Contextual Information-Directed Sampling

Abstract

Information-directed sampling (IDS) has recently demonstrated its potential as a dataefficient reinforcement learning algorithm (Lu et al., 2021). However, it is still unclear what is the right form of information ratio to optimize when contextual information is available. We investigate the IDS design through two contextual bandit problems: contextual bandits with graph feedback and sparse linear contextual bandits. We provably demonstrate the advantage of contextual IDS over conditional IDS and emphasize the importance of considering the context distribution. The main message is that an intelligent agent should invest more on the actions that are beneficial for the future unseen contexts while the conditional IDS can be myopic. We further propose a computationallyefficient version of contextual IDS based on Actor-Critic and evaluate it empirically on a neural network contextual bandit.

A Definition of Non-Stationary Bandits

“…An information ratio is the ratio between the squared instantaneous regret and an information gain. Various information ratios have been proposed in the literature [4,6,9,11,13,17,19,20,21].…”