Decentralized High-Dimensional Bayesian Optimization with Factor Graphs

TL;DR

This paper introduces DEC-HBO, a decentralized Bayesian optimization method that efficiently handles high-dimensional problems by exploiting interdependencies via factor graphs, achieving scalability and improved performance.

Contribution

It proposes a novel factor graph-based representation for high-dimensional Bayesian optimization that enables decentralized, scalable, and effective optimization without prior dimension reduction.

Findings

DEC-HBO outperforms existing HBO algorithms in experiments.

The method scales to problems with over 1800 hyperparameters.

It guarantees asymptotic no-regret performance.

Abstract

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.