BOBA: Dynamic Bayesian Optimization through Bayesian Active Inference
Authors: Merlin Angel Kelly, Rishan Patel, Alexander Thomas, Ziyue Zhu, Zikun Quan, Tom Carlson, Youngjun Cho
Organizations: Department of Computer Science UCL Aspire Create University College London · Department of Electronic and Electrical Engineering University College London · UCL Aspire Create University College London
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.
Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying, expensive, noisy black-box function f. However, most of the asymptotic guarantees offered by TVBO algorithms rely on the assumption that observations are acquired at a constant frequency. As the GP inference complexity scales with the cube of its dataset size, this assumption is unrealistic in the long run. In this paper, we relax this assumption and derive the first upper regret bound that explicitly accounts for changes in the observations sampling frequency. Based on this analysis, we formulate practical recommendations about dataset sizes and stale data policies of TVBO algorithms. We illustrate how an algorithm (BOLT) that follows these recommendations performs better than the state-of-the-art of TVBO through experiments on synthetic and real-world problems.
Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose STAGE-BO, Sequential Targeting Adaptive Gap-Filling ε-Constraint Bayesian Optimization: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in ε-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.
This paper presents a general acceleration mechanism for multi-objective Bayesian optimisation (MOBO) that leverages Gaussian process predictive gradients as auxiliary signals. Rather than replacing existing Pareto-compliant acquisition functions, the proposed approach augments them with local stationarity information derived from surrogate-derived gradients, enabling faster convergence toward the global Pareto set under limited evaluation budgets. Two catalyst instantiations are investigated: an adaptive Multiple-Gradient Descent Algorithm-Based Catalyst (MGDA) and a predefined-weight variant that enables focused exploration when budgets are tight. Experiments on the DTLZ benchmark suite (using 2 objectives and 10 decision variables) show that predictive gradient catalysis can deliver significant acceleration compared to other acquisition functions (EHVI, AugTch, tMPoI, SAF) when surrogates are accurate, particularly for stationary problems.