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Carola Doerr

Publications and source records attributed to Carola Doerr.

At least 55 records · Page 3Linked to original sources
arXiv2023

Using Automated Algorithm Configuration for Parameter Control

Dynamic Algorithm Configuration (DAC) tackles the question of how to automatically learn policies to control parameters of algorithms in a data-driven fashion. This question has received considerable attention from the evolutionary community in recent years. Having a good benchmark collection to gain structural understanding on the effectiveness and limitations of different solution methods for DAC is therefore strongly desirable. Following recent work on proposing DAC benchmarks with well-understood theoretical properties and ground truth information, in this work, we suggest as a new DAC benchmark the controlling of the key parameter $λ$ in the $(1+(λ,λ))$~Genetic Algorithm for solving OneMax problems. We conduct a study on how to solve the DAC problem via the use of (static) automated algorithm configuration on the benchmark, and propose techniques to significantly improve the performance of the approach. Our approach is able to consistently outperform the default parameter control policy of the benchmark derived from previous theoretical work on sufficiently large problem sizes. We also present new findings on the landscape of the parameter-control search policies and propose methods to compute stronger baselines for the benchmark via numerical approximations of the true optimal policies.

cs.LG↗
arXiv2023

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.

cs.LG↗
arXiv2023

Comparing Algorithm Selection Approaches on Black-Box Optimization Problems

Performance complementarity of solvers available to tackle black-box optimization problems gives rise to the important task of algorithm selection (AS). Automated AS approaches can help replace tedious and labor-intensive manual selection, and have already shown promising performance in various optimization domains. Automated AS relies on machine learning (ML) techniques to recommend the best algorithm given the information about the problem instance. Unfortunately, there are no clear guidelines for choosing the most appropriate one from a variety of ML techniques. Tree-based models such as Random Forest or XGBoost have consistently demonstrated outstanding performance for automated AS. Transformers and other tabular deep learning models have also been increasingly applied in this context. We investigate in this work the impact of the choice of the ML technique on AS performance. We compare four ML models on the task of predicting the best solver for the BBOB problems for 7 different runtime budgets in 2 dimensions. While our results confirm that a per-instance AS has indeed impressive potential, we also show that the particular choice of the ML technique is of much minor importance.

cs.NE↗
arXiv2023

Computing Star Discrepancies with Numerical Black-Box Optimization Algorithms

The $L_{\infty}$ star discrepancy is a measure for the regularity of a finite set of points taken from $[0,1)^d$. Low discrepancy point sets are highly relevant for Quasi-Monte Carlo methods in numerical integration and several other applications. Unfortunately, computing the $L_{\infty}$ star discrepancy of a given point set is known to be a hard problem, with the best exact algorithms falling short for even moderate dimensions around 8. However, despite the difficulty of finding the global maximum that defines the $L_{\infty}$ star discrepancy of the set, local evaluations at selected points are inexpensive. This makes the problem tractable by black-box optimization approaches. In this work we compare 8 popular numerical black-box optimization algorithms on the $L_{\infty}$ star discrepancy computation problem, using a wide set of instances in dimensions 2 to 15. We show that all used optimizers perform very badly on a large majority of the instances and that in many cases random search outperforms even the more sophisticated solvers. We suspect that state-of-the-art numerical black-box optimization techniques fail to capture the global structure of the problem, an important shortcoming that may guide their future development. We also provide a parallel implementation of the best-known algorithm to compute the discrepancy.

cs.NE↗
arXiv2023

MA-BBOB: Many-Affine Combinations of BBOB Functions for Evaluating AutoML Approaches in Noiseless Numerical Black-Box Optimization Contexts

Extending a recent suggestion to generate new instances for numerical black-box optimization benchmarking by interpolating pairs of the well-established BBOB functions from the COmparing COntinuous Optimizers (COCO) platform, we propose in this work a further generalization that allows multiple affine combinations of the original instances and arbitrarily chosen locations of the global optima. We demonstrate that the MA-BBOB generator can help fill the instance space, while overall patterns in algorithm performance are preserved. By combining the landscape features of the problems with the performance data, we pose the question of whether these features are as useful for algorithm selection as previous studies suggested. MA-BBOB is built on the publicly available IOHprofiler platform, which facilitates standardized experimentation routines, provides access to the interactive IOHanalyzer module for performance analysis and visualization, and enables comparisons with the rich and growing data collection available for the (MA-)BBOB functions.

