arXiv subjects

Carola Doerr

Publications and source records attributed to Carola Doerr.

At least 19 recordsLinked to original sources

arXiv2026

Unsupervised Multi-kernel Learning for Automated Algorithm Selection

Automated algorithm selection in black-box optimization typically relies on supervised models that map landscape features to algorithm performance labels. Such models are costly to train, benchmark-dependent, and often fail to generalize to unseen problem classes. We study an unsupervised alternative: multi-kernel clustering over heterogeneous landscape representations, in which problem instances are grouped without using performance labels in the clustering stage, and the resulting clusters are mapped post hoc to solver recommendations through a strictly separated three-stage evaluation protocol. Drawing on two decades of advances in multiple kernel learning, we adopt a multi-kernel k-means formulation that jointly learns cluster assignments and kernel weights over four heterogeneous landscape views: ELA, DeepELA, DoE2Vec, and TransOptAS. On affine BBOB-derived selector tasks for Differential Evolution (DE) and Particle Swarm Optimization (PSO) at a fixed evaluation budget, we report mean plus or minus standard deviation selector profiles over 50 independent random seeds for stochastic configurations. Multi-kernel clustering obtains the strongest mean profile on the DE portfolio and remains competitive with, and nominally ahead of, the leading baselines on the more compressed PSO portfolio, where differences among the best methods are small relative to stochastic variation. In representative median-seed runs used for visualization, the learned kernel weights retain ELA and TransOptAS while assigning zero weight to DeepELA and DoE2Vec, providing a task-specific interpretation of which representations are retained by the multi-kernel model for selector-oriented grouping.

cs.LG↗

arXiv2026

Discovering Interpretable Multi-Parameter Control Policies for Evolutionary Algorithms Using Deep Reinforcement Learning

While deep Reinforcement Learning (deep-RL) has been increasingly applied to parameter control in evolutionary algorithms, rigorous theoretical analysis of parameter control remains largely restricted to single-parameter settings, owing to the difficulty of deriving effective, interpretable multi-parameter policies amenable to formal study. We demonstrate how deep-RL can be leveraged to overcome this barrier, using the (1+($\lambda$,$\lambda$))-genetic algorithm optimizing OneMax, one of the few problems where a super-constant speedup of dynamic control has been formally proven, as a representative case study. We first show that standard approaches struggle to converge in this multi-parameter setting, and introduce algorithm-agnostic enhancements targeting action-space decomposition, reward shifting, and long-horizon discounting. With these in place, we compare common deep-RL methods and find that Double Deep Q-Networks uniquely avoid the policy collapse observed in Proximal Policy Optimization, yielding trajectories suitable for downstream analysis. Crucially, we move beyond the ``black-box'' nature of neural networks by distilling the learned behaviors into a transparent, symbolic control policy. This resulting policy does not only offer interpretability for future theoretical analysis but also yields exceptional performance, consistently outperforming existing baselines across a wide range of problem sizes.

cs.LG↗

arXiv2026

On the Structural (Dis)Agreement of Landscape Representations in Black-Box Optimization

Landscape feature representations play a central role in automated algorithm selection and meta-learning for black-box optimization, yet little is known about how different representations agree (or disagree) in the structures they impose on problem spaces. This paper presents a systematic unsupervised evaluation of four state-of-the-art representations (ELA, DeepELA, TransOptAS, and DoE2Vec) using a diverse set of affine combinations of BBOB functions (MA-BBOB). By applying extensive clustering analyses, coverage-based stability measures, and cross-representation similarity assessments, we show that each representation organizes the same problems in markedly different ways: ELA and TransOptAS form compact geometric structures, DeepELA provides a balanced intermediate view, and DoE2Vec achieves strong semantic alignment but with substantial fragmentation. Our results reveal that no single representation dominates; rather, they capture complementary aspects of the underlying landscapes. These findings highlight the importance of multi-view analyses for understanding representation behavior and offer guidance on selecting or combining representations in downstream meta-learning and algorithm selection tasks. In addition, across two different algorithm families (Differential Evolution and Particle Swarm Optimization), we show that landscape representations face an inherent trade-off in how well they align structural landscape descriptions with observed performance, indicating that no single representation can fully capture algorithm performance.

