Wei-Ting Tang

Wei-Ting Tang, Joel A. Paulson

Trust Region Bayesian Optimization (TuRBO) is an effective strategy for alleviating the curse of dimensionality in high-dimensional black-box optimization. However, inappropriate lengthscale design can cause the local Gaussian process (GP) model within the trust region to degenerate, leading to suboptimal performance in high dimensions. In this work, we show that TuRBO's local GP may remain either excessively complex or overly simple as the dimension $D$ and trust region side length $L$ vary. To address this issue, we propose a straightforward variant, AdaScale-TuRBO, which scales the GP lengthscale with both the problem dimension and trust region size, thereby preserving kernel geometry and maintaining consistent prior complexity. Empirically, we show that AdaScale-TuRBO can robustly outperform standard TuRBO and other popular high-dimensional BO methods on synthetic benchmarks and real-world trajectory planning tasks.

Wei-Ting Tang, Akshay Kudva, Calvin Tsay et al.

We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is challenging because it remains nonlinear and nonconvex. Existing exact deterministic approaches become increasingly difficult to scale as the number of training data points grows, leading to approximation-based methods that improve tractability by optimizing a modified (inexact) objective. In this work, we propose PALM-Mean, a piecewise-analytic lower-bounding framework embedded in reduced-space spatial branch-and-bound. At each node, kernel terms that are locally important are replaced by a sign-aware piecewise-linear relaxation in an appropriate scalar distance variable, while the remaining terms are bounded analytically in closed form. We show this hybrid approach yields a valid lower bound for the posterior mean, while limiting the size of the branch-and-bound subproblems. We establish validity of the node lower bounds and $\varepsilon$-global convergence of the resulting algorithm. Computational results on synthetic benchmarks and real-world application problems show that PALM-Mean improves scalability relative to representative general-purpose deterministic global solvers, particularly as the number of training data points increases.

Wei-Ting Tang, Joel A. Paulson

Bayesian optimization (BO) is a popular approach for optimizing expensive-to-evaluate black-box objective functions. An important challenge in BO is its application to high-dimensional search spaces due in large part to the curse of dimensionality. One way to overcome this challenge is to focus on local BO methods that aim to efficiently learn gradients, which have shown strong empirical performance on high-dimensional problems including policy search in reinforcement learning (RL). Current local BO methods assume access to only a single high-fidelity information source whereas, in many problems, one has access to multiple cheaper approximations of the objective. We propose a novel algorithm, Cost-Aware Gradient Entropy Search (CAGES), for local BO of multi-fidelity black-box functions. CAGES makes no assumption about the relationship between different information sources, making it more flexible than other multi-fidelity methods. It also employs a new information-theoretic acquisition function, which enables systematic identification of samples that maximize the information gain about the unknown gradient per evaluation cost. We demonstrate CAGES can achieve significant performance improvements compared to other state-of-the-art methods on synthetic and benchmark RL problems.

Akshay Kudva, Wei-Ting Tang, Joel A. Paulson

Designing modern industrial systems requires balancing several competing objectives, such as profitability, resilience, and sustainability, while accounting for complex interactions between technological, economic, and environmental factors. Multi-objective optimization (MOO) methods are commonly used to navigate these tradeoffs, but selecting the appropriate algorithm to tackle these problems is often unclear, particularly when system representations vary from fully equation-based (white-box) to entirely data-driven (black-box) models. While grey-box MOO methods attempt to bridge this gap, they typically impose rigid assumptions on system structure, requiring models to conform to the underlying structural assumptions of the solver rather than the solver adapting to the natural representation of the system of interest. In this chapter, we introduce a unifying approach to grey-box MOO by leveraging network representations, which provide a general and flexible framework for modeling interconnected systems as a series of function nodes that share various inputs and outputs. Specifically, we propose MOBONS, a novel Bayesian optimization-inspired algorithm that can efficiently optimize general function networks, including those with cyclic dependencies, enabling the modeling of feedback loops, recycle streams, and multi-scale simulations - features that existing methods fail to capture. Furthermore, MOBONS incorporates constraints, supports parallel evaluations, and preserves the sample efficiency of Bayesian optimization while leveraging network structure for improved scalability. We demonstrate the effectiveness of MOBONS through two case studies, including one related to sustainable process design. By enabling efficient MOO under general graph representations, MOBONS has the potential to significantly enhance the design of more profitable, resilient, and sustainable engineering systems.

Wei-Ting Tang, Akshay Kudva, Joel A. Paulson

Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a local BO method that targets the Newton step by jointly learning gradient and Hessian information with Gaussian process surrogates, and selecting evaluations via a one-step lookahead bound on Newton-step error. We show that this bound (and hence the step error) contracts with batch size, so NeST-BO directly inherits inexact-Newton convergence: global progress under mild stability assumptions and quadratic local rates once steps are sufficiently accurate. To scale, we optimize the acquisition in low-dimensional subspaces (e.g., random embeddings or learned sparse subspaces), reducing the dominant cost of learning curvature from $O(d^2)$ to $O(m^2)$ with $m \ll d$ while preserving step targeting. Across high-dimensional synthetic and real-world problems, including cases with thousands of variables and unknown active subspaces, NeST-BO consistently yields faster convergence and lower regret than state-of-the-art local and high-dimensional BO baselines.

Wei-Ting Tang, Ankush Chakrabarty, Joel A. Paulson

Novelty search (NS) refers to a class of exploration algorithms that seek to uncover diverse system behaviors through simulations or experiments. Such diversity is central to many AI-driven discovery and design tasks, including material and drug development, neural architecture search, and reinforcement learning. However, existing NS methods typically rely on evolutionary strategies and other meta-heuristics that require dense sampling of the input space, making them impractical for expensive black-box systems. In this work, we introduce BEACON, a sample-efficient, Bayesian optimization-inspired approach to NS that is tailored for settings where the input-to-behavior relationship is opaque and costly to evaluate. BEACON models this mapping using multi-output Gaussian processes (MOGPs) and selects new inputs by maximizing a novelty metric computed from posterior samples of the MOGP, effectively balancing the exploration-exploitation trade-off. By leveraging recent advances in posterior sampling and high-dimensional GP modeling, our method remains scalable to large input spaces and datasets. We evaluate BEACON across ten synthetic benchmarks and eight real-world tasks, including the design of diverse materials for clean energy applications. Our results show that BEACON significantly outperforms existing NS baselines, consistently discovering a broader set of behaviors under tight evaluation budgets.