We consider the problem of optimizing a grey-box objective function, i.e., nested function composed of both black-box and white-box functions. A general formulation for such grey-box problems is given, which covers the existing grey-box optimization formulations as special cases. We then design an optimism-driven algorithm to solve it. Under certain regularity assumptions, our algorithm achieves similar regret bound as that for the standard black-box Bayesian optimization algorithm, up to a constant multiplicative term depending on the Lipschitz constants of the functions considered. We further extend our method to the constrained case and discuss special cases. For the commonly used kernel functions, the regret bounds allow us to derive a convergence rate to the optimal solution. Experimental results show that our grey-box optimization method empirically improves the speed of finding the global optimal solution significantly, as compared to the standard black-box optimization algorithm.
Bayesian Optimization (BO) is a class of surrogate-based, sample-efficient algorithms for optimizing black-box problems with small evaluation budgets. The BO pipeline itself is highly configurable with many different design choices regarding the initial design, surrogate model, and acquisition function (AF). Unfortunately, our understanding of how to select suitable components for a problem at hand is very limited. In this work, we focus on the definition of the AF, whose main purpose is to balance the trade-off between exploring regions with high uncertainty and those with high promise for good solutions. We propose Self-Adjusting Weighted Expected Improvement (SAWEI), where we let the exploration-exploitation trade-off self-adjust in a data-driven manner, based on a convergence criterion for BO. On the noise-free black-box BBOB functions of the COCO benchmarking platform, our method exhibits a favorable any-time performance compared to handcrafted baselines and serves as a robust default choice for any problem structure. The suitability of our method also transfers to HPOBench. With SAWEI, we are a step closer to on-the-fly, data-driven, and robust BO designs that automatically adjust their sampling behavior to the problem at hand.
Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior, hyperparameters, and inducing points, making accurate learning challenging. Here, we present a method to keep all such errors in check using the recently proposed dual sparse variational GP. Our method enables accurate inference for generic likelihoods and improves learning by actively building and updating a memory of past data. We demonstrate its effectiveness in several applications involving Bayesian optimization, active learning, and continual learning.
In this work, geometry optimization of mechanical truss using computer-aided finite element analysis is presented. The shape of the truss is a dominant factor in determining the capacity of load it can bear. At a given parameter space, our goal is to find the parameters of a hull that maximize the load-bearing capacity and also don't yield to the induced stress. We rely on finite element analysis, which is a computationally costly design analysis tool for design evaluation. For such expensive to-evaluate functions, we chose Bayesian optimization as our optimization framework which has empirically proven sample efficient than other simulation-based optimization methods. By utilizing Bayesian optimization algorithms, the truss design involves iteratively evaluating a set of candidate truss designs and updating a probabilistic model of the design space based on the results. The model is used to predict the performance of each candidate design, and the next candidate design is selected based on the prediction and an acquisition function that balances exploration and exploitation of the design space. Our result can be used as a baseline for future study on AI-based optimization in expensive engineering domains especially in finite element Analysis.
Large language models~(LLMs) are instruction followers, but it can be challenging to find the best instruction for different situations, especially for black-box LLMs on which backpropagation is forbidden. Instead of directly optimizing the discrete instruction, we optimize a low-dimensional soft prompt applied to an open-source LLM to generate the instruction for the black-box LLM. On each iteration of the proposed method, which we call InstructZero, a soft prompt is converted into an instruction using the open-source LLM, which is then submitted to the black-box LLM for zero-shot evaluation, and the performance is sent to Bayesian optimization to produce new soft prompts improving the zero-shot performance. We evaluate InstructZero on different combinations of open-source LLMs and APIs including Vicuna and ChatGPT. Our results show that InstructZero outperforms SOTA auto-instruction methods across a variety of downstream tasks. Our code and data are publicly available at https://github.com/Lichang-Chen/InstructZero.