cs.NE↗

arXiv2026

Similarity-based Portfolio Construction for Black-box Optimization

In black-box optimization, a central question is which algorithm to use to solve a given, previously unseen, problem. Selecting a single algorithm, however, entails inherent risks: inaccuracies in the selector may lead to poor choices, and even well-performing algorithms with high variance can yield unsatisfactory results in a single run. A natural remedy is to split the evaluation budget across multiple runs of potentially different algorithms. Such sequential algorithm portfolios benefit from variance reduction and complementarities between algorithms, often outperforming approaches that allocate the entire budget to a single solver. While effective portfolios can be constructed post-hoc, transferring this idea to the algorithm selection setting is non-trivial. We show that a naive portfolio constructed over the full training set already outperforms the strongest traditional baseline, the virtual best solver. We then propose a simple yet effective k-nearest-neighbor-based finetuning approach to construct portfolios tailored to unseen instances, yielding further improvements and highlighting the effectiveness of portfolio selection in fixed-budget black-box optimization.

cs.NE↗

arXiv2026

When Switching Algorithms Helps: A Theoretical Study of Online Algorithm Selection

Online algorithm selection (OAS) aims to adapt the optimization process to changes in the fitness landscape and is expected to outperform any single algorithm from a given portfolio. Although this expectation is supported by numerous empirical studies, there are currently no theoretical results proving that OAS can yield asymptotic speedups (apart from some artificial examples for hyper-heuristics). Moreover, theory-based guidelines for when and how to switch between algorithms are largely missing. In this paper, we present the first theoretical example in which switching between two algorithms -- the $(1+\lambda)$ EA and the $(1+(\lambda,\lambda))$ GA -- solves the OneMax problem asymptotically faster than either algorithm used in isolation. We show that an appropriate choice of population sizes for the two algorithms allows the optimum to be reached in $O(n\log\log n)$ expected time, faster than the $\Theta(n\sqrt{\frac{\log n \log\log\log n}{\log\log n}})$ runtime of the best of these two algorithms with optimally tuned parameters. We first establish this bound under an idealized switching rule that changes from the $(1+\lambda)$ to the $(1+(\lambda,\lambda))$ GA at the optimal time. We then propose a realistic switching strategy that achieves the same performance. Our analysis combines fixed-start and fixed-target perspectives, illustrating how different algorithms dominate at different stages of the optimization process. This approach offers a promising path toward a deeper theoretical understanding of OAS.

cs.NE↗

arXiv2026

Finding Low Star Discrepancy 3D Kronecker Point Sets Using Algorithm Configuration Techniques

The L infinity star discrepancy is a measure for how uniformly a point set is distributed in a given space. Point sets of low star discrepancy are used as designs of experiments, as initial designs for Bayesian optimization algorithms, for quasi-Monte Carlo integration methods, and many other applications. Recent work has shown that classical constructions such as Sobol', Halton, or Hammersley sequences can be outperformed by large margins when considering point sets of fixed sizes rather than their convergence behavior. These results, highly relevant to the aforementioned applications, raise the question of how much existing constructions can be improved through size-specific optimization. In this work, we study this question for the so-called Kronecker construction. Focusing on the 3-dimensional setting, we show that optimizing the two configurable parameters of its construction yields point sets outperforming the state-of-the-art value for sets of at least 500 points. Using the algorithm configuration technique irace, we then derive parameters that yield new state-of-the-art discrepancy values for whole ranges of set sizes.

