CobBO: Coordinate Backoff Bayesian Optimization with Two-Stage Kernels
This work addresses computational inefficiency in high-dimensional Bayesian optimization, an incremental improvement for researchers and practitioners in fields like hyperparameter tuning and simulation-based optimization.
The paper tackles the challenge of Bayesian optimization becoming computationally prohibitive in high dimensions by introducing CobBO, a method that uses two-stage kernels and coordinate backoff to reduce computational burden while maintaining or improving solution quality, achieving comparable or better results than state-of-the-art methods across dimensions from tens to hundreds.
Bayesian optimization is a popular method for optimizing expensive black-box functions. Yet it oftentimes struggles in high dimensions where the computation could be prohibitively heavy. To alleviate this problem, we introduce Coordinate backoff Bayesian Optimization (CobBO) with two-stage kernels. During each round, the first stage uses a simple coarse kernel that sacrifices the approximation accuracy for computational efficiency. It captures the global landscape by purposely smoothing away local fluctuations. Then, in the second stage of the same round, past observed points in the full space are projected to the selected subspace to form virtual points. These virtual points, along with the means and variances of their unknown function values estimated using the simple kernel of the first stage, are fitted to a more sophisticated kernel model in the second stage. Within the selected low dimensional subspace, the computational cost of conducting Bayesian optimization therein becomes affordable. To further enhance the performance, a sequence of consecutive observations in the same subspace are collected, which can effectively refine the approximation of the function. This refinement lasts until a stopping rule is met determining when to back off from a certain subspace and switch to another. This decoupling significantly reduces the computational burden in high dimensions, which fully leverages the observations in the whole space rather than only relying on observations in each coordinate subspace. Extensive evaluations show that CobBO finds solutions comparable to or better than other state-of-the-art methods for dimensions ranging from tens to hundreds, while reducing both the trial complexity and computational costs.