Bayesian optimization (BO) provides a powerful framework for optimizing black-box, expensive-to-evaluate functions. It is therefore an attractive tool for engineering design problems, typically involving multiple objectives. Thanks to the rapid advances in fabrication and measurement methods as well as parallel computing infrastructure, querying many design problems can be heavily parallelized. This class of problems challenges BO with an unprecedented setup where it has to deal with very large batches, shifting its focus from sample efficiency to iteration efficiency. We present a novel Bayesian optimization framework specifically tailored to address these limitations. Our key contribution is a highly scalable, sample-based acquisition function that performs a non-dominated sorting of not only the objectives but also their associated uncertainty. We show that our acquisition function in combination with different Bayesian neural network surrogates is effective in data-intensive environments with a minimal number of iterations. We demonstrate the superiority of our method by comparing it with state-of-the-art multi-objective optimizations. We perform our evaluation on two real-world problems -- airfoil design and 3D printing -- showcasing the applicability and efficiency of our approach. Our code is available at: https://github.com/an-on-ym-ous/lbn_mobo
We introduce an efficient and robust auto-tuning framework for hyperparameter selection in dimension reduction (DR) algorithms, focusing on large-scale datasets and arbitrary performance metrics. By leveraging Bayesian optimization (BO) with a surrogate model, our approach enables efficient hyperparameter selection with multi-objective trade-offs and allows us to perform data-driven sensitivity analysis. By incorporating normalization and subsampling, the proposed framework demonstrates versatility and efficiency, as shown in applications to visualization techniques such as t-SNE and UMAP. We evaluate our results on various synthetic and real-world datasets using multiple quality metrics, providing a robust and efficient solution for hyperparameter selection in DR algorithms.
Many scientific and industrial applications require the joint optimization of multiple, potentially competing objectives. Multi-objective Bayesian optimization (MOBO) is a sample-efficient framework for identifying Pareto-optimal solutions. At the heart of MOBO is the acquisition function, which determines the next candidate to evaluate by navigating the best compromises among the objectives. In this paper, we show a natural connection between non-dominated solutions and the extreme quantile of the joint cumulative distribution function (CDF). Motivated by this link, we propose the Pareto-compliant CDF indicator and the associated acquisition function, BOtied. BOtied inherits desirable invariance properties of the CDF, and an efficient implementation with copulas allows it to scale to many objectives. Our experiments on a variety of synthetic and real-world problems demonstrate that BOtied outperforms state-of-the-art MOBO acquisition functions while being computationally efficient for many objectives.
Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support exact inference. While standard GP surrogates have been well-established in Bayesian optimization, Bayesian neural networks (BNNs) have recently become practical function approximators, with many benefits over standard GPs such as the ability to naturally handle non-stationarity and learn representations for high-dimensional data. In this paper, we study BNNs as alternatives to standard GP surrogates for optimization. We consider a variety of approximate inference procedures for finite-width BNNs, including high-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics such as deep ensembles. We also consider infinite-width BNNs, linearized Laplace approximations, and partially stochastic models such as deep kernel learning. We evaluate this collection of surrogate models on diverse problems with varying dimensionality, number of objectives, non-stationarity, and discrete and continuous inputs. We find: (i) the ranking of methods is highly problem dependent, suggesting the need for tailored inductive biases; (ii) HMC is the most successful approximate inference procedure for fully stochastic BNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is relatively competitive; (iv) deep ensembles perform relatively poorly; (v) infinite-width BNNs are particularly promising, especially in high dimensions.
We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph structure and, if available, an observational dataset; and then solves the restricted optimization problem by modelling target and constraint quantities using Gaussian processes and by sequentially selecting interventions via a constrained expected improvement acquisition function. We propose different surrogate models that enable to integrate observational and interventional data while capturing correlation among effects with increasing levels of sophistication. We evaluate cCBO on artificial and real-world causal graphs showing successful trade off between fast convergence and percentage of feasible interventions.
Bayesian Optimization (BO) is typically used to optimize an unknown function $f$ that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for $f$. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of $f$ without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of $f$ comprises high-dimensional factors.
