In many real-world bandit learning problems, the underlying environment evolves over time, requiring decision-makers to continually acquire information and adapt their action selection accordingly. In this talk, I study Bayesian formulations of nonstationary bandit problems, where environmental dynamics are modeled as stochastic processes, and develop an information-theoretic framework for analyzing attainable performance.

Our analysis yields generic regret upper bounds that extend classical results from stationary Bayesian bandits to nonstationary settings. A key insight is that the entropy rate of the optimal action process naturally quantifies the intrinsic difficulty introduced by nonstationarity. I further connect our results to existing frequentist analyses of nonstationary bandits, showing that several well-known regret bounds in the literature can be recovered as special cases within our unified framework.