cs.LG↗
arXiv2023

DynamoRep: Trajectory-Based Population Dynamics for Classification of Black-box Optimization Problems

The application of machine learning (ML) models to the analysis of optimization algorithms requires the representation of optimization problems using numerical features. These features can be used as input for ML models that are trained to select or to configure a suitable algorithm for the problem at hand. Since in pure black-box optimization information about the problem instance can only be obtained through function evaluation, a common approach is to dedicate some function evaluations for feature extraction, e.g., using random sampling. This approach has two key downsides: (1) It reduces the budget left for the actual optimization phase, and (2) it neglects valuable information that could be obtained from a problem-solver interaction. In this paper, we propose a feature extraction method that describes the trajectories of optimization algorithms using simple descriptive statistics. We evaluate the generated features for the task of classifying problem classes from the Black Box Optimization Benchmarking (BBOB) suite. We demonstrate that the proposed DynamoRep features capture enough information to identify the problem class on which the optimization algorithm is running, achieving a mean classification accuracy of 95% across all experiments.

cs.LG↗
arXiv2023

Algorithm Instance Footprint: Separating Easily Solvable and Challenging Problem Instances

In black-box optimization, it is essential to understand why an algorithm instance works on a set of problem instances while failing on others and provide explanations of its behavior. We propose a methodology for formulating an algorithm instance footprint that consists of a set of problem instances that are easy to be solved and a set of problem instances that are difficult to be solved, for an algorithm instance. This behavior of the algorithm instance is further linked to the landscape properties of the problem instances to provide explanations of which properties make some problem instances easy or challenging. The proposed methodology uses meta-representations that embed the landscape properties of the problem instances and the performance of the algorithm into the same vector space. These meta-representations are obtained by training a supervised machine learning regression model for algorithm performance prediction and applying model explainability techniques to assess the importance of the landscape features to the performance predictions. Next, deterministic clustering of the meta-representations demonstrates that using them captures algorithm performance across the space and detects regions of poor and good algorithm performance, together with an explanation of which landscape properties are leading to it.

cs.NE↗
arXiv2023

Assessing the Generalizability of a Performance Predictive Model

A key component of automated algorithm selection and configuration, which in most cases are performed using supervised machine learning (ML) methods is a good-performing predictive model. The predictive model uses the feature representation of a set of problem instances as input data and predicts the algorithm performance achieved on them. Common machine learning models struggle to make predictions for instances with feature representations not covered by the training data, resulting in poor generalization to unseen problems. In this study, we propose a workflow to estimate the generalizability of a predictive model for algorithm performance, trained on one benchmark suite to another. The workflow has been tested by training predictive models across benchmark suites and the results show that generalizability patterns in the landscape feature space are reflected in the performance space.

cs.LG↗
arXiv2023

Sensitivity Analysis of RF+clust for Leave-one-problem-out Performance Prediction

Leave-one-problem-out (LOPO) performance prediction requires machine learning (ML) models to extrapolate algorithms' performance from a set of training problems to a previously unseen problem. LOPO is a very challenging task even for state-of-the-art approaches. Models that work well in the easier leave-one-instance-out scenario often fail to generalize well to the LOPO setting. To address the LOPO problem, recent work suggested enriching standard random forest (RF) performance regression models with a weighted average of algorithms' performance on training problems that are considered similar to a test problem. More precisely, in this RF+clust approach, the weights are chosen proportionally to the distances of the problems in some feature space. Here in this work, we extend the RF+clust approach by adjusting the distance-based weights with the importance of the features for performance regression. That is, instead of considering cosine distance in the feature space, we consider a weighted distance measure, with weights depending on the relevance of the feature for the regression model. Our empirical evaluation of the modified RF+clust approach on the CEC 2014 benchmark suite confirms its advantages over the naive distance measure. However, we also observe room for improvement, in particular with respect to more expressive feature portfolios.

