Empirical Bound Information-Directed Sampling for Norm-Agnostic Bandits

Information-directed sampling (IDS) is a powerful framework for solving bandit problems which has shown strong results in both Bayesian and frequentist settings. However, frequentist IDS, like many other bandit algorithms, requires that one have prior knowledge of a (relatively) tight upper bound on the norm of the true parameter vector governing the reward model in order to achieve good performance. Unfortunately, this requirement is rarely satisfied in practice. As we demonstrate, using a poorly calibrated bound can lead to significant regret accumulation. To address this issue, we introduce a novel frequentist IDS algorithm that iteratively refines a high-probability upper bound on the true parameter norm using accumulating data. We focus on the linear bandit setting with heteroskedastic subgaussian noise. Our method leverages a mixture of relevant information gain criteria to balance exploration aimed at tightening the estimated parameter norm bound and directly searching for the optimal action. We establish regret bounds for our algorithm that do not depend on an initially assumed parameter norm bound and demonstrate that our method outperforms state-of-the-art IDS and UCB algorithms.

Bayesian Transfer Learning

Transfer learning is a burgeoning concept in statistical machine learning that seeks to improve inference and/or predictive accuracy on a domain of interest by leveraging data from related domains. While the term "transfer learning" has garnered much recent interest, its foundational principles have existed for years under various guises. Prior literature reviews in computer science and electrical engineering have sought to bring these ideas into focus, primarily surveying general methodologies and works from these disciplines. This article highlights Bayesian approaches to transfer learning, which have received relatively limited attention despite their innate compatibility with the notion of drawing upon prior knowledge to guide new learning tasks. Our survey encompasses a wide range of Bayesian transfer learning frameworks applicable to a variety of practical settings. We discuss how these methods address the problem of finding the optimal information to transfer between domains, which is a central question in transfer learning. We illustrate the utility of Bayesian transfer learning methods via a simulation study where we compare performance against frequentist competitors.