arXiv subjects

Szu Hui Ng

Publications and source records attributed to Szu Hui Ng.

15 recordsLinked to original sources

arXiv2026

Local Constrained Bayesian Optimization

Bayesian optimization (BO) for high-dimensional constrained problems remains a significant challenge due to the curse of dimensionality. We propose Local Constrained Bayesian Optimization (LCBO), a novel framework tailored for such settings. Unlike trust-region methods that are prone to premature shrinking when confronting tight or complex constraints, LCBO leverages the differentiable landscape of constraint-penalized surrogates to alternate between rapid local descent and uncertainty-driven exploration. Theoretically, we prove that LCBO achieves a convergence rate for the Karush-Kuhn-Tucker (KKT) residual that depends polynomially on the dimension $d$ for common kernels under mild assumptions, offering a rigorous alternative to global BO where regret bounds typically scale exponentially. Extensive evaluations on high-dimensional benchmarks (up to 100D) demonstrate that LCBO consistently outperforms state-of-the-art baselines.

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arXiv2026

Improving Bayesian Optimization via Training-Aware Conditional Diffusion Models

Bayesian optimization (BO) is a widely used approach for black-box optimization that uses a Gaussian process (GP) as a surrogate and guides sequential evaluations via an acquisition function, with the ultimate goal of locating the global optimum $\mathbf{x}^{\star}$. To align with this goal, information-based acquisition functions such as Predictive Entropy Search (PES) model $\mathbf{x}^{\star}$ as a random variable and reduce the entropy of its distribution, but approximating this distribution via traditional GP posterior sampling is computationally expensive. To address this limitation, we leverage Conditional Diffusion Models (CDMs) to efficiently approximate the distribution of $\mathbf{x}^{\star}$ and develop BO-inherent training strategies for CDMs. Motivated by the structural properties of the CDM-learned distribution, we further develop an acquisition strategy termed Diffusion-based Mode Seeking (DMS) to guide the sequential evaluation. We establish a sub-optimality guarantee for the CDM-learned distribution and demonstrate through extensive experiments that DMS outperforms standard BO baselines.

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arXiv2026

Convergence Rates of Constrained Expected Improvement

Constrained Bayesian optimization (CBO) methods have seen significant success in black-box optimization with constraints. One of the most commonly used CBO methods is the constrained expected improvement (CEI) algorithm. CEI is a natural extension of expected improvement (EI) when constraints are incorporated. However, the theoretical convergence rate of CEI has not been established. In this work, we study the convergence rate of CEI by analyzing its simple regret upper bound. First, we show that when the objective function $f$ and constraint function $c$ are assumed to each lie in a reproducing kernel Hilbert space (RKHS), CEI achieves the convergence rates of $\mathcal{O} \left(t^{-\frac{1}{2}}\log^{\frac{d+1}{2}}(t) \right) \ \text{and }\ \mathcal{O}\left(t^{\frac{-ν}{2ν+d}} \log^{\fracν{2ν+d}}(t)\right)$ for the commonly used squared exponential and Matérn kernels ($ν>\frac{1}{2}$), respectively. Second, we show that when $f$ is assumed to be sampled from Gaussian processes (GPs), CEI achieves similar convergence rates with a high probability. Numerical experiments are performed to validate the theoretical analysis.

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arXiv2025

Bayesian Optimization with Expected Improvement: No Regret and the Choice of Incumbent

Expected improvement (EI) is one of the most widely used acquisition functions in Bayesian optimization (BO). Despite its proven empirical success in applications, the cumulative regret upper bound of EI remains an open question. In this paper, we analyze the classic noisy Gaussian process expected improvement (GP-EI) algorithm. We consider the Bayesian setting, where the objective is a sample from a GP. Three commonly used incumbents, namely the best posterior mean incumbent (BPMI), the best sampled posterior mean incumbent (BSPMI), and the best observation incumbent (BOI) are considered as the choices of the current best value in GP-EI. We present for the first time the cumulative regret upper bounds of GP-EI with BPMI and BSPMI. Importantly, we show that in both cases, GP-EI is a no-regret algorithm for both squared exponential (SE) and Matérn kernels. Further, we present for the first time that GP-EI with BOI either achieves a sublinear cumulative regret upper bound or has a fast converging noisy simple regret bound for SE and Matérn kernels. Our results provide theoretical guidance to the choice of incumbent when practitioners apply GP-EI in the noisy setting. Numerical experiments are conducted to validate our findings.