Dynamic control is emerging as an effective methodology for operating stormwater systems under stress from rapidly evolving weather patterns. Informed by rainfall predictions and real-time sensor measurements, control assets in the stormwater network can be dynamically configured to tune the behavior of the stormwater network to reduce the risk of urban flooding, equalize flows to the water reclamation facilities, and protect the receiving water bodies. However, developing such control strategies requires significant human and computational resources, and a methodology does not yet exist for quantifying the risks associated with implementing these control strategies. To address these challenges, in this paper, we introduce a Bayesian Optimization-based approach for identifying stormwater control strategies and estimating the associated uncertainties. We evaluate the efficacy of this approach in identifying viable control strategies in a simulated environment on real-world inspired combined and separated stormwater networks. We demonstrate the computational efficiency of the proposed approach by comparing it against a Genetic algorithm. Furthermore, we extend the Bayesian Optimization-based approach to quantify the uncertainty associated with the identified control strategies and evaluate it on a synthetic stormwater network. To our knowledge, this is the first-ever stormwater control methodology that quantifies uncertainty associated with the identified control actions. This Bayesian optimization-based stormwater control methodology is an off-the-shelf control approach that can be applied to control any stormwater network as long we have access to the rainfall predictions, and there exists a model for simulating the behavior of the stormwater network.
Inverse protein folding -- the task of predicting a protein sequence from its backbone atom coordinates -- has surfaced as an important problem in the "top down", de novo design of proteins. Contemporary approaches have cast this problem as a conditional generative modelling problem, where a large generative model over protein sequences is conditioned on the backbone. While these generative models very rapidly produce promising sequences, independent draws from generative models may fail to produce sequences that reliably fold to the correct backbone. Furthermore, it is challenging to adapt pure generative approaches to other settings, e.g., when constraints exist. In this paper, we cast the problem of improving generated inverse folds as an optimization problem that we solve using recent advances in "deep" or "latent space" Bayesian optimization. Our approach consistently produces protein sequences with greatly reduced structural error to the target backbone structure as measured by TM score and RMSD while using fewer computational resources. Additionally, we demonstrate other advantages of an optimization-based approach to the problem, such as the ability to handle constraints.
In this paper, we use Prior-data Fitted Networks (PFNs) as a flexible surrogate for Bayesian Optimization (BO). PFNs are neural processes that are trained to approximate the posterior predictive distribution (PPD) through in-context learning on any prior distribution that can be efficiently sampled from. We describe how this flexibility can be exploited for surrogate modeling in BO. We use PFNs to mimic a naive Gaussian process (GP), an advanced GP, and a Bayesian Neural Network (BNN). In addition, we show how to incorporate further information into the prior, such as allowing hints about the position of optima (user priors), ignoring irrelevant dimensions, and performing non-myopic BO by learning the acquisition function. The flexibility underlying these extensions opens up vast possibilities for using PFNs for BO. We demonstrate the usefulness of PFNs for BO in a large-scale evaluation on artificial GP samples and three different hyperparameter optimization testbeds: HPO-B, Bayesmark, and PD1. We publish code alongside trained models at github.com/automl/PFNs4BO.
The deployment of large-scale generative models is often restricted by their potential risk of causing harm to users in unpredictable ways. We focus on the problem of black-box red teaming, where a red team generates test cases and interacts with the victim model to discover a diverse set of failures with limited query access. Existing red teaming methods construct test cases based on human supervision or language model (LM) and query all test cases in a brute-force manner without incorporating any information from past evaluations, resulting in a prohibitively large number of queries. To this end, we propose Bayesian red teaming (BRT), novel query-efficient black-box red teaming methods based on Bayesian optimization, which iteratively identify diverse positive test cases leading to model failures by utilizing the pre-defined user input pool and the past evaluations. Experimental results on various user input pools demonstrate that our method consistently finds a significantly larger number of diverse positive test cases under the limited query budget than the baseline methods. The source code is available at https://github.com/snu-mllab/Bayesian-Red-Teaming.
This work explores the use of gradient boosting in the context of classification. Four popular implementations, including original GBM algorithm and selected state-of-the-art gradient boosting frameworks (i.e. XGBoost, LightGBM and CatBoost), have been thoroughly compared on several publicly available real-world datasets of sufficient diversity. In the study, special emphasis was placed on hyperparameter optimization, specifically comparing two tuning strategies, i.e. randomized search and Bayesian optimization using the Tree-stuctured Parzen Estimator. The performance of considered methods was investigated in terms of common classification accuracy metrics as well as runtime and tuning time. Additionally, obtained results have been validated using appropriate statistical testing. An attempt was made to indicate a gradient boosting variant showing the right balance between effectiveness, reliability and ease of use.
