Offline to Online Conversion
This work addresses a foundational challenge in machine learning for researchers and practitioners dealing with sequential prediction, though it appears incremental in nature.
The paper tackles the problem of converting offline estimators into online predictors with minimal additional regret, framing it as merging probability measures over finite strings into a measure over infinite sequences. It determines the computational complexity of online estimators with good guarantees as its main result.
We consider the problem of converting offline estimators into an online predictor or estimator with small extra regret. Formally this is the problem of merging a collection of probability measures over strings of length 1,2,3,... into a single probability measure over infinite sequences. We describe various approaches and their pros and cons on various examples. As a side-result we give an elementary non-heuristic purely combinatoric derivation of Turing's famous estimator. Our main technical contribution is to determine the computational complexity of online estimators with good guarantees in general.