One Arrow, Two Kills: An Unified Framework for Achieving Optimal Regret Guarantees in Sleeping Bandits

TL;DR

This paper introduces a unified framework for sleeping bandits, proposing a new internal regret measure, an algorithm with sublinear regret, and extending results to dueling bandits, with empirical validation.

Contribution

It unifies various notions of regret in sleeping bandits, introduces a new internal regret concept, and extends the framework to dueling bandits with stochastic preferences.

Findings

Proposed an algorithm with sublinear regret in adversarial sleeping bandits.

Established low internal regret implies low external and policy regret.

Extended results to sleeping dueling bandits with empirical validation.

Abstract

We address the problem of \emph{`Internal Regret'} in \emph{Sleeping Bandits} in the fully adversarial setup, as well as draw connections between different existing notions of sleeping regrets in the multiarmed bandits (MAB) literature and consequently analyze the implications: Our first contribution is to propose the new notion of \emph{Internal Regret} for sleeping MAB. We then proposed an algorithm that yields sublinear regret in that measure, even for a completely adversarial sequence of losses and availabilities. We further show that a low sleeping internal regret always implies a low external regret, and as well as a low policy regret for iid sequence of losses. The main contribution of this work precisely lies in unifying different notions of existing regret in sleeping bandits and understand the implication of one to another. Finally, we also extend our results to the setting of \emph{Dueling Bandits} (DB)--a preference feedback variant of MAB, and proposed a reduction to MAB idea to design a low regret algorithm for sleeping dueling bandits with stochastic preferences and adversarial availabilities. The efficacy of our algorithms is justified through empirical evaluations.