arXiv subjects

Luigi Nardi

Publications and source records attributed to Luigi Nardi.

At least 19 recordsLinked to original sources

arXiv2025

Understanding High-Dimensional Bayesian Optimization

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

cs.LG↗

arXiv2025

A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization

Bayesian optimization is a widely used method for optimizing expensive black-box functions, with Expected Improvement being one of the most commonly used acquisition functions. In contrast, information-theoretic acquisition functions aim to reduce uncertainty about the function's optimum and are often considered fundamentally distinct from EI. In this work, we challenge this prevailing perspective by introducing a unified theoretical framework, Variational Entropy Search, which reveals that EI and information-theoretic acquisition functions are more closely related than previously recognized. We demonstrate that EI can be interpreted as a variational inference approximation of the popular information-theoretic acquisition function, named Max-value Entropy Search. Building on this insight, we propose VES-Gamma, a novel acquisition function that balances the strengths of EI and MES. Extensive empirical evaluations across both low- and high-dimensional synthetic and real-world benchmarks demonstrate that VES-Gamma is competitive with state-of-the-art acquisition functions and in many cases outperforms EI and MES.

stat.ML↗

arXiv2025

Bencher: Simple and Reproducible Benchmarking for Black-Box Optimization

We present Bencher, a modular benchmarking framework for black-box optimization that fundamentally decouples benchmark execution from optimization logic. Unlike prior suites that focus on combining many benchmarks in a single project, Bencher introduces a clean abstraction boundary: each benchmark is isolated in its own virtual Python environment and accessed via a unified, version-agnostic remote procedure call (RPC) interface. This design eliminates dependency conflicts and simplifies the integration of diverse, real-world benchmarks, which often have complex and conflicting software requirements. Bencher can be deployed locally or remotely via Docker or on high-performance computing (HPC) clusters via Singularity, providing a containerized, reproducible runtime for any benchmark. Its lightweight client requires minimal setup and supports drop-in evaluation of 80 benchmarks across continuous, categorical, and binary domains.

cs.LG↗

arXiv2025

CATBench: A Compiler Autotuning Benchmarking Suite for Black-box Optimization

Bayesian optimization is a powerful method for automating tuning of compilers. The complex landscape of autotuning provides a myriad of rarely considered structural challenges for black-box optimizers, and the lack of standardized benchmarks has limited the study of Bayesian optimization within the domain. To address this, we present CATBench, a comprehensive benchmarking suite that captures the complexities of compiler autotuning, ranging from discrete, conditional, and permutation parameter types to known and unknown binary constraints, as well as both multi-fidelity and multi-objective evaluations. The benchmarks in CATBench span a range of machine learning-oriented computations, from tensor algebra to image processing and clustering, and uses state-of-the-art compilers, such as TACO and RISE/ELEVATE. CATBench offers a unified interface for evaluating Bayesian optimization algorithms, promoting reproducibility and innovation through an easy-to-use, fully containerized setup of both surrogate and real-world compiler optimization tasks. We validate CATBench on several state-of-the-art algorithms, revealing their strengths and weaknesses and demonstrating the suite's potential for advancing both Bayesian optimization and compiler autotuning research.

cs.LG↗

arXiv2025

Leveraging Axis-Aligned Subspaces for High-Dimensional Bayesian Optimization with Group Testing

Bayesian optimization (BO ) is an effective method for optimizing expensive-to-evaluate black-box functions. While high-dimensional problems can be particularly challenging, due to the multitude of parameter choices and the potentially high number of data points required to fit the model, this limitation can be addressed if the problem satisfies simplifying assumptions. Axis-aligned subspace approaches, where few dimensions have a significant impact on the objective, motivated several algorithms for high-dimensional BO . However, the validity of this assumption is rarely verified, and the assumption is rarely exploited to its full extent. We propose a group testing ( GT) approach to identify active variables to facilitate efficient optimization in these domains. The proposed algorithm, Group Testing Bayesian Optimization (GTBO), first runs a testing phase where groups of variables are systematically selected and tested on whether they influence the objective, then terminates once active dimensions are identified. To that end, we extend the well-established GT theory to functions over continuous domains. In the second phase, GTBO guides optimization by placing more importance on the active dimensions. By leveraging the axis-aligned subspace assumption, GTBO outperforms state-of-the-art methods on benchmarks satisfying the assumption of axis-aligned subspaces, while offering improved interpretability.

