Bayesian optimization (BO) is a class of popular methods for expensive black-box optimization, and has been widely applied to many scenarios. However, BO suffers from the curse of dimensionality, and scaling it to high-dimensional problems is still a challenge. In this paper, we propose a variable selection method MCTS-VS based on Monte Carlo tree search (MCTS), to iteratively select and optimize a subset of variables. That is, MCTS-VS constructs a low-dimensional subspace via MCTS and optimizes in the subspace with any BO algorithm. We give a theoretical analysis of the general variable selection method to reveal how it can work. Experiments on high-dimensional synthetic functions and real-world problems (e.g., MuJoCo locomotion tasks) show that MCTS-VS equipped with a proper BO optimizer can achieve state-of-the-art performance.

Bayesian Optimization (BO), guided by Gaussian process (GP) surrogates, has proven to be an invaluable technique for efficient, high-dimensional, black-box optimization, a critical problem inherent to many applications such as industrial design and scientific computing. Recent contributions have introduced reinforcement learning (RL) to improve the optimization performance on both single function optimization and \textit{few-shot} multi-objective optimization. However, even few-shot techniques fail to exploit similarities shared between closely related objectives. In this paper, we combine recent developments in Deep Kernel Learning (DKL) and attention-based Transformer models to improve the modeling powers of GP surrogates with meta-learning. We propose a novel method for improving meta-learning BO surrogates by incorporating attention mechanisms into DKL, empowering the surrogates to adapt to contextual information gathered during the BO process. We combine this Transformer Deep Kernel with a learned acquisition function trained with continuous Soft Actor-Critic Reinforcement Learning to aid in exploration. This Reinforced Transformer Deep Kernel (RTDK-BO) approach yields state-of-the-art results in continuous high-dimensional optimization problems.

Bayesian Optimization has become the reference method for the global optimization of black box, expensive and possibly noisy functions. Bayesian Op-timization learns a probabilistic model about the objective function, usually a Gaussian Process, and builds, depending on its mean and variance, an acquisition function whose optimizer yields the new evaluation point, leading to update the probabilistic surrogate model. Despite its sample efficiency, Bayesian Optimiza-tion does not scale well with the dimensions of the problem. The optimization of the acquisition function has received less attention because its computational cost is usually considered negligible compared to that of the evaluation of the objec-tive function. Its efficient optimization is often inhibited, particularly in high di-mensional problems, by multiple extrema. In this paper we leverage the addition-ality of the objective function into mapping both the kernel and the acquisition function of the Bayesian Optimization in lower dimensional subspaces. This ap-proach makes more efficient the learning/updating of the probabilistic surrogate model and allows an efficient optimization of the acquisition function. Experi-mental results are presented for real-life application, that is the control of pumps in urban water distribution systems.

Bayesian optimization (BO) has been broadly applied to computational expensive problems, but it is still challenging to extend BO to high dimensions. Existing works are usually under strict assumption of an additive or a linear embedding structure for objective functions. This paper directly introduces a supervised dimension reduction method, Sliced Inverse Regression (SIR), to high dimensional Bayesian optimization, which could effectively learn the intrinsic sub-structure of objective function during the optimization. Furthermore, a kernel trick is developed to reduce computational complexity and learn nonlinear subset of the unknowing function when applying SIR to extremely high dimensional BO. We present several computational benefits and derive theoretical regret bounds of our algorithm. Extensive experiments on synthetic examples and two real applications demonstrate the superiority of our algorithms for high dimensional Bayesian optimization.

Scaling Bayesian optimization to high dimensions is challenging task as the global optimization of high-dimensional acquisition function can be expensive and often infeasible. Existing methods depend either on limited active variables or the additive form of the objective function. We propose a new method for high-dimensional Bayesian optimization, that uses a dropout strategy to optimize only a subset of variables at each iteration. We derive theoretical bounds for the regret and show how it can inform the derivation of our algorithm. We demonstrate the efficacy of our algorithms for optimization on two benchmark functions and two real-world applications- training cascade classifiers and optimizing alloy composition.