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Workshop on Cognition and Control

Relative value iteration for controlled diffusions
Vivek Borkar
Professor Vivek Borkar received his Ph.D. in Electrical Engineering and Computer Sciences from the University of California, Berkeley, in 1980. He was with Technische Hogeschool Twente, Holland, 1980-81, and Tata Institute of Fundamental Research, Bangalore Centre, 1982-89. He currently is with the Indian Institute of Science, Department of Computer Science and Automation. His interests include stochastic control, stochastic recursive algorithms and adaptive and learning systems.
This talk will describe some recent work on the continuous time and state space counterpart of the classical relative value iteration algorithm for average cost control of Markov chains. This leads to a  quasi-linear parabolic equation whose well-posedness is analyzed. Under suitable stability assumptions, the convergence of its solution to the solution of the Hamilton-Jacobi-Bellman equation of ergodic control can be established using results from the theory of monotone dynamical systems or reverse martingales. Extensions to zero-sum stochastic differential games and their implications to relative value iteration for infinite horizon risk-sensitive control will also be discussed. Extension of the main result to near-monotone cost functions under relaxed stability requirements will be mentioned. This is joint work with Prof. Ari Arapostathis of University of Texas at Austin and Prof. K. Suresh Kumar of Indian Institute of Technology, Mumbai.
February 23
9:00 am
Larsen 234

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