Online Learning for Changing Environments using Coin Betting
This addresses the problem of slow adaptation in online learning for applications like expert advice and metric learning, representing an incremental advance with specific performance gains.
The paper tackles the challenge of online learning algorithms adapting to changing environments by introducing a new meta algorithm that improves strongly-adaptive regret by a factor of √log(T) and achieves a first-order bound for the first time, with empirical results showing it outperforms state-of-the-art methods.
A key challenge in online learning is that classical algorithms can be slow to adapt to changing environments. Recent studies have proposed "meta" algorithms that convert any online learning algorithm to one that is adaptive to changing environments, where the adaptivity is analyzed in a quantity called the strongly-adaptive regret. This paper describes a new meta algorithm that has a strongly-adaptive regret bound that is a factor of $\sqrt{\log(T)}$ better than other algorithms with the same time complexity, where $T$ is the time horizon. We also extend our algorithm to achieve a first-order (i.e., dependent on the observed losses) strongly-adaptive regret bound for the first time, to our knowledge. At its heart is a new parameter-free algorithm for the learning with expert advice (LEA) problem in which experts sometimes do not output advice for consecutive time steps (i.e., \emph{sleeping} experts). This algorithm is derived by a reduction from optimal algorithms for the so-called coin betting problem. Empirical results show that our algorithm outperforms state-of-the-art methods in both learning with expert advice and metric learning scenarios.