cs.NE↗

arXiv2026

How Sequential Algorithm Portfolios can benefit Black Box Optimization

In typical black-box optimization applications, the available computational budget is often allocated to a single algorithm, typically chosen based on user preference with limited knowledge about the problem at hand or according to some expert knowledge. However, we show that splitting the budget across several algorithms yield significantly better results. This approach benefits from both algorithm complementarity across diverse problems and variance reduction within individual functions, and shows that algorithm portfolios do NOT require parallel evaluation capabilities. To demonstrate the advantage of sequential algorithm portfolios, we apply it to the COCO data archive, using over 200 algorithms evaluated on the BBOB test suite. The proposed sequential portfolios consistently outperform single-algorithm baselines, achieving relative performance gains of over 14%, and offering new insights into restart mechanisms and potential for warm-started execution strategies.

cs.NE↗

arXiv2025

Deep Reinforcement Learning for Dynamic Algorithm Configuration: A Case Study on Optimizing OneMax with the (1+($\lambda$,$\lambda$))-GA

Dynamic Algorithm Configuration (DAC) studies the efficient identification of control policies for parameterized optimization algorithms. Numerous studies leverage Reinforcement Learning (RL) to address DAC challenges; however, applying RL often requires extensive domain expertise. In this work, we conduct a comprehensive study of two deep-RL algorithms--Double Deep Q-Networks (DDQN) and Proximal Policy Optimization (PPO)--for controlling the population size of the $(1+(\lambda,\lambda))$-GA on OneMax instances. Although OneMax is structurally simple, learning effective control policies for the $(1+(\lambda,\lambda))$-GA induces a highly challenging DAC landscape, making it a controlled yet demanding benchmark. Our investigation reveals two fundamental challenges limiting DDQN and PPO: scalability degradation and learning instability, traced to under-exploration and planning horizon coverage. To address under-exploration, we introduce an adaptive reward shifting mechanism that leverages reward distribution statistics to enhance DDQN exploration. This eliminates instance-specific hyperparameter tuning and ensures consistent effectiveness across problem scales. To resolve planning horizon coverage, we demonstrate that undiscounted learning succeeds in DDQN, while PPO faces fundamental variance issues necessitating alternative designs. We further show that while hyperparameter optimization enhances PPO's stability, it consistently fails to identify effective policies. Finally, DDQN with adaptive reward shifting achieves performance comparable to theoretically derived policies with vastly improved sample efficiency, outperforming prior DAC approaches by orders of magnitude. Our findings provide insights into the fundamental obstacles faced by standard deep-RL approaches in this challenging DAC setting and highlight the key methodological ingredients required for effective learning.

cs.LG↗

arXiv2025

MECHBench: A Set of Black-Box Optimization Benchmarks originated from Structural Mechanics

Benchmarking is essential for developing and evaluating black-box optimization algorithms, providing a structured means to analyze their search behavior. Its effectiveness relies on carefully selected problem sets used for evaluation. To date, most established benchmark suites for black-box optimization consist of abstract or synthetic problems that only partially capture the complexities of real-world engineering applications, thereby severely limiting the insights that can be gained for application-oriented optimization scenarios and reducing their practical impact. To close this gap, we propose a new benchmarking suite that addresses it by presenting a curated set of optimization benchmarks rooted in structural mechanics. The current implemented benchmarks are derived from vehicle crashworthiness scenarios, which inherently require the use of gradient-free algorithms due to the non-smooth, highly non-linear nature of the underlying models. Within this paper, the reader will find descriptions of the physical context of each case, the corresponding optimization problem formulations, and clear guidelines on how to employ the suite.

cs.NE↗

arXiv2025

Optimizing Kernel Discrepancies via Subset Selection

Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of kernel discrepancies, selecting an m-element subset from a large population of size $n \gg m$. We introduce a novel subset selection algorithm applicable to general kernel discrepancies to efficiently generate low-discrepancy samples from both the uniform distribution on the unit hypercube, the traditional setting of classical QMC, and from more general distributions $F$ with known density functions by employing the kernel Stein discrepancy. We also explore the relationship between the classical $L_2$ star discrepancy and its $L_\infty$ counterpart.

