Malhar A. Managoli

Malhar A. Managoli, Vinod M. Prabhakaran

We study adversarial binary hypothesis testing under memory constraints. The test is a time-invariant randomized finite state machine (FSM) with S states. Associated with each hypothesis is a set of distributions. Given the hypothesis, the distribution of each sample is chosen from the set associated with the hypothesis by an adversary who has access to past samples and the history of states of the FSM so far. We obtain upper and lower bounds on the minimax asymptotic probability of error as a function of S. The bounds have the same exponential behaviour in S and match for a class of problems.

Malhar A. Managoli, Vinod M. Prabhakaran, Suhas Diggavi

Federated learning with heterogeneous data and personalization has received significant recent attention. Separately, robustness to corrupted data in the context of federated learning has also been studied. In this paper we explore combining personalization for heterogeneous data with robustness, where a constant fraction of the clients are corrupted. Motivated by this broad problem, we formulate a simple instantiation which captures some of its difficulty. We focus on the specific problem of personalized mean estimation where the data is drawn from a Gaussian mixture model. We give an algorithm whose error depends almost linearly on the ratio of corrupted to uncorrupted samples, and show a lower bound with the same behavior, albeit with a gap of a constant factor.