  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.
