Optimistic Information Directed Sampling
This provides a more robust algorithmic framework for contextual bandits, addressing a bottleneck in combining Bayesian and worst-case theories, though it is incremental in bridging existing lines of work.
The paper tackles the problem of online learning in contextual bandit problems with parametric loss functions by proposing Optimistic Information-Directed Sampling, which achieves instance-dependent regret guarantees similar to Bayesian methods without requiring Bayesian assumptions.
We study the problem of online learning in contextual bandit problems where the loss function is assumed to belong to a known parametric function class. We propose a new analytic framework for this setting that bridges the Bayesian theory of information-directed sampling due to Russo and Van Roy (2018) and the worst-case theory of Foster, Kakade, Qian, and Rakhlin (2021) based on the decision-estimation coefficient. Drawing from both lines of work, we propose a algorithmic template called Optimistic Information-Directed Sampling and show that it can achieve instance-dependent regret guarantees similar to the ones achievable by the classic Bayesian IDS method, but with the major advantage of not requiring any Bayesian assumptions. The key technical innovation of our analysis is introducing an optimistic surrogate model for the regret and using it to define a frequentist version of the Information Ratio of Russo and Van Roy (2018), and a less conservative version of the Decision Estimation Coefficient of Foster et al. (2021). Keywords: Contextual bandits, information-directed sampling, decision estimation coefficient, first-order regret bounds.