arXiv subjects

Juergen Branke

Publications and source records attributed to Juergen Branke.

At least 19 recordsLinked to original sources

arXiv2026

How much Data do We Need? Sequential Data Collection for Stochastic Programming

Data-driven optimization often requires collecting data to estimate uncertain model parameters before solving the underlying decision problem. In practice, however, data acquisition may incur non-negligible costs, making it critical to determine when to stop additional data collection. In this paper, we study an optimal stopping problem for sequential data collection in stochastic optimization under parameter uncertainty. We propose a benefit-driven stopping framework that balances information gain and sampling cost. We model the unknown distribution parameter within a Bayesian learning framework and update beliefs sequentially as new observations are collected. At each iteration, the decision maker evaluates the expected marginal benefit of additional data relative to the unit sampling cost and determines whether to continue sampling or stop and implement the optimization decision. Based on this framework, we develop several stopping policies. The proposed policies are evaluated through a newsvendor problem with exponentially distributed demand. Numerical experiments compare the policies with fixed-budget and hindsight benchmark strategies. The results show that benefit-driven stopping rules can substantially reduce unnecessary data collection while achieving near-optimal decision performance, demonstrating the effectiveness of adaptive stopping in data-driven optimization.

math.OC↗

arXiv2026

Annealed Entropic Allocation for Ranking and Selection

We propose annealed entropic allocation, an adaptive sampling policy based on an annealed, weighted soft-min formulation of static budget allocation. We replace the maximin large-deviation rate objective with a weighted log-sum-exp surrogate that blends challenger-specific pairwise scores through soft-min weights, avoiding hard switching when several challengers are nearly active. To capture tail behavior beyond the leading exponent, the surrogate incorporates saddlepoint prefactors from refined pairwise tail asymptotics. Because these corrections are subexponential, decreasing the annealing temperature with the budget preserves the same first-order target allocation. For the static problem, we prove uniform convergence to the hard minimum, concentration of soft-min weights on active challengers, and continuity of the induced target-allocation map under fixed weights. Experiments show that the proposed methods are consistently competitive: the no-saddlepoint ablation performs best in symmetric Gaussian and exponential slippage settings, while saddlepoint weighting can help in heterogeneous or asymmetric cases.

stat.ML↗

arXiv2026

Maximizing Reliability with Bayesian Optimization

Bayesian optimization (BO) is a popular, sample-efficient technique for expensive, black-box optimization. One such problem arising in manufacturing is that of maximizing the reliability, or equivalently minimizing the probability of a failure, of a design which is subject to random perturbations - a problem that can involve extremely rare failures ($P_\mathrm{fail} = 10^{-6}-10^{-8}$). In this work, we propose two BO methods based on Thompson sampling and knowledge gradient, the latter approximating the one-step Bayes-optimal policy for minimizing the logarithm of the failure probability. Both methods incorporate importance sampling to target extremely small failure probabilities. Empirical results show the proposed methods outperform existing methods in both extreme and non-extreme regimes.

cs.LG↗

arXiv2026

Bayesian Optimization with Preference Exploration using a Monotonic Neural Network Ensemble

Many real-world black-box optimization problems have multiple conflicting objectives. Rather than attempting to approximate the entire set of Pareto-optimal solutions, interactive preference learning allows to focus the search on the most relevant subset. However, few previous studies have exploited the fact that utility functions are usually monotonic. In this paper, we address the Bayesian Optimization with Preference Exploration (BOPE) problem and propose using a neural network ensemble as a utility surrogate model. This approach naturally integrates monotonicity and supports pairwise comparison data. Our experiments demonstrate that the proposed method outperforms state-of-the-art approaches and exhibits robustness to noise in utility evaluations. An ablation study highlights the critical role of monotonicity in enhancing performance.

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arXiv2025

Bayesian Optimisation: Which Constraints Matter?

Bayesian optimisation has proven to be a powerful tool for expensive global black-box optimisation problems. In this paper, we propose new Bayesian optimisation variants of the popular Knowledge Gradient acquisition functions for problems with \emph{decoupled} black-box constraints, in which subsets of the objective and constraint functions may be evaluated independently. In particular, our methods aim to take into account that often only a handful of the constraints may be binding at the optimum, and hence we should evaluate only relevant constraints when trying to optimise a function. We empirically benchmark these methods against existing methods and demonstrate their superiority over the state-of-the-art.

cs.LG↗

arXiv2025

Learning in Repeated Multi-Objective Stackelberg Games with Payoff Manipulation

We study payoff manipulation in repeated multi-objective Stackelberg games, where a leader may strategically influence a follower's deterministic best response, e.g., by offering a share of their own payoff. We assume that the follower's utility function, representing preferences over multiple objectives, is unknown but linear, and its weight parameter must be inferred through interaction. This introduces a sequential decision-making challenge for the leader, who must balance preference elicitation with immediate utility maximisation. We formalise this problem and propose manipulation policies based on expected utility (EU) and long-term expected utility (longEU), which guide the leader in selecting actions and offering incentives that trade off short-term gains with long-term impact. We prove that under infinite repeated interactions, longEU converges to the optimal manipulation. Empirical results across benchmark environments demonstrate that our approach improves cumulative leader utility while promoting mutually beneficial outcomes, all without requiring explicit negotiation or prior knowledge of the follower's utility function.

cs.GT↗

arXiv2025

Respecting the limit:Bayesian optimization with a bound on the optimal value

In many real-world optimization problems, we have prior information about what objective function values are achievable. In this paper, we study the scenario that we have either exact knowledge of the minimum value or a, possibly inexact, lower bound on its value. We propose bound-aware Bayesian optimization (BABO), a Bayesian optimization method that uses a new surrogate model and acquisition function to utilize such prior information. We present SlogGP, a new surrogate model that incorporates bound information and adapts the Expected Improvement (EI) acquisition function accordingly. Empirical results on a variety of benchmarks demonstrate the benefit of taking prior information about the optimal value into account, and that the proposed approach significantly outperforms existing techniques. Furthermore, we notice that even in the absence of prior information on the bound, the proposed SlogGP surrogate model still performs better than the standard GP model in most cases, which we explain by its larger expressiveness.

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arXiv2025

Knowledge Gradient for Multi-Objective Bayesian Optimization with Decoupled Evaluations

Multi-objective Bayesian optimization aims to find the Pareto front of trade-offs between a set of expensive objectives while collecting as few samples as possible. In some cases, it is possible to evaluate the objectives separately, and a different latency or evaluation cost can be associated with each objective. This decoupling of the objectives presents an opportunity to learn the Pareto front faster by avoiding unnecessary, expensive evaluations. We propose a scalarization based knowledge gradient acquisition function which accounts for the different evaluation costs of the objectives. We prove asymptotic consistency of the estimator of the optimum for an arbitrary, D-dimensional, real compact search space and show empirically that the algorithm performs comparably with the state of the art and significantly outperforms versions which always evaluate both objectives.

stat.ML↗

arXiv2025

Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems

Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In the first stage of a two-stage problem, here-and-now decisions must be made in the face of uncertainty, while in the second stage, wait-and-see decisions are made after the uncertainty has been resolved. Many methods in stochastic programming assume that the objective is cheap to evaluate and linear or convex. We apply Bayesian optimization to solve non-convex, two-stage stochastic programs which are black-box and expensive to evaluate as, for example, is often the case with simