From Bandits to Experts: On the Value of Side-Observations

TL;DR

This paper studies an adversarial online learning framework where side observations, represented by a graph, enhance decision-making, bridging the gap between full information and bandit feedback, with algorithms and bounds based on graph properties.

Contribution

It introduces algorithms with regret guarantees that leverage graph-structured side observations, extending the classical bandit and expert models.

Findings

Algorithms with provable regret bounds based on graph properties

Lower bounds that nearly match the upper bounds

Framework unifies bandit and expert feedback models

Abstract

We consider an adversarial online learning setting where a decision maker can choose an action in every stage of the game. In addition to observing the reward of the chosen action, the decision maker gets side observations on the reward he would have obtained had he chosen some of the other actions. The observation structure is encoded as a graph, where node i is linked to node j if sampling i provides information on the reward of j. This setting naturally interpolates between the well-known "experts" setting, where the decision maker can view all rewards, and the multi-armed bandits setting, where the decision maker can only view the reward of the chosen action. We develop practical algorithms with provable regret guarantees, which depend on non-trivial graph-theoretic properties of the information feedback structure. We also provide partially-matching lower bounds.