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.

翻译：本文首次对带上下文的顺序概率赋值问题进行平滑分析研究。我们研究了信息论意义上最优的极小极大速率，以及涉及最大似然估计预言机的算法归约框架。我们的方法建立了一个从平滑对抗者场景下顺序概率赋值的极小极大速率到直推学习极小极大速率的通用归约机制。这为参数类及有限VC维类实现了最优（对数）快速收敛速率。在算法层面，我们开发了一种能高效调用MLE预言机的算法，适用于一般函数类。研究表明，在一般条件下该算法方法可达到次线性遗憾值。