cs.LG↗
arXiv2023

Automated Algorithm Selection for Radar Network Configuration

The configuration of radar networks is a complex problem that is often performed manually by experts with the help of a simulator. Different numbers and types of radars as well as different locations that the radars shall cover give rise to different instances of the radar configuration problem. The exact modeling of these instances is complex, as the quality of the configurations depends on a large number of parameters, on internal radar processing, and on the terrains on which the radars need to be placed. Classic optimization algorithms can therefore not be applied to this problem, and we rely on "trial-and-error" black-box approaches. In this paper, we study the performances of 13 black-box optimization algorithms on 153 radar network configuration problem instances. The algorithms perform considerably better than human experts. Their ranking, however, depends on the budget of configurations that can be evaluated and on the elevation profile of the location. We therefore also investigate automated algorithm selection approaches. Our results demonstrate that a pipeline that extracts instance features from the elevation of the terrain performs on par with the classical, far more expensive approach that extracts features from the objective function.

cs.NE↗
arXiv2023

Using Affine Combinations of BBOB Problems for Performance Assessment

Benchmarking plays a major role in the development and analysis of optimization algorithms. As such, the way in which the used benchmark problems are defined significantly affects the insights that can be gained from any given benchmark study. One way to easily extend the range of available benchmark functions is through affine combinations between pairs of functions. From the perspective of landscape analysis, these function combinations smoothly transition between the two base functions. In this work, we show how these affine function combinations can be used to analyze the behavior of optimization algorithms. In particular, we highlight that by varying the weighting between the combined problems, we can gain insights into the effects of added global structure on the performance of optimization algorithms. By analyzing performance trajectories on more function combinations, we also show that aspects such as the scaling of objective functions and placement of the optimum can greatly impact how these results are interpreted.

cs.NE↗
arXiv2023

RF+clust for Leave-One-Problem-Out Performance Prediction

Per-instance automated algorithm configuration and selection are gaining significant moments in evolutionary computation in recent years. Two crucial, sometimes implicit, ingredients for these automated machine learning (AutoML) methods are 1) feature-based representations of the problem instances and 2) performance prediction methods that take the features as input to estimate how well a specific algorithm instance will perform on a given problem instance. Non-surprisingly, common machine learning models fail to make predictions for instances whose feature-based representation is underrepresented or not covered in the training data, resulting in poor generalization ability of the models for problems not seen during training.In this work, we study leave-one-problem-out (LOPO) performance prediction. We analyze whether standard random forest (RF) model predictions can be improved by calibrating them with a weighted average of performance values obtained by the algorithm on problem instances that are sufficiently close to the problem for which a performance prediction is sought, measured by cosine similarity in feature space. While our RF+clust approach obtains more accurate performance prediction for several problems, its predictive power crucially depends on the chosen similarity threshold as well as on the feature portfolio for which the cosine similarity is measured, thereby opening a new angle for feature selection in a zero-shot learning setting, as LOPO is termed in machine learning.

cs.NE↗
arXiv2023

Using Knowledge Graphs for Performance Prediction of Modular Optimization Algorithms

Empirical data plays an important role in evolutionary computation research. To make better use of the available data, ontologies have been proposed in the literature to organize their storage in a structured way. However, the full potential of these formal methods to capture our domain knowledge has yet to be demonstrated. In this work, we evaluate a performance prediction model built on top of the extension of the recently proposed OPTION ontology. More specifically, we first extend the OPTION ontology with the vocabulary needed to represent modular black-box optimization algorithms. Then, we use the extended OPTION ontology, to create knowledge graphs with fixed-budget performance data for two modular algorithm frameworks, modCMA, and modDE, for the 24 noiseless BBOB benchmark functions. We build the performance prediction model using a knowledge graph embedding-based methodology. Using a number of different evaluation scenarios, we show that a triple classification approach, a fairly standard predictive modeling task in the context of knowledge graphs, can correctly predict whether a given algorithm instance will be able to achieve a certain target precision for a given problem instance. This approach requires feature representation of algorithms and problems. While the latter is already well developed, we hope that our work will motivate the community to collaborate on appropriate algorithm representations.

