Seminar on control theory
Wednesday, 24 January, 2.30-3.30
Venue: Room 105, Dept. of Mathematics
Host: Sudhir Ghorpade
Speaker: Chandrajit Bajaj
Affiliation: University of Texas at Austin, USA
Title: Optimized Decision-Making via Active Learning of Stochastic Hamiltonians
Abstract: A Hamiltonian represents the energy of a dynamical system in phase space with coordinates of position and momentum. Hamilton’s equations of motion are obtainable as coupled symplectic differential equations. In this talk, I shall show how optimized decision-making (action sequences) can be obtained via a reinforcement learning problem wherein the agent interacts with the unknown environment to simultaneously learn a Hamiltonian surrogate and the optimal action sequences using Hamilton dynamics, by invoking the Pontryagin Maximum Principle. We use optimal control theory to define an optimal control gradient flow, which guides the reinforcement learning process of the agent to progressively optimize the Hamiltonian while simultaneously converging to the optimal action sequence. Extensions to stochastic Hamiltonians leading to stochastic action sequences and the free-energy principle shall also be discussed.
This is joint work with Taemin Heo, Minh Nguyen
Brief Bio: Professor Chandrajit Bajaj is a Computational Applied Mathematics Chair in Visualization at the Department of Computer Science and the Oden Institute of Computational Engineering and Sciences at the University of Texas at Austin, USA. He is a Fellow of AAAS, ACM. IEEE and SIAM. More information about him is available at: http://www.cs.utexas.edu/~bajaj
Probability and Statistics seminar
Wednesday, 24 January, 3.00-4.00 pm
Venue: Ramanujan Hall
Speaker: Hira Koul
Affiliation: Professor, Department of Statistics and Probability, Michigan State University
Distinguished Visiting Professor, Department of Mathematics, IIT Bombay
Title: A signed-rank estimator in nonlinear regression models when covariates and errors are dependent
Abstract: This talk will describe the asymptotic uniform linearity of a signed rank statistic of the residuals in a class of nonlinear parametric regression models when regression errors are possibly dependent on the covariates. This result is used to prove the asymptotic normality of a signed rank estimator of the regression parameter vector in the given nonlinear regression model where covariates and regression errors are dependent. The latter result in turn is used to derive the asymptotic distribution of this signed rank estimator in the errors in variables linear regression model. The asymptotic relative efficiency of this SR estimator relative to the bias-corrected least squares estimator is shown to increase to infinity, as the measurement error variance increases to infinity, thereby establishing another robustness property of this estimator.
Venue: Ramanujan Hall
Host: Sudhir R Ghorpade
Speaker: S K Jain
Affiliation: Ohio University, Athens, OH, USA
DATE: Wednesday, January 24 at 4 pm.