The paper extends REMBO to multiple random embeddings modeled jointly by an index-conditioned product-kernel Gaussian process, but provides no empirical evidence that the method works.
High dimensional Bayesian Optimization via Condensing-Expansion Projection
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abstract
In high-dimensional settings, Bayesian optimization (BO) can be expensive and infeasible. The random embedding Bayesian optimization algorithm is commonly used to address high-dimensional BO challenges. However, this method relies on the effective subspace assumption on the optimization problem's objective function, which limits its applicability. In this paper, we introduce Condensing-Expansion Projection Bayesian optimization (CEPBO), a novel random projection-based approach for high-dimensional BO that does not reply on the effective subspace assumption. The approach is both simple to implement and highly practical. We present two algorithms based on different random projection matrices: the Gaussian projection matrix and the hashing projection matrix. Experimental results demonstrate that both algorithms outperform existing random embedding-based algorithms in most cases, achieving superior performance on high-dimensional BO problems. The code is available in \url{https://anonymous.4open.science/r/CEPBO-14429}.
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Adaptive Linear Embedding for Nonstationary High-Dimensional Optimization
The paper extends REMBO to multiple random embeddings modeled jointly by an index-conditioned product-kernel Gaussian process, but provides no empirical evidence that the method works.