Stat Colloquium (Virtual): Dr. Debabrota Basu

Title: When privacy meets partial information: Privacy-utility trade-offs in sequential testing and learning problems

Abstract: Bandits act as an archetypal model of sequential learning and extension of sequential testing, where one has limited information regarding the utilities of a set of decisions and can know more about the utility of a decision only by choosing it. The goal of a bandit algorithm is either (a) to maximise the total accumulated utility over a given number of interactions, or (b) to find the decision with maximal utility through minimal number of interactions. As bandits are progressively used for data-sensitive applications, such as designing adaptive clinical trials, recommender systems etc., it is imperative to ensure data privacy of these algorithms. Motivated by this concern, we study the impact of preserving Differential Privacy (DP) in bandits with different goals (both (a) and (b)). Specifically, we answer three questions:

i. How to define Differential Privacy (DP) in bandits as both the input and output are generated progressively through past data-driven interactions?
ii. What are the changes in the fundamental hardness of bandits problems (both (a) and (b)) if we ensure ε-Differential Privacy?
iii. How to modify the existing bandit algorithms (both (a) and (b)) to simultaneously ensure ε-Differential Privacy and achieve optimal performance?
Our study yields new information-theoretic quantities and a generic algorithm demonstrating that in most of the cases, ε-Differential Privacy can be achieved almost for free in bandits and also in sequentially probability ratio tests (SPRTs).

The talk is based on the works: https://arxiv.org/abs/2505.05613, https://arxiv.org/abs/2406.06408, and https://arxiv.org/abs/2508.06377v2.