Smoothed Analysis of Sequential Probability Assignment
This work addresses theoretical and algorithmic challenges in sequential prediction for smoothed adversaries, with incremental contributions to information theory and machine learning.
The paper tackles the sequential probability assignment problem with contexts by establishing a reduction from minimax rates for smoothed adversaries to transductive learning, achieving optimal logarithmic fast rates for parametric and finite VC dimension classes, and develops an algorithm using an MLE oracle that yields sublinear regret under general conditions.
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.