stat.ML↗

arXiv2025

Enhancing Parameter Control Policies with State Information

Parameter control and dynamic algorithm configuration study how to dynamically choose suitable configurations of a parametrized algorithm during the optimization process. Despite being an intensively researched topic in evolutionary computation, optimal control policies are known only for very few cases, limiting the development of automated approaches to achieve them. With this work we propose four new benchmarks for which we derive optimal or close-to-optimal control policies. More precisely, we consider the optimization of the \LeadingOnes function via RLS$_{k}$, a local search algorithm allowing for a dynamic choice of the mutation strength $k$. The benchmarks differ in which information the algorithm can exploit to set its parameters and to select offspring. In existing running time results, the exploitable information is typically limited to the quality of the current-best solution. In this work, we consider how additional information about the current state of the algorithm can help to make better choices of parameters, and how these choices affect the performance. Namely, we allow the algorithm to use information about the current \OneMax value, and we find that it allows much better parameter choices, especially in marginal states. Although those states are rarely visited by the algorithm, such policies yield a notable speed-up in terms of expected runtime. This makes the proposed benchmarks a challenging, but promising testing ground for analysis of parameter control methods in rich state spaces and of their ability to find optimal policies by catching the performance improvements yielded by correct parameter choices.

cs.NE↗

arXiv2025

Geometric Learning in Black-Box Optimization: A GNN Framework for Algorithm Performance Prediction

Automated algorithm performance prediction in numerical blackbox optimization often relies on problem characterizations, such as exploratory landscape analysis features. These features are typically used as inputs to machine learning models and are represented in a tabular format. However, such approaches often overlook algorithm configurations, a key factor influencing performance. The relationships between algorithm operators, parameters, problem characteristics, and performance outcomes form a complex structure best represented as a graph. This work explores the use of heterogeneous graph data structures and graph neural networks to predict the performance of optimization algorithms by capturing the complex dependencies between problems, algorithm configurations, and performance outcomes. We focus on two modular frameworks, modCMA-ES and modDE, which decompose two widely used derivative-free optimization algorithms: the covariance matrix adaptation evolution strategy (CMA-ES) and differential evolution (DE). We evaluate 324 modCMA-ES and 576 modDE variants on 24 BBOB problems across six runtime budgets and two problem dimensions. Achieving up to 36.6% improvement in MSE over traditional tabular-based methods, this work highlights the potential of geometric learning in black-box optimization.

cs.AI↗

arXiv2025

carps: A Framework for Comparing N Hyperparameter Optimizers on M Benchmarks

Hyperparameter Optimization (HPO) is crucial to develop well-performing machine learning models. In order to ease prototyping and benchmarking of HPO methods, we propose carps, a benchmark framework for Comprehensive Automated Research Performance Studies allowing to evaluate N optimizers on M benchmark tasks. In this first release of carps, we focus on the four most important types of HPO task types: blackbox, multi-fidelity, multi-objective and multi-fidelity-multi-objective. With 3 336 tasks from 5 community benchmark collections and 28 variants of 9 optimizer families, we offer the biggest go-to library to date to evaluate and compare HPO methods. The carps framework relies on a purpose-built, lightweight interface, gluing together optimizers and benchmark tasks. It also features an analysis pipeline, facilitating the evaluation of optimizers on benchmarks. However, navigating a huge number of tasks while developing and comparing methods can be computationally infeasible. To address this, we obtain a subset of representative tasks by minimizing the star discrepancy of the subset, in the space spanned by the full set. As a result, we propose an initial subset of 10 to 30 diverse tasks for each task type, and include functionality to re-compute subsets as more benchmarks become available, enabling efficient evaluations. We also establish a first set of baseline results on these tasks as a measure for future comparisons. With carps (https://www.github.com/automl/CARP-S), we make an important step in the standardization of HPO evaluation.