cs.LG↗

arXiv2025

Falsification of Cyber-Physical Systems using Bayesian Optimization

Cyber-physical systems (CPSs) are often complex and safety-critical, making it both challenging and crucial to ensure that the system's specifications are met. Simulation-based falsification is a practical testing technique for increasing confidence in a CPS's correctness, as it only requires that the system be simulated. Reducing the number of computationally intensive simulations needed for falsification is a key concern. In this study, we investigate Bayesian optimization (BO), a sample-efficient approach that learns a surrogate model to capture the relationship between input signal parameterization and specification evaluation. We propose two enhancements to the basic BO for improving falsification: (1) leveraging local surrogate models, and (2) utilizing the user's prior knowledge. Additionally, we address the formulation of acquisition functions for falsification by proposing and evaluating various alternatives. Our benchmark evaluation demonstrates significant improvements when using local surrogate models in BO for falsifying challenging benchmark examples. Incorporating prior knowledge is found to be especially beneficial when the simulation budget is constrained. For some benchmark problems, the choice of acquisition function noticeably impacts the number of simulations required for successful falsification.

eess.SY↗

arXiv2025

Exploring Exploration in Bayesian Optimization

A well-balanced exploration-exploitation trade-off is crucial for successful acquisition functions in Bayesian optimization. However, there is a lack of quantitative measures for exploration, making it difficult to analyze and compare different acquisition functions. This work introduces two novel approaches - observation traveling salesman distance and observation entropy - to quantify the exploration characteristics of acquisition functions based on their selected observations. Using these measures, we examine the explorative nature of several well-known acquisition functions across a diverse set of black-box problems, uncover links between exploration and empirical performance, and reveal new relationships among existing acquisition functions. Beyond enabling a deeper understanding of acquisition functions, these measures also provide a foundation for guiding their design in a more principled and systematic manner.

cs.LG↗

arXiv2024

Vanilla Bayesian Optimization Performs Great in High Dimensions

High-dimensional problems have long been considered the Achilles' heel of Bayesian optimization algorithms. Spurred by the curse of dimensionality, a large collection of algorithms aim to make it more performant in this setting, commonly by imposing various simplifying assumptions on the objective. In this paper, we identify the degeneracies that make vanilla Bayesian optimization poorly suited to high-dimensional tasks, and further show how existing algorithms address these degeneracies through the lens of lowering the model complexity. Moreover, we propose an enhancement to the prior assumptions that are typical to vanilla Bayesian optimization algorithms, which reduces the complexity to manageable levels without imposing structural restrictions on the objective. Our modification - a simple scaling of the Gaussian process lengthscale prior with the dimensionality - reveals that standard Bayesian optimization works drastically better than previously thought in high dimensions, clearly outperforming existing state-of-the-art algorithms on multiple commonly considered real-world high-dimensional tasks.

cs.LG↗

arXiv2024

Bounce: Reliable High-Dimensional Bayesian Optimization for Combinatorial and Mixed Spaces

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.

cs.LG↗

arXiv2024

A General Framework for User-Guided Bayesian Optimization

The optimization of expensive-to-evaluate black-box functions is prevalent in various scientific disciplines. Bayesian optimization is an automatic, general and sample-efficient method to solve these problems with minimal knowledge of the underlying function dynamics. However, the ability of Bayesian optimization to incorporate prior knowledge or beliefs about the function at hand in order to accelerate the optimization is limited, which reduces its appeal for knowledgeable practitioners with tight budgets. To allow domain experts to customize the optimization routine, we propose ColaBO, the first Bayesian-principled framework for incorporating prior beliefs beyond the typical kernel structure, such as the likely location of the optimizer or the optimal value. The generality of ColaBO makes it applicable across different Monte Carlo acquisition functions and types of user beliefs. We empirically demonstrate ColaBO's ability to substantially accelerate optimization when the prior information is accurate, and to retain approximately default performance when it is misleading.

cs.LG↗

arXiv2024

Self-Correcting Bayesian Optimization through Bayesian Active Learning

Gaussian processes are the model of choice in Bayesian optimization and active learning. Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding good hyperparameters in the literature. We demonstrate the impact of selecting good hyperparameters for GPs and present two acquisition functions that explicitly prioritize hyperparameter learning. Statistical distance-based Active Learning (SAL) considers the average disagreement between samples from the posterior, as measured by a statistical distance. SAL outperforms the state-of-the-art in Bayesian active learning on several test functions. We then introduce Self-Correcting Bayesian Optimization (SCoreBO), which extends SAL to perform Bayesian optimization and active learning simultaneously. SCoreBO learns the model hyperparameters at improved rates compared to vanilla BO, while outperforming the latest Bayesian optimization methods on traditional benchmarks. Moreover, we demonstrate the importance of self-correction on atypical Bayesian optimization tasks.

