Somnath Pradhan (IISER Bhopal)

Department Colloquium

Speaker: Somnath Pradhan (IISER Bhopal)

Title: Stochastic Control under Model Uncertainty: Robustness, Approximation, and Learning

Abstract: Mathematical models of stochastic systems are rarely exact: model parameters must be estimated, continuous dynamics are often discretized for computation, and the noise driving the system may itself be an approximation. These issues raise a fundamental question in stochastic control: how sensitive are optimal decisions to errors in the underlying model?

In this talk, we examine this question from several mathematical perspectives. We first consider controlled diffusion processes and study the continuity of optimal values and the performance of policies designed using approximate models. We then discuss the approximation of continuous-time control problems by discrete-time Markov decision processes, highlighting the role of suitable topologies on policy spaces in establishing near-optimality for structured policies. Next, we examine stochastic systems driven by approximations of Brownian motion, where rough path theory provides a natural framework for establishing the stability of controlled dynamics and optimal decisions.

Finally, we explore the connection with learning-based control, where the underlying model is inferred from data rather than known a priori. This leads to broader questions concerning the interaction between statistical estimation, optimization, and model robustness. This talk is based on joint work with Prof. Serdar Yuksel.