Existing NAS methods suffer from either an excessive amount of time for repetitive sampling and training of many task-irrelevant architectures. To tackle such limitations of existing NAS methods, we propose a paradigm shift from NAS to a novel conditional Neural Architecture Generation (NAG) framework based on diffusion models, dubbed DiffusionNAG. Specifically, we consider the neural architectures as directed graphs and propose a graph diffusion model for generating them. Moreover, with the guidance of parameterized predictors, DiffusionNAG can flexibly generate task-optimal architectures with the desired properties for diverse tasks, by sampling from a region that is more likely to satisfy the properties. This conditional NAG scheme is significantly more efficient than previous NAS schemes which sample the architectures and filter them using the property predictors. We validate the effectiveness of DiffusionNAG through extensive experiments in two predictor-based NAS scenarios: Transferable NAS and Bayesian Optimization (BO)-based NAS. DiffusionNAG achieves superior performance with speedups of up to 35 times when compared to the baselines on Transferable NAS benchmarks. Furthermore, when integrated into a BO-based algorithm, DiffusionNAG outperforms existing BO-based NAS approaches, particularly in the large MobileNetV3 search space on the ImageNet 1K dataset. Code is available at https://github.com/CownowAn/DiffusionNAG.
Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of efficiently finding a global optimum of an expensive-to-evaluate black-box function. In general, a probabilistic regression model is widely used as a surrogate function to model an explicit distribution over function evaluations given an input to estimate and a training dataset. Beyond the probabilistic regression-based methods, density ratio estimation-based Bayesian optimization has been suggested in order to estimate a density ratio of the groups relatively close and relatively far to a global optimum. Developing this line of research further, supervised classifiers are employed to estimate a class probability for the two groups instead of a density ratio. However, the supervised classifiers used in this strategy are prone to be overconfident for known knowledge on global solution candidates. Supposing that we have access to unlabeled points, e.g., predefined fixed-size pools, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning to solve this challenge. Finally, we show the empirical results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool and analyze the validity of our proposed methods in diverse experiments.
Contextual Bayesian Optimization (CBO) efficiently optimizes black-box functions with respect to design variables, while simultaneously integrating contextual information regarding the environment, such as experimental conditions. However, the relevance of contextual variables is not necessarily known beforehand. Moreover, contextual variables can sometimes be optimized themselves at an additional cost, a setting overlooked by current CBO algorithms. Cost-sensitive CBO would simply include optimizable contextual variables as part of the design variables based on their cost. Instead, we adaptively select a subset of contextual variables to include in the optimization, based on the trade-off between their relevance and the additional cost incurred by optimizing them compared to leaving them to be determined by the environment. We learn the relevance of contextual variables by sensitivity analysis of the posterior surrogate model while minimizing the cost of optimization by leveraging recent developments on early stopping for BO. We empirically evaluate our proposed Sensitivity-Analysis-Driven Contextual BO (SADCBO) method against alternatives on both synthetic and real-world experiments, together with extensive ablation studies, and demonstrate a consistent improvement across examples.
Automated Machine Learning (AutoML) is a promising direction for democratizing AI by automatically deploying Machine Learning systems with minimal human expertise. The core technical challenge behind AutoML is optimizing the pipelines of Machine Learning systems (e.g. the choice of preprocessing, augmentations, models, optimizers, etc.). Existing Pipeline Optimization techniques fail to explore deep interactions between pipeline stages/components. As a remedy, this paper proposes a novel neural architecture that captures the deep interaction between the components of a Machine Learning pipeline. We propose embedding pipelines into a latent representation through a novel per-component encoder mechanism. To search for optimal pipelines, such pipeline embeddings are used within deep-kernel Gaussian Process surrogates inside a Bayesian Optimization setup. Furthermore, we meta-learn the parameters of the pipeline embedding network using existing evaluations of pipelines on diverse collections of related datasets (a.k.a. meta-datasets). Through extensive experiments on three large-scale meta-datasets, we demonstrate that pipeline embeddings yield state-of-the-art results in Pipeline Optimization.