High dimensional Bayesian Optimization Algorithm for Complex System in Time Series

TL;DR

This paper introduces a novel high-dimensional Bayesian optimization algorithm tailored for complex time-series models, incorporating dimension reduction, innovative sampling strategies, and local search to enhance solution accuracy.

Contribution

It presents a new high-dimensional Bayesian optimization method that integrates dimension reduction, multi-armed bandit sampling, and local search, addressing limitations of existing algorithms.

Findings

Achieves high-quality solutions in high-dimensional time-series optimization.

Outperforms existing methods in computational experiments.

Demonstrates effectiveness in complex control models.

Abstract

At present, high-dimensional global optimization problems with time-series models have received much attention from engineering fields. Since it was proposed, Bayesian optimization has quickly become a popular and promising approach for solving global optimization problems. However, the standard Bayesian optimization algorithm is insufficient to solving the global optimal solution when the model is high-dimensional. Hence, this paper presents a novel high dimensional Bayesian optimization algorithm by considering dimension reduction and different dimension fill-in strategies. Most existing literature about Bayesian optimization algorithms did not discuss the sampling strategies to optimize the acquisition function. This study proposed a new sampling method based on both the multi-armed bandit and random search methods while optimizing the acquisition function. Besides, based on the time-dependent or dimension-dependent characteristics of the model, the proposed algorithm can reduce the dimension evenly. Then, five different dimension fill-in strategies were discussed and compared in this study. Finally, to increase the final accuracy of the optimal solution, the proposed algorithm adds a local search based on a series of Adam-based steps at the final stage. Our computational experiments demonstrated that the proposed Bayesian optimization algorithm could achieve reasonable solutions with excellent performances for high dimensional global optimization problems with a time-series optimal control model.