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

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.

Entropy

References in corpus (2)

• Guided Policy Exploration for Markov Decision Processes using an Uncertainty-Based Value-of-Information Criterion
• Analysis of Agent Expertise in Ms. Pac-Man using Value-of-Information-based Policies

Cited by in corpus (4)

• Guided Policy Exploration for Markov Decision Processes using an Uncertainty-Based Value-of-Information Criterion
• Analysis of Agent Expertise in Ms. Pac-Man using Value-of-Information-based Policies
• Reduction of Markov Chains using a Value-of-Information-Based Approach
• An Information-Theoretic Approach for Automatically Determining the Number of States when Aggregating Markov Chains