cs.LG↗

arXiv2023

PriorBand: Practical Hyperparameter Optimization in the Age of Deep Learning

Hyperparameters of Deep Learning (DL) pipelines are crucial for their downstream performance. While a large number of methods for Hyperparameter Optimization (HPO) have been developed, their incurred costs are often untenable for modern DL. Consequently, manual experimentation is still the most prevalent approach to optimize hyperparameters, relying on the researcher's intuition, domain knowledge, and cheap preliminary explorations. To resolve this misalignment between HPO algorithms and DL researchers, we propose PriorBand, an HPO algorithm tailored to DL, able to utilize both expert beliefs and cheap proxy tasks. Empirically, we demonstrate PriorBand's efficiency across a range of DL benchmarks and show its gains under informative expert input and robustness against poor expert beliefs

cs.LG↗

arXiv2023

High-dimensional Bayesian Optimization with Group Testing

Bayesian optimization is an effective method for optimizing expensive-to-evaluate black-box functions. High-dimensional problems are particularly challenging as the surrogate model of the objective suffers from the curse of dimensionality, which makes accurate modeling difficult. We propose a group testing approach to identify active variables to facilitate efficient optimization in these domains. The proposed algorithm, Group Testing Bayesian Optimization (GTBO), first runs a testing phase where groups of variables are systematically selected and tested on whether they influence the objective. To that end, we extend the well-established theory of group testing to functions of continuous ranges. In the second phase, GTBO guides optimization by placing more importance on the active dimensions. By exploiting the axis-aligned subspace assumption, GTBO is competitive against state-of-the-art methods on several synthetic and real-world high-dimensional optimization tasks. Furthermore, GTBO aids in the discovery of active parameters in applications, thereby enhancing practitioners' understanding of the problem at hand.

cs.LG↗

arXiv2023

Out-of-Distribution Detection for Adaptive Computer Vision

It is well known that computer vision can be unreliable when faced with previously unseen imaging conditions. This paper proposes a method to adapt camera parameters according to a normalizing flow-based out-of-distibution detector. A small-scale study is conducted which shows that adapting camera parameters according to this out-of-distibution detector leads to an average increase of 3 to 4 percentage points in mAP, mAR and F1 performance metrics of a YOLOv4 object detector. As a secondary result, this paper also shows that it is possible to train a normalizing flow model for out-of-distribution detection on the COCO dataset, which is larger and more diverse than most benchmarks for out-of-distibution detectors.

cs.CV↗

arXiv2023

Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspaces

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.

cs.LG↗

arXiv2023

BaCO: A Fast and Portable Bayesian Compiler Optimization Framework

We introduce the Bayesian Compiler Optimization framework (BaCO), a general purpose autotuner for modern compilers targeting CPUs, GPUs, and FPGAs. BaCO provides the flexibility needed to handle the requirements of modern autotuning tasks. Particularly, it deals with permutation, ordered, and continuous parameter types along with both known and unknown parameter constraints. To reason about these parameter types and efficiently deliver high-quality code, BaCO uses Bayesian optimiza tion algorithms specialized towards the autotuning domain. We demonstrate BaCO's effectiveness on three modern compiler systems: TACO, RISE & ELEVATE, and HPVM2FPGA for CPUs, GPUs, and FPGAs respectively. For these domains, BaCO outperforms current state-of-the-art autotuners by delivering on average 1.36x-1.56x faster code with a tiny search budget, and BaCO is able to reach expert-level performance 2.9x-3.9x faster.

cs.PL↗

arXiv2023

Joint Entropy Search for Maximally-Informed Bayesian Optimization

Information-theoretic Bayesian optimization techniques have become popular for optimizing expensive-to-evaluate black-box functions due to their non-myopic qualities. Entropy Search and Predictive Entropy Search both consider the entropy over the optimum in the input space, while the recent Max-value Entropy Search considers the entropy over the optimal value in the output space. We propose Joint Entropy Search (JES), a novel information-theoretic acquisition function that considers an entirely new quantity, namely the entropy over the joint optimal probability density over both input and output space. To incorporate this information, we consider the reduction in entropy from conditioning on fantasized optimal input/output pairs. The resulting approach primarily relies on standard GP machinery and removes complex approximations typically associated with information-theoretic methods. With minimal computational overhead, JES shows superior decision-making, and yields state-of-the-art performance for information-theoretic approaches across a wide suite of tasks. As a light-weight approach with superior results, JES provides a new go-to acquisition function for Bayesian optimization.

cs.LG↗

arXiv2022

Combining Planning, Reasoning and Reinforcement Learning to solve Industrial Robot Tasks

One of today's goals for industrial robot systems is to allow fast and easy provisioning for new tasks. Skill-based systems that use planning and knowledge representation have long been one possible answer to this. However, especially with contact-rich robot tasks that need careful parameter settings, such reasoning techniques can fall short if the required knowledge not adequately modeled. We show an approach that provides a combination of task-level planning and reasoning with targeted learning of skill parameters for a task at hand. Starting from a task goal formulated in PDDL, the learnable parameters in the plan are identified and an operator can choose reward functions and parameters for the learning process. A tight integration with a knowledge framework allows to form a prior for learning and the usage of multi-objective Bayesian optimization eases to balance aspects such as safety and task performance that can often affect each other. We demonstrate the efficacy and versatility of our approach by learning skill parameters for two different contact-rich tasks and show their successful execution on a real 7-DOF KUKA-iiwa.

cs.RO↗