BOBA: Dynamic Bayesian Optimization through Bayesian Active Inference

Dynamic black-box optimization presents significant challenges for Bayesian Optimization (BO), as the objective function evolves over time, causing optimal locations to shift continuously. Existing dynamic BO (DBO) methods using standard acquisition functions such as Upper Confidence Bound (UCB) fail to explicitly account for temporal variations, leading to suboptimal sample allocation and poor tracking of moving optima. Here, we propose BOBA (Bayesian Optimization through Bayesian Active Inference), a novel acquisition function inspired by free energy principles from active inference that explicitly minimizes predictive uncertainty about future states in dynamic environments. BOBA extends traditional acquisition functions by incorporating a forward-looking uncertainty quantification that estimates uncertainty in function changes, enabling more informed exploration-exploitation trade-offs in non-stationary settings. We evaluate BOBA on synthetic dynamic benchmarks, comparing against state-of-the-art DBO methods. Our experiments demonstrate that BOBA significantly improves regret in query-restricted settings, while remaining competitive in time-limited settings. We further analyze variants of BOBA with different exploration strategies, showing how the exploration-exploitation balance can be tuned for different types of dynamic functions. This work contributes both a free energy-based acquisition function for DBO and insights into how active inference principles can enhance optimization in non-stationary environments, with implications for real-time applications requiring continuous adaptation.