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arXiv2025

An Online Non-Stationary Simulation Optimization Approach Based on Regime Switching

Dynamic and evolving operational and economic environments present significant challenges for decision-making. We explore a simulation optimization problem characterized by non-stationary input distributions with regime-switching dynamics across sequential decision stages. This problem encompasses both prediction uncertainty, arising from the regime-switching behavior of input distributions, and input uncertainty, resulting from parameter estimation for these distributions and their dynamics using finite data streams. To address these uncertainties, we develop a Bayesian framework that approximates the true objective function using a Markov Switching Model (MSM). We rigorously validate this approximation by establishing the consistency and asymptotic normality of the objective functions and optimal solutions. To solve the problem in an online fashion, we propose a metamodel-based algorithm that leverages simulation results from previous stages to enhance decision-making. Furthermore, we tackle scenarios with an unknown number of regimes through a Bayesian nonparametric method. Numerical experiments demonstrate that our algorithm achieves superior performance and robust adaptability.

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arXiv2025

A Trajectory-Based Bayesian Approach to Multi-Objective Hyperparameter Optimization with Epoch-Aware Trade-Offs

Training machine learning models inherently involves a resource-intensive and noisy iterative learning procedure that allows epoch-wise monitoring of the model performance. However, the insights gained from the iterative learning procedure typically remain underutilized in multi-objective hyperparameter optimization scenarios. Despite the limited research in this area, existing methods commonly identify the trade-offs only at the end of model training, overlooking the fact that trade-offs can emerge at earlier epochs in cases such as overfitting. To bridge this gap, we propose an enhanced multi-objective hyperparameter optimization problem that treats the number of training epochs as a decision variable, rather than merely an auxiliary parameter, to account for trade-offs at an earlier training stage. To solve this problem and accommodate its iterative learning, we then present a trajectory-based multi-objective Bayesian optimization algorithm characterized by two features: 1) a novel acquisition function that captures the improvement along the predictive trajectory of model performances over epochs for any hyperparameter setting and 2) a multi-objective early stopping mechanism that determines when to terminate the training to maximize epoch efficiency. Experiments on synthetic simulations and hyperparameter tuning benchmarks demonstrate that our algorithm can effectively identify the desirable trade-offs while improving tuning efficiency.

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arXiv2025

Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Models

Gaussian Process (GP) models are widely utilized as surrogate models in scientific and engineering fields. However, standard GP models are limited to continuous variables due to the difficulties in establishing correlation structures for categorical variables. To overcome this limitati on, we introduce WEighted Euclidean distance matrices Gaussian Process (WEGP). WEGP constructs the kernel function for each categorical input by estimating the Euclidean distance matrix (EDM) among all categorical choices of this input. The EDM is represented as a linear combination of several predefined base EDMs, each scaled by a positive weight. The weights, along with other kernel hyperparameters, are inferred using a fully Bayesian framework. We analyze the predictive performance of WEGP theoretically. Numerical experiments validate the accuracy of our GP model, and by WEGP, into Bayesian Optimization (BO), we achieve superior performance on both synthetic and real-world optimization problems.

