Learning The Best Expert Efficiently

TL;DR

This paper introduces a lazy online subgradient algorithm that efficiently achieves minimal regret comparable to the best expert in various regimes, surpassing traditional regret bounds in easy cases.

Contribution

It presents a novel lazy online subgradient method that attains minimal regret in easy regimes while maintaining worst-case guarantees, and identifies regimes where minimal regret strategies are feasible.

Findings

Lazy online subgradient algorithm achieves minimal regret in easy regimes.

The method retains $O( oot n)$ worst-case regret guarantees.

Minimal regret strategies exist for certain hard regimes.

Abstract

We consider online learning problems where the aim is to achieve regret which is efficient in the sense that it is the same order as the lowest regret amongst K experts. This is a substantially stronger requirement that achieving $O(\sqrt{n})$ or $O(\log n)$ regret with respect to the best expert and standard algorithms are insufficient, even in easy cases where the regrets of the available actions are very different from one another. We show that a particular lazy form of the online subgradient algorithm can be used to achieve minimal regret in a number of "easy" regimes while retaining an $O(\sqrt{n})$ worst-case regret guarantee. We also show that for certain classes of problem minimal regret strategies exist for some of the remaining "hard" regimes.