Coin Betting and Parameter-Free Online Learning
This work provides a unified approach for parameter-free online learning, which is incremental but simplifies algorithm design and improves efficiency for machine learning practitioners.
The paper tackles the problem of designing parameter-free algorithms for online linear optimization and learning with expert advice by introducing a framework based on coin betting, resulting in algorithms that require no tuning and achieve optimal regret bounds.
In the recent years, a number of parameter-free algorithms have been developed for online linear optimization over Hilbert spaces and for learning with expert advice. These algorithms achieve optimal regret bounds that depend on the unknown competitors, without having to tune the learning rates with oracle choices. We present a new intuitive framework to design parameter-free algorithms for \emph{both} online linear optimization over Hilbert spaces and for learning with expert advice, based on reductions to betting on outcomes of adversarial coins. We instantiate it using a betting algorithm based on the Krichevsky-Trofimov estimator. The resulting algorithms are simple, with no parameters to be tuned, and they improve or match previous results in terms of regret guarantee and per-round complexity.