Information theory for sequential decision-making

Abstract: Data-driven decision-making systems seamlessly integrate into every facet of our daily lives. Despite this ubiquity, the current era has also brought with it a host of emerging challenges such as the need to make good decisions in the presence of uncertainty (about the future and the environment) as well as the storage and processing of high-volume data to improve decision-making.

In this talk, I will discuss my research program, which takes an information-theoretic approach to modern problems arising in sequential decision-making. This approach will be illustrated via the example application of portfolio selection that leverages side-information/hints to make better decisions, and even with uncertainty about the future can achieve gain comparable to an omniscient investor with knowledge of the future.

In the path towards solving this problem, I will first revisit and expand upon the information-theoretic concept of universal probability. This approach gives us general principles and guidelines for assigning sequential probabilities to data (based on which a decision can then be made), and can be used to address concrete engineering applications in compression, prediction and estimation among others. I will then illustrate our new results on construction of universal probability assignments to solve the portfolio selection with side-information problem, as well as results in settings with a much more powerful adversary. Finally, I will conclude the talk with open problems and new directions I plan to address in future work.

Bio:

Alankrita Bhatt is a Center for the Mathematics of Information postdoctoral fellow, in the Computing and Mathematical Sciences department at Caltech. Before that, she was a research fellow at the Simons Institute for the Theory of Computing, UC Berkeley. She received a Ph.D. in Electrical Engineering as well as a M.S. in Statistics from UC San Diego, and a B.Tech. in Electrical Engineering from the Indian Institute of Technology Kanpur. Her research interests lie broadly at the intersection of information theory, statistics, and data science, with a recent focus on sequential decision-making.