LLaMEA-BO: A Large Language Model Evolutionary Algorithm for Automatically Generating Bayesian Optimization Algorithms

Bayesian optimization (BO) is a powerful class of algorithms for optimizing expensive black-box functions, but designing effective BO algorithms remains a manual, expertise-driven task. Recent advancements in Large Language Models (LLMs) have opened new avenues for automating scientific discovery, including the automatic design of optimization algorithms. While prior work has used LLMs within optimization loops or to generate non-BO algorithms, we tackle a new challenge: Using LLMs to automatically generate full BO algorithm code. Our framework uses an evolution strategy to guide an LLM in generating Python code that preserves the key components of BO algorithms: An initial design, a surrogate model, and an acquisition function. The LLM is prompted to produce multiple candidate algorithms, which are evaluated on the established Black-Box Optimization Benchmarking (BBOB) test suite from the COmparing Continuous Optimizers (COCO) platform. Based on their performance, top candidates are selected, combined, and mutated via controlled prompt variations, enabling iterative refinement. Despite no additional fine-tuning, the LLM-generated algorithms outperform state-of-the-art BO baselines in 19 (out of 24) BBOB functions in dimension 5 and generalize well to higher dimensions, and different tasks (from the Bayesmark framework). This work demonstrates that LLMs can serve as algorithmic co-designers, offering a new paradigm for automating BO development and accelerating the discovery of novel algorithmic combinations. The source code is provided at https://github.com/Ewendawi/LLaMEA-BO.

Why Are You Wrong? Counterfactual Explanations for Language Grounding with 3D Objects

Combining natural language and geometric shapes is an emerging research area with multiple applications in robotics and language-assisted design. A crucial task in this domain is object referent identification, which involves selecting a 3D object given a textual description of the target. Variability in language descriptions and spatial relationships of 3D objects makes this a complex task, increasing the need to better understand the behavior of neural network models in this domain. However, limited research has been conducted in this area. Specifically, when a model makes an incorrect prediction despite being provided with a seemingly correct object description, practitioners are left wondering: "Why is the model wrong?". In this work, we present a method answering this question by generating counterfactual examples. Our method takes a misclassified sample, which includes two objects and a text description, and generates an alternative yet similar formulation that would have resulted in a correct prediction by the model. We have evaluated our approach with data from the ShapeTalk dataset along with three distinct models. Our counterfactual examples maintain the structure of the original description, are semantically similar and meaningful. They reveal weaknesses in the description, model bias and enhance the understanding of the models behavior. Theses insights help practitioners to better interact with systems as well as engineers to improve models.

Cascading CMA-ES Instances for Generating Input-diverse Solution Batches

Rather than obtaining a single good solution for a given optimization problem, users often seek alternative design choices, because the best-found solution may perform poorly with respect to additional objectives or constraints that are difficult to capture into the modeling process. Aiming for batches of diverse solutions of high quality is often desirable, as it provides flexibility to accommodate post-hoc user preferences. At the same time, it is crucial that the quality of the best solution found is not compromised. One particular problem setting balancing high quality and diversity is fixing the required minimum distance between solutions while simultaneously obtaining the best possible fitness. Recent work by Santoni et al. [arXiv 2024] revealed that this setting is not well addressed by state-of-the-art algorithms, performing in par or worse than pure random sampling. Driven by this important limitation, we propose a new approach, where parallel runs of the covariance matrix adaptation evolution strategy (CMA-ES) inherit tabu regions in a cascading fashion. We empirically demonstrate that our CMA-ES-Diversity Search (CMA-ES-DS) algorithm generates trajectories that allow to extract high-quality solution batches that respect a given minimum distance requirement, clearly outperforming those obtained from off-the-shelf random sampling, multi-modal optimization algorithms, and standard CMA-ES.

Illuminating the Diversity-Fitness Trade-Off in Black-Box Optimization

In real-world applications, users often favor structurally diverse design choices over one high-quality solution. It is hence important to consider more solutions that decision-makers can compare and further explore based on additional criteria. Alongside the existing approaches of evolutionary diversity optimization, quality diversity, and multimodal optimization, this paper presents a fresh perspective on this challenge by considering the problem of identifying a fixed number of solutions with a pairwise distance above a specified threshold while maximizing their average quality. We obtain first insight into these objectives by performing a subset selection on the search trajectories of different well-established search heuristics, whether specifically designed with diversity in mind or not. We emphasize that the main goal of our work is not to present a new algorithm but to look at the problem in a more fundamental and theoretically tractable way by asking the question: What trade-off exists between the minimum distance within batches of solutions and the average quality of their fitness? These insights also provide us with a way of making general claims concerning the properties of optimization problems that shall be useful in turn for benchmarking algorithms of the approaches enumerated above. A possibly surprising outcome of our empirical study is the observation that naive uniform random sampling establishes a very strong baseline for our problem, hardly ever outperformed by the search trajectories of the considered heuristics. We interpret these results as a motivation to develop algorithms tailored to produce diverse solutions of high average quality.