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arXiv2024

Adjusted Expected Improvement for Cumulative Regret Minimization in Noisy Bayesian Optimization

The expected improvement (EI) is one of the most popular acquisition functions for Bayesian optimization (BO) and has demonstrated good empirical performances in many applications for the minimization of simple regret. However, under the evaluation metric of cumulative regret, the performance of EI may not be competitive, and its existing theoretical regret upper bound still has room for improvement. To adapt the EI for better performance under cumulative regret, we introduce a novel quantity called the evaluation cost which is compared against the acquisition function, and with this, develop the expected improvement-cost (EIC) algorithm. In each iteration of EIC, a new point with the largest acquisition function value is sampled, only if that value exceeds its evaluation cost. If none meets this criteria, the current best point is resampled. This evaluation cost quantifies the potential downside of sampling a point, which is important under the cumulative regret metric as the objective function value in every iteration affects the performance measure. We establish in theory a high-probability regret upper bound of EIC based on the maximum information gain, which is tighter than the bound of existing EI-based algorithms. It is also comparable to the regret bound of other popular BO algorithms such as Thompson sampling (GP-TS) and upper confidence bound (GP-UCB). We further perform experiments to illustrate the improvement of EIC over several popular BO algorithms.

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arXiv2024

Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimization

Local Bayesian optimization is a promising practical approach to solve the high dimensional black-box function optimization problem. Among them is the approximated gradient class of methods, which implements a strategy similar to gradient descent. These methods have achieved good experimental results and theoretical guarantees. However, given the distributional properties of the Gaussian processes applied on these methods, there may be potential to further exploit the information of the Gaussian processes to facilitate the BO search. In this work, we develop the relationship between the steps of the gradient descent method and one that minimizes the Upper Confidence Bound (UCB), and show that the latter can be a better strategy than direct gradient descent when a Gaussian process is applied as a surrogate. Through this insight, we propose a new local Bayesian optimization algorithm, MinUCB, which replaces the gradient descent step with minimizing UCB in GIBO. We further show that MinUCB maintains a similar convergence rate with GIBO. We then improve the acquisition function of MinUCB further through a look ahead strategy, and obtain a more efficient algorithm LA-MinUCB. We apply our algorithms on different synthetic and real-world functions, and the results show the effectiveness of our method. Our algorithms also illustrate improvements on local search strategies from an upper bound perspective in Bayesian optimization, and provides a new direction for future algorithm design.

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arXiv2024

A Data-Driven Bayesian Nonparametric Approach for Black-Box Optimization

We present a data-driven Bayesian nonparametric approach for global optimization (DaBNO) of stochastic black-box function. The function value depends on the distribution of a random vector. However, this distribution is usually complex and hardly known in practice, and is often inferred from data (realizations of random vectors). The DaBNO accounts for the finite-data error that arises when estimating the distribution and relaxes the commonly-used parametric assumption to reduce the distribution-misspecified error. We show that the DaBNO objective formulation can converge to the true objective asymptotically. We further develop a surrogate-assisted algorithm DaBNO-K to efficiently optimize the proposed objective function based on a carefully designed kernel. Numerical experiments are conducted with several synthetic and practical problems, demonstrating the empirical global convergence of this algorithm and its finite-sample performance.

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arXiv2023

A Novel Framework for Improving the Breakdown Point of Robust Regression Algorithms

We present an effective framework for improving the breakdown point of robust regression algorithms. Robust regression has attracted widespread attention due to the ubiquity of outliers, which significantly affect the estimation results. However, many existing robust least-squares regression algorithms suffer from a low breakdown point, as they become stuck around local optima when facing severe attacks. By expanding on the previous work, we propose a novel framework that enhances the breakdown point of these algorithms by inserting a prior distribution in each iteration step, and adjusting the prior distribution according to historical information. We apply this framework to a specific algorithm and derive the consistent robust regression algorithm with iterative local search (CORALS). The relationship between CORALS and momentum gradient descent is described, and a detailed proof of the theoretical convergence of CORALS is presented. Finally, we demonstrate that the breakdown point of CORALS is indeed higher than that of the algorithm from which it is derived. We apply the proposed framework to other robust algorithms, and show that the improved algorithms achieve better results than the original algorithms, indicating the effectiveness of the proposed framework.

