Dying Experts: Efficient Algorithms with Optimal Regret Bounds

TL;DR

This paper introduces the 'dying experts' model in online learning, providing optimal regret bounds and efficient algorithms for scenarios where experts can permanently become unavailable, advancing the understanding of adversarial expert advice settings.

Contribution

It defines the dying experts setting, derives matching regret bounds for known and unknown death orders, and develops efficient algorithms achieving these bounds.

Findings

Optimal regret bounds are established for both known and unknown expert death orders.

New efficient algorithms are proposed that match the theoretical regret bounds.

The study extends the sleeping experts framework by considering permanently unavailable experts.

Abstract

We study a variant of decision-theoretic online learning in which the set of experts that are available to Learner can shrink over time. This is a restricted version of the well-studied sleeping experts problem, itself a generalization of the fundamental game of prediction with expert advice. Similar to many works in this direction, our benchmark is the ranking regret. Various results suggest that achieving optimal regret in the fully adversarial sleeping experts problem is computationally hard. This motivates our relaxation where any expert that goes to sleep will never again wake up. We call this setting "dying experts" and study it in two different cases: the case where the learner knows the order in which the experts will die and the case where the learner does not. In both cases, we provide matching upper and lower bounds on the ranking regret in the fully adversarial setting. Furthermore, we present new, computationally efficient algorithms that obtain our optimal upper bounds.