cs.NE↗
arXiv2023

Switching between Numerical Black-box Optimization Algorithms with Warm-starting Policies

When solving optimization problems with black-box approaches, the algorithms gather valuable information about the problem instance during the optimization process. This information is used to adjust the distributions from which new solution candidates are sampled. In fact, a key objective in evolutionary computation is to identify the most effective ways to collect and exploit instance knowledge. However, while considerable work is devoted to adjusting hyper-parameters of black-box optimization algorithms on the fly or exchanging some of its modular components, we barely know how to effectively switch between different black-box optimization algorithms. In this work, we build on the recent study of Vermetten et al. [GECCO 2020], who presented a data-driven approach to investigate promising switches between pairs of algorithms for numerical black-box optimization. We replicate their approach with a portfolio of five algorithms and investigate whether the predicted performance gains are realized when executing the most promising switches. Our results suggest that with a single switch between two algorithms, we outperform the best static choice among the five algorithms on 48 out of the 120 considered problem instances, the 24 BBOB functions in five different dimensions. We also show that for switching between BFGS and CMA-ES, a proper warm-starting of the parameters is crucial to realize high-performance gains. Lastly, with a sensitivity analysis, we find the actual performance gain per run is largely affected by the switching point, and in some cases, the switching point yielding the best actual performance differs from the one computed from the theoretical gain.

cs.NE↗
arXiv2022

Explainable Model-specific Algorithm Selection for Multi-Label Classification

Multi-label classification (MLC) is an ML task of predictive modeling in which a data instance can simultaneously belong to multiple classes. MLC is increasingly gaining interest in different application domains such as text mining, computer vision, and bioinformatics. Several MLC algorithms have been proposed in the literature, resulting in a meta-optimization problem that the user needs to address: which MLC approach to select for a given dataset? To address this algorithm selection problem, we investigate in this work the quality of an automated approach that uses characteristics of the datasets - so-called features - and a trained algorithm selector to choose which algorithm to apply for a given task. For our empirical evaluation, we use a portfolio of 38 datasets. We consider eight MLC algorithms, whose quality we evaluate using six different performance metrics. We show that our automated algorithm selector outperforms any of the single MLC algorithms, and this is for all evaluated performance measures. Our selection approach is explainable, a characteristic that we exploit to investigate which meta-features have the largest influence on the decisions made by the algorithm selector. Finally, we also quantify the importance of the most significant meta-features for various domains.

cs.LG↗
arXiv2022

OPTION: OPTImization Algorithm Benchmarking ONtology

Many optimization algorithm benchmarking platforms allow users to share their experimental data to promote reproducible and reusable research. However, different platforms use different data models and formats, which drastically complicates the identification of relevant datasets, their interpretation, and their interoperability. Therefore, a semantically rich, ontology-based, machine-readable data model that can be used by different platforms is highly desirable. In this paper, we report on the development of such an ontology, which we call OPTION (OPTImization algorithm benchmarking ONtology). Our ontology provides the vocabulary needed for semantic annotation of the core entities involved in the benchmarking process, such as algorithms, problems, and evaluation measures. It also provides means for automatic data integration, improved interoperability, and powerful querying capabilities, thereby increasing the value of the benchmarking data. We demonstrate the utility of OPTION, by annotating and querying a corpus of benchmark performance data from the BBOB collection of the COCO framework and from the Yet Another Black-Box Optimization Benchmark (YABBOB) family of the Nevergrad environment. In addition, we integrate features of the BBOB functional performance landscape into the OPTION knowledge base using publicly available datasets with exploratory landscape analysis. Finally, we integrate the OPTION knowledge base into the IOHprofiler environment and provide users with the ability to perform meta-analysis of performance data.

cs.AI↗
arXiv2022

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 naïve 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.

cs.LG↗
arXiv2022

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.

cs.LG↗