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arXiv2022

A model aggregation approach for high-dimensional large-scale optimization

Bayesian optimization (BO) has been widely used in machine learning and simulation optimization. With the increase in computational resources and storage capacities in these fields, high-dimensional and large-scale problems are becoming increasingly common. In this study, we propose a model aggregation method in the Bayesian optimization (MamBO) algorithm for efficiently solving high-dimensional large-scale optimization problems. MamBO uses a combination of subsampling and subspace embeddings to collectively address high dimensionality and large-scale issues; in addition, a model aggregation method is employed to address the surrogate model uncertainty issue that arises when embedding is applied. This surrogate model uncertainty issue is largely ignored in the embedding literature and practice, and it is exacerbated when the problem is high-dimensional and data are limited. Our proposed model aggregation method reduces these lower-dimensional surrogate model risks and improves the robustness of the BO algorithm. We derive an asymptotic bound for the proposed aggregated surrogate model and prove the convergence of MamBO. Benchmark numerical experiments indicate that our algorithm achieves superior or comparable performance to other commonly used high-dimensional BO algorithms. Moreover, we apply MamBO to a cascade classifier of a machine learning algorithm for face detection, and the results reveal that MamBO finds settings that achieve higher classification accuracy than the benchmark settings and is computationally faster than other high-dimensional BO algorithms.

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arXiv2022

Enhanced Global Optimization with Parallel Global and Local Structures

In practice, objective functions of real-time control systems can have multiple local minimums or can dramatically change over the function space, making them hard to optimize. To efficiently optimize such systems, in this paper, we develop a parallel global optimization framework that combines direct search methods with Bayesian parallel optimization. It consists of an iterative global and local search that searches broadly through the entire global space for promising regions and then efficiently exploits each local promising region. We prove the asymptotic convergence properties of the proposed framework and conduct an extensive numerical comparison to illustrate its empirical performance.

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arXiv2021

Combined Global and Local Search for Optimization with Gaussian Process Models

Gaussian process (GP) model based optimization is widely applied in simulation and machine learning. In general, it first estimates a GP model based on a few observations from the true response and then employs this model to guide the search, aiming to quickly locate the global optimum. Despite its successful applications, it has several limitations that may hinder its broader usage. First, building an accurate GP model can be difficult and computationally expensive, especially when the response function is multi-modal or varies significantly over the design space. Second, even with an appropriate model, the search process can be trapped in suboptimal regions before moving to the global optimum due to the excessive effort spent around the current best solution. In this work, we adopt the Additive Global and Local GP (AGLGP) model in the optimization framework. The model is rooted in the inducing-points-based GP sparse approximations and is combined with independent local models in different regions. With these properties, the AGLGP model is suitable for multi-modal responses with relatively large data sizes. Based on this AGLGP model, we propose a Combined Global and Local search for Optimization (CGLO) algorithm. It first divides the whole design space into disjoint local regions and identifies a promising region with the global model. Next, a local model in the selected region is fit to guide detailed search within this region. The algorithm then switches back to the global step when a good local solution is found. The global and local natures of CGLO enable it to enjoy the benefits of both global and local search to efficiently locate the global optimum.

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arXiv2019

A Multi-Level Simulation Optimization Approach for Quantile Functions

Quantile is a popular performance measure for a stochastic system to evaluate its variability and risk. To reduce the risk, selecting the actions that minimize the tail quantiles of some loss distributions is typically of interest for decision makers. When the loss distribution is observed via simulations, evaluating and optimizing its quantile functions can be challenging, especially when the simulations are expensive, as it may cost a large number of simulation runs to obtain accurate quantile estimators. In this work, we propose a multi-level metamodel (co-kriging) based algorithm to optimize quantile functions more efficiently. Utilizing non-decreasing properties of quantile functions, we first search on cheaper and informative lower quantiles which are more accurate and easier to optimize. The quantile level iteratively increases to the objective level while the search has a focus on the possible promising regions identified by the previous levels. This enables us to leverage the accurate information from the lower quantiles to find the optimums faster and improve algorithm efficiency.

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