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1. Bayesian Optimization with High-Dimensional Outputs

   https://doi.org/10.48550/arXiv.2106.12997  

   Maddox, W. J.; Balandat, M.; Wilson, A. G.; Bakshy, E (January 2021, Advances in neural information processing systems)

   Bayesian optimization is a sample-efficient black-box optimization procedure that is typically applied to a small number of independent objectives. However, in practice we often wish to optimize objectives defined over many correlated outcomes (or “tasks”). For example, scientists may want to optimize the coverage of a cell tower network across a dense grid of locations. Similarly, engineers may seek to balance the performance of a robot across dozens of different environments via constrained or robust optimization. However, the Gaussian Process (GP) models typically used as probabilistic surrogates for multi-task Bayesian optimization scale poorly with the number of outcomes, greatly limiting applicability. We devise an efficient technique for exact multi-task GP sampling that combines exploiting Kronecker structure in the covariance matrices with Matheron’s identity, allowing us to perform Bayesian optimization using exact multi-task GP models with tens of thousands of correlated outputs. In doing so, we achieve substantial improvements in sample efficiency compared to existing approaches that model solely the outcome metrics. We demonstrate how this unlocks a new class of applications for Bayesian optimization across a range of tasks in science and engineering, including optimizing interference patterns of an optical interferometer with 65,000 outputs. 

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2. Hybrid Batch Attacks: Finding Black-box Adversarial Examples with Limited Queries

   Fnu, Suya; Chi, Jianfeng; Evans, David; Tian, Yuan (January 2020, USENIX Security Symposium)

   In a black-box setting, the adversary only has API access to the target model and each query is expensive. Prior work on black-box adversarial examples follows one of two main strategies: (1) transfer attacks use white-box attacks on local models to find candidate adversarial examples that transfer to the target model, and (2) optimization-based attacks use queries to the target model and apply optimization techniques to search for adversarial examples. We propose hybrid attacks that combine both strategies, using candidate adversarial examples from local models as starting points for optimization-based attacks and using labels learned in optimization-based attacks to tune local models for finding transfer candidates. We empirically demonstrate on the MNIST, CIFAR10, and ImageNet datasets that our hybrid attack strategy reduces cost and improves success rates, and in combination with our seed prioritization strategy, enables batch attacks that can efficiently find adversarial examples with only a handful of queries. 

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3. They Might NOT Be Giants: Crafting Black-Box Adversarial Examples Using Particle Swarm Optimization

   https://doi.org/10.1007/978-3-030-59013-0_22  

   Mosli, Rayan; Wright, Matthew; Yuan, Bo; Pan, Yin (September 2020, Lecture notes in computer science)

   null (Ed.)

   As machine learning is deployed in more settings, including in security-sensitive applications such as malware detection, the risks posed by adversarial examples that fool machine-learning classifiers have become magnified. Black-box attacks are especially dangerous, as they only require the attacker to have the ability to query the target model and observe the labels it returns, without knowing anything else about the model. Current black-box attacks either have low success rates, require a high number of queries, produce adversarial images that are easily distinguishable from their sources, or are not flexible in controlling the outcome of the attack. In this paper, we present AdversarialPSO, (Code available: https://github.com/rhm6501/AdversarialPSOImages) a black-box attack that uses few queries to create adversarial examples with high success rates. AdversarialPSO is based on Particle Swarm Optimization, a gradient-free evolutionary search algorithm, with special adaptations to make it effective for the black-box setting. It is flexible in balancing the number of queries submitted to the target against the quality of the adversarial examples. We evaluated AdversarialPSO on CIFAR-10, MNIST, and Imagenet, achieving success rates of 94.9%, 98.5%, and 96.9%, respectively, while submitting numbers of queries comparable to prior work. Our results show that black-box attacks can be adapted to favor fewer queries or higher quality adversarial images, while still maintaining high success rates. 

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4. Conformal Frequency Estimation using Discrete Sketched Data with Coverage for Distinct Queries

   Sesia, Matteo; Favaro, Stefano; Dobriban, Edgar (December 2023, Journal of machine learning research)

   Michael Mahoney (Ed.)

   This paper develops conformal inference methods to construct a confidence interval for the frequency of a queried object in a very large discrete data set, based on a sketch with a lower memory footprint. This approach requires no knowledge of the data distribution and can be combined with any sketching algorithm, including but not limited to the renowned count-min sketch, the count-sketch, and variations thereof. After explaining how to achieve marginal coverage for exchangeable random queries, we extend our solution to provide stronger inferences that can account for the discreteness of the data and for heterogeneous query frequencies, increasing also robustness to possible distribution shifts. These results are facilitated by a novel conformal calibration technique that guarantees valid coverage for a large fraction of distinct random queries. Finally, we show our methods have improved empirical performance compared to existing frequentist and Bayesian alternatives in simulations as well as in examples of text and SARS-CoV-2 DNA data. 

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5. BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertainty

   https://doi.org/10.1016/j.compchemeng.2025.109393  

   Kudva, Akshay; Paulson, Joel A (January 2026, Computers & Chemical Engineering)

   Optimal design under uncertainty remains a fundamental challenge in advancing reliable, next-generation process systems. Robust optimization (RO) offers a principled approach by safeguarding against worst-case scenarios across a range of uncertain parameters. However, traditional RO methods typically require known problem structure, which limits their applicability to high-fidelity simulation environments. To overcome these limitations, recent work has explored robust Bayesian optimization (RBO) as a flexible alternative that can accommodate expensive, black-box objectives. Existing RBO methods, however, generally ignore available structural information and struggle to scale to high-dimensional settings. In this work, we introduce BONSAI (Bayesian Optimization of Network Systems under uncertAInty), a new RBO framework that leverages partial structural knowledge commonly available in simulation-based models. Instead of treating the objective as a monolithic black box, BONSAI represents it as a directed graph of interconnected white- and black-box components, allowing the algorithm to utilize intermediate information within the optimization process. We further propose a scalable Thompson sampling-based acquisition function tailored to the structured RO setting, which can be efficiently optimized using gradient-based methods. We evaluate BONSAI across a diverse set of synthetic and real-world case studies, including applications in process systems engineering. Compared to existing simulation-based RO algorithms, BONSAI consistently delivers more sample-efficient and higher-quality robust solutions, highlighting its practical advantages for uncertainty-aware design in complex engineering systems. 

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