Recent work reported that simple Bayesian optimization methods perform well for high-dimensional real-world tasks, seemingly contradicting prior work and tribal knowledge. This paper investigates the 'why'. We identify fundamental challenges that arise in high-dimensional Bayesian optimization and explain why recent methods succeed. Our analysis shows that vanishing gradients caused by Gaussian process initialization schemes play a major role in the failures of high-dimensional Bayesian optimization and that methods that promote local search behaviors are better suited for the task. We find that maximum likelihood estimation of Gaussian process length scales suffices for state-of-the-art performance. Based on this, we propose a simple variant of maximum likelihood estimation called MSR that leverages these findings to achieve state-of-the-art performance on a comprehensive set of real-world applications. We also present targeted experiments to illustrate and confirm our findings.

In MOO, there is usually not a single optimal solution, but a range of so-called Pareto optimal or non-dominated Many real-world black-box optimization problems solutions with different trade-offs. A widely adopted approach have multiple conflicting objectives. Rather aims to search for a good representation of these than attempting to approximate the entire set of Pareto-optimal solutions by maximizing their hypervolume. Pareto-optimal solutions, interactive preference Two prominent methods stand out in this regard: ParEGO learning, i.e., optimization with a decision maker (Knowles, 2006), which employs random augmented Chebyshev in the loop, allows to focus the search on the scalarizations for optimization in each iteration, and most relevant subset. However, few previous studies expected hypervolume maximization (Yang et al., 2019; have exploited the fact that utility functions Daulton et al., 2020), which directly maximizes the hypervolume are usually monotonic.

In many real-world optimization problems, we have prior information about what objective function values are achievable. In this paper, we study the scenario that we have either exact knowledge of the minimum value or a, possibly inexact, lower bound on its value. We propose bound-aware Bayesian optimization (BABO), a Bayesian optimization method that uses a new surrogate model and acquisition function to utilize such prior information. We present SlogGP, a new surrogate model that incorporates bound information and adapts the Expected Improvement (EI) acquisition function accordingly. Empirical results on a variety of benchmarks demonstrate the benefit of taking prior information about the optimal value into account, and that the proposed approach significantly outperforms existing techniques. Furthermore, we notice that even in the absence of prior information on the bound, the proposed SlogGP surrogate model still performs better than the standard GP model in most cases, which we explain by its larger expressiveness.

Reinforcement learning in sparse-reward navigation environments with expensive and limited interactions is challenging and poses a need for effective exploration. Motivated by complex navigation tasks that require real-world training (when cheap simulators are not available), we consider an agent that faces an unknown distribution of environments and must decide on an exploration strategy. It may leverage a series of training environments to improve its policy before it is evaluated in a test environment drawn from the same environment distribution. Most existing approaches focus on fixed exploration strategies, while the few that view exploration as a meta-optimization problem tend to ignore the need for cost-efficient exploration. We propose a cost-aware Bayesian optimization approach that efficiently searches over a class of dynamic subgoal-based exploration strategies. The algorithm adjusts a variety of levers -- the locations of the subgoals, the length of each episode, and the number of replications per trial -- in order to overcome the challenges of sparse rewards, expensive interactions, and noise. An experimental evaluation demonstrates that the new approach outperforms existing baselines across a number of problem domains. We also provide a theoretical foundation and prove that the method asymptotically identifies a near-optimal subgoal design.

Impactful applications such as materials discovery, hardware design, neural architecture search, or portfolio optimization require optimizing high-dimensional black-box functions with mixed and combinatorial input spaces. While Bayesian optimization has recently made significant progress in solving such problems, an in-depth analysis reveals that the current state-of-the-art methods are not reliable. Their performances degrade substantially when the unknown optima of the function do not have a certain structure. To fill the need for a reliable algorithm for combinatorial and mixed spaces, this paper proposes Bounce that relies on a novel map of various variable types into nested embeddings of increasing dimensionality. Comprehensive experiments show that Bounce reliably achieves and often even improves upon state-of-the-art performance on a variety of high-dimensional problems.

Recent advances have extended the scope of Bayesian optimization (BO) to expensive-to-evaluate black-box functions with dozens of dimensions, aspiring to unlock impactful applications, for example, in the life sciences, neural architecture search, and robotics. However, a closer examination reveals that the state-of-the-art methods for high-dimensional Bayesian optimization (HDBO) suffer from degrading performance as the number of dimensions increases or even risk failure if certain unverifiable assumptions are not met. This paper proposes BAxUS that leverages a novel family of nested random subspaces to adapt the space it optimizes over to the problem. This ensures high performance while removing the risk of failure, which we assert via theoretical guarantees. A comprehensive evaluation demonstrates that BAxUS achieves better results than the state-of-the-art methods for a broad set of applications.

We consider Bayesian methods for multi-information source optimization (MISO), in which we seek to optimize an expensive-to-evaluate black-box objective function while also accessing cheaper but biased and noisy approximations ("information sources"). We present a novel algorithm that outperforms the state of the art for this problem by using a Gaussian process covariance kernel better suited to MISO than those used by previous approaches, and an acquisition function based on a one-step optimality analysis supported by efficient parallelization. We also provide a novel technique to guarantee the asymptotic quality of the solution provided by this algorithm. Experimental evaluations demonstrate that this algorithm consistently finds designs of higher value at less cost than previous approaches. Papers published at the Neural Information Processing Systems Conference.

Bayesian optimization has recently emerged as a popular method for the sample-efficient optimization of expensive black-box functions. However, the application to high-dimensional problems with several thousand observations remains challenging, and on difficult problems Bayesian optimization is often not competitive with other paradigms. In this paper we take the view that this is due to the implicit homogeneity of the global probabilistic models and an overemphasized exploration that results from global acquisition. This motivates the design of a local probabilistic approach for global optimization of large-scale high-dimensional problems. We propose the $\texttt{TuRBO}$ algorithm that fits a collection of local models and performs a principled global allocation of samples across these models via an implicit bandit approach. A comprehensive evaluation demonstrates that $\texttt{TuRBO}$ outperforms state-of-the-art methods from machine learning and operations research on problems spanning reinforcement learning, robotics, and the natural sciences.

Bayesian optimization is a powerful tool for expensive stochastic black-box optimization problems such as simulation-based optimization or machine learning hyperparameter tuning. Many stochastic objective functions implicitly require a random number seed as input. By explicitly reusing a seed a user can exploit common random numbers, comparing two or more inputs under the same randomly generated scenario, such as a common customer stream in a job shop problem, or the same random partition of training data into training and validation set for a machine learning algorithm. With the aim of finding an input with the best average performance over infinitely many seeds, we propose a novel Gaussian process model that jointly models both the output for each seed and the average. We then introduce the Knowledge gradient for Common Random Numbers that iteratively determines a combination of input and random seed to evaluate the objective and automatically trades off reusing old seeds and querying new seeds, thus overcoming the need to evaluate inputs in batches or measuring differences of pairs as suggested in previous methods. We investigate the Knowledge Gradient for Common Random Numbers both theoretically and empirically, finding it achieves significant performance improvements with only moderate added computational cost.

The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly evaluations pose challenges for current techniques in discrete optimization and machine learning, and critically require new algorithmic ideas (NIPS BayesOpt 2017). This article proposes, to the best of our knowledge, the first algorithm to overcome these challenges, based on an adaptive, scalable model that identifies useful combinatorial structure even when data is scarce. Our acquisition function pioneers the use of semidefinite programming to achieve efficiency and scalability. Experimental evaluations demonstrate that this algorithm consistently outperforms other methods from combinatorial and Bayesian optimization.