timescale Stochastic Approximation, Random Topology and their connections to  Reinforcement Learning and Data Analysis
Speaker: Gugan Thoppe, Duke University, Durham, USA
Date: Monday – 29th  April ,2019

Time: (3:45 Tea) 4:00 – 5:00 PM

Venue: ECE, Golden Jubilee Hall (Talk will also be available on Skype)


The first part of the talk concerns Stochastic Approximation (SA). SA is quite natural in reinforcement learning, adaptive control, etc. and refers to the class of iterative methods that are useful for computing the zeroes or optima of a function if one has access to only its noisy measurements. When you are about to run a SA method, a foremost question of concern is that of stepsize choice. We shall provide a definitive answer to this question in the context of linear two-timescale SA—a subclass that includes methods mimicking nested loops. Specifically, we shall derive a tight convergence rate estimate and see how the stepsize choice influences it. The second part of the talk concerns Random Topology (RT). This is the study of quantifiers useful for characterizing the shape of random spaces. Imagine you are interested in knowing the topology of an unknown space and you are given samples from it. One approach would be to place discs of a suitable radius centred at each of these data points and study the topology of their union. Clearly, the estimation quality would crucially depend on the radius choice. To overcome this, an alternative approach is to look at the Persistence Diagram (PD), i.e., a record of the changes in the topology of the union of discs as their common radius is increased from 0 to infinity. In this talk, we shall discuss the properties of a PD and its connections to minimal spanning acycles, the generalizations of MST, and also study its behaviour in randomized settings.

Gugan Thoppe is a Postdoctoral Associate at the Duke University, USA with Prof. Sayan Mukherjee. Earlier, he worked with Prof. Robert Adler as an EC Senior Researcher (postdoc) at Technion, Israel. He did his PhD in Systems Science with Prof. Vivek Borkar at TIFR, India. His work won the TAA-Sasken best thesis award for 2017. He is also a two-time recipient of the IBM PhD fellowship award (2013–14 and 2014-15). His research interests include random topology and stochastic approximation.


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