An Analysis of the Value of Information when Exploring Stochastic, Discrete Multi-Armed Bandits

TL;DR

This paper introduces an information-theoretic exploration strategy for stochastic multi-armed bandits that optimally balances exploration and exploitation, achieving logarithmic regret through a simulated-annealing-like parameter update.

Contribution

It proposes a novel exploration strategy based on the value of information criterion that guarantees optimal regret in stochastic multi-armed bandits.

Findings

Achieves logarithmic regret with a proper cooling schedule.

Balances exploration and exploitation effectively.

Demonstrates the effectiveness through theoretical analysis.

Abstract

In this paper, we propose an information-theoretic exploration strategy for stochastic, discrete multi-armed bandits that achieves optimal regret. Our strategy is based on the value of information criterion. This criterion measures the trade-off between policy information and obtainable rewards. High amounts of policy information are associated with exploration-dominant searches of the space and yield high rewards. Low amounts of policy information favor the exploitation of existing knowledge. Information, in this criterion, is quantified by a parameter that can be varied during search. We demonstrate that a simulated-annealing-like update of this parameter, with a sufficiently fast cooling schedule, leads to an optimal regret that is logarithmic with respect to the number of episodes.