Smoothed Analysis of Sequential Probability Assignment
Abstract
We initiate the study of smoothed analysis for the sequential probability assignment problem with contexts. We study information-theoretically optimal minmax rates as well as a framework for algorithmic reduction involving the maximum likelihood estimator oracle. Our approach establishes a general-purpose reduction from minimax rates for sequential probability assignment for smoothed adversaries to minimax rates for transductive learning. This leads to optimal (logarithmic) fast rates for parametric classes and classes with finite VC dimension. On the algorithmic front, we develop an algorithm that efficiently taps into the MLE oracle, for general classes of functions. We show that under general conditions this algorithmic approach yields sublinear regret.
Cite
@article{arxiv.2303.04845,
title = {Smoothed Analysis of Sequential Probability Assignment},
author = {Alankrita Bhatt and Nika Haghtalab and Abhishek Shetty},
journal= {arXiv preprint arXiv:2303.04845},
year = {2023}
}