Decentralized High-Dimensional Bayesian Optimization with Factor Graphs
This work addresses scalability and efficiency issues in high-dimensional optimization for machine learning practitioners, representing an incremental improvement over existing HBO algorithms.
The paper tackles the challenge of high-dimensional Bayesian optimization by introducing a decentralized algorithm that exploits interdependent input effects without requiring low-dimensional assumptions, achieving superior performance over state-of-the-art methods in experiments with up to 1811 hyperparameters.
This paper presents a novel decentralized high-dimensional Bayesian optimization (DEC-HBO) algorithm that, in contrast to existing HBO algorithms, can exploit the interdependent effects of various input components on the output of the unknown objective function f for boosting the BO performance and still preserve scalability in the number of input dimensions without requiring prior knowledge or the existence of a low (effective) dimension of the input space. To realize this, we propose a sparse yet rich factor graph representation of f to be exploited for designing an acquisition function that can be similarly represented by a sparse factor graph and hence be efficiently optimized in a decentralized manner using distributed message passing. Despite richly characterizing the interdependent effects of the input components on the output of f with a factor graph, DEC-HBO can still guarantee no-regret performance asymptotically. Empirical evaluation on synthetic and real-world experiments (e.g., sparse Gaussian process model with 1811 hyperparameters) shows that DEC-HBO outperforms the state-of-the-art HBO algorithms.