cs.LG↗

arXiv2025

Multi-parameter Control for the $(1+(\lambda,\lambda))$-GA on OneMax via Deep Reinforcement Learning

It is well known that evolutionary algorithms can benefit from dynamic choices of the key parameters that control their behavior, to adjust their search strategy to the different stages of the optimization process. A prominent example where dynamic parameter choices have shown a provable super-constant speed-up is the $(1+(\lambda,\lambda))$ Genetic Algorithm optimizing the OneMax function. While optimal parameter control policies result in linear expected running times, this is not possible with static parameter choices. This result has spurred a lot of interest in parameter control policies. However, many works, in particular theoretical running time analyses, focus on controlling one single parameter. Deriving policies for controlling multiple parameters remains very challenging. In this work we reconsider the problem of the $(1+(\lambda,\lambda))$ Genetic Algorithm optimizing OneMax. We decouple its four main parameters and investigate how well state-of-the-art deep reinforcement learning techniques can approximate good control policies. We show that although making deep reinforcement learning learn effectively is a challenging task, once it works, it is very powerful and is able to find policies that outperform all previously known control policies on the same benchmark. Based on the results found through reinforcement learning, we derive a simple control policy that consistently outperforms the default theory-recommended setting by $27\%$ and the irace-tuned policy, the strongest existing control policy on this benchmark, by $13\%$, for all tested problem sizes up to $40{,}000$.

cs.LG↗

arXiv2025

On the Importance of Reward Design in Reinforcement Learning-based Dynamic Algorithm Configuration: A Case Study on OneMax with (1+($\lambda$,$\lambda$))-GA

Dynamic Algorithm Configuration (DAC) has garnered significant attention in recent years, particularly in the prevalence of machine learning and deep learning algorithms. Numerous studies have leveraged the robustness of decision-making in Reinforcement Learning (RL) to address the optimization challenges associated with algorithm configuration. However, making an RL agent work properly is a non-trivial task, especially in reward design, which necessitates a substantial amount of handcrafted knowledge based on domain expertise. In this work, we study the importance of reward design in the context of DAC via a case study on controlling the population size of the $(1+(\lambda,\lambda))$-GA optimizing OneMax. We observed that a poorly designed reward can hinder the RL agent's ability to learn an optimal policy because of a lack of exploration, leading to both scalability and learning divergence issues. To address those challenges, we propose the application of a reward shaping mechanism to facilitate enhanced exploration of the environment by the RL agent. Our work not only demonstrates the ability of RL in dynamically configuring the $(1+(\lambda,\lambda))$-GA, but also confirms the advantages of reward shaping in the scalability of RL agents across various sizes of OneMax problems.

cs.LG↗

arXiv2025

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.

cs.NE↗

arXiv2024

MO-IOHinspector: Anytime Benchmarking of Multi-Objective Algorithms using IOHprofiler

Benchmarking is one of the key ways in which we can gain insight into the strengths and weaknesses of optimization algorithms. In sampling-based optimization, considering the anytime behavior of an algorithm can provide valuable insights for further developments. In the context of multi-objective optimization, this anytime perspective is not as widely adopted as in the single-objective context. In this paper, we propose a new software tool which uses principles from unbounded archiving as a logging structure. This leads to a clearer separation between experimental design and subsequent analysis decisions. We integrate this approach as a new Python module into the IOHprofiler framework and demonstrate the benefits of this approach by showcasing the ability to change indicators, aggregations, and ranking procedures during the analysis pipeline.

cs.NE↗

arXiv2024

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 they have been 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 understand the capability of off-the-shelf algorithms to quantify the trade-off between the minimum pairwise distance within batches of solutions and their average quality. We also analyze how this trade-off depends on the properties of the underlying optimization problem. 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.

cs.LG↗