Automated Federated Learning via Informed Pruning

Federated learning (FL) represents a pivotal shift in machine learning (ML) as it enables collaborative training of local ML models coordinated by a central aggregator, all without the need to exchange local data. However, its application on edge devices is hindered by limited computational capabilities and data communication challenges, compounded by the inherent complexity of Deep Learning (DL) models. Model pruning is identified as a key technique for compressing DL models on devices with limited resources. Nonetheless, conventional pruning techniques typically rely on manually crafted heuristics and demand human expertise to achieve a balance between model size, speed, and accuracy, often resulting in sub-optimal solutions. In this study, we introduce an automated federated learning approach utilizing informed pruning, called AutoFLIP, which dynamically prunes and compresses DL models within both the local clients and the global server. It leverages a federated loss exploration phase to investigate model gradient behavior across diverse datasets and losses, providing insights into parameter significance. Our experiments showcase notable enhancements in scenarios with strong non-IID data, underscoring AutoFLIP's capacity to tackle computational constraints and achieve superior global convergence.

Optimizing with Low Budgets: a Comparison on the Black-box Optimization Benchmarking Suite and OpenAI Gym

The growing ubiquity of machine learning (ML) has led it to enter various areas of computer science, including black-box optimization (BBO). Recent research is particularly concerned with Bayesian optimization (BO). BO-based algorithms are popular in the ML community, as they are used for hyperparameter optimization and more generally for algorithm configuration. However, their efficiency decreases as the dimensionality of the problem and the budget of evaluations increase. Meanwhile, derivative-free optimization methods have evolved independently in the optimization community. Therefore, we urge to understand whether cross-fertilization is possible between the two communities, ML and BBO, i.e., whether algorithms that are heavily used in ML also work well in BBO and vice versa. Comparative experiments often involve rather small benchmarks and show visible problems in the experimental setup, such as poor initialization of baselines, overfitting due to problem-specific setting of hyperparameters, and low statistical significance. With this paper, we update and extend a comparative study presented by Hutter et al. in 2013. We compare BBO tools for ML with more classical heuristics, first on the well-known BBOB benchmark suite from the COCO environment and then on Direct Policy Search for OpenAI Gym, a reinforcement learning benchmark. Our results confirm that BO-based optimizers perform well on both benchmarks when budgets are limited, albeit with a higher computational cost, while they are often outperformed by algorithms from other families when the evaluation budget becomes larger. We also show that some algorithms from the BBO community perform surprisingly well on ML tasks.

Self-Adjusting Weighted Expected Improvement for Bayesian Optimization

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.

Comparison of High-Dimensional Bayesian Optimization Algorithms on BBOB

Bayesian Optimization (BO) is a class of black-box, surrogate-based heuristics that can efficiently optimize problems that are expensive to evaluate, and hence admit only small evaluation budgets. BO is particularly popular for solving numerical optimization problems in industry, where the evaluation of objective functions often relies on time-consuming simulations or physical experiments. However, many industrial problems depend on a large number of parameters. This poses a challenge for BO algorithms, whose performance is often reported to suffer when the dimension grows beyond 15 variables. Although many new algorithms have been proposed to address this problem, it is not well understood which one is the best for which optimization scenario. In this work, we compare five state-of-the-art high-dimensional BO algorithms, with vanilla BO and CMA-ES on the 24 BBOB functions of the COCO environment at increasing dimensionality, ranging from 10 to 60 variables. Our results confirm the superiority of BO over CMA-ES for limited evaluation budgets and suggest that the most promising approach to improve BO is the use of trust regions. However, we also observe significant performance differences for different function landscapes and budget exploitation phases, indicating improvement potential, e.g., through hybridization of algorithmic components.

Towards Automated Design of Bayesian Optimization via Exploratory Landscape Analysis

Bayesian optimization (BO) algorithms form a class of surrogate-based heuristics, aimed at efficiently computing high-quality solutions for numerical black-box optimization problems. The BO pipeline is highly modular, with different design choices for the initial sampling strategy, the surrogate model, the acquisition function (AF), the solver used to optimize the AF, etc. We demonstrate in this work that a dynamic selection of the AF can benefit the BO design. More precisely, we show that already a na\"ive random forest regression model, built on top of exploratory landscape analysis features that are computed from the initial design points, suffices to recommend AFs that outperform any static choice, when considering performance over the classic BBOB benchmark suite for derivative-free numerical optimization methods on the COCO platform. Our work hence paves a way towards AutoML-assisted, on-the-fly BO designs that adjust their behavior on a run-by-run basis.

PI is back! Switching Acquisition Functions in Bayesian Optimization

Bayesian Optimization (BO) is a powerful, sample-efficient technique to optimize expensive-to-evaluate functions. Each of the BO components, such as the surrogate model, the acquisition function (AF), or the initial design, is subject to a wide range of design choices. Selecting the right components for a given optimization task is a challenging task, which can have significant impact on the quality of the obtained results. In this work, we initiate the analysis of which AF to favor for which optimization scenarios. To this end, we benchmark SMAC3 using Expected Improvement (EI) and Probability of Improvement (PI) as acquisition functions on the 24 BBOB functions of the COCO environment. We compare their results with those of schedules switching between AFs. One schedule aims to use EI's explorative behavior in the early optimization steps, and then switches to PI for a better exploitation in the final steps. We also compare this to a random schedule and round-robin selection of EI and PI. We observe that dynamic schedules oftentimes outperform any single static one. Our results suggest that a schedule that allocates the first 25 % of the optimization budget to EI and the last 75 % to PI is a reliable default. However, we also observe considerable performance differences for the 24 functions, suggesting that a per-instance allocation, possibly learned on the fly, could offer significant improvement over the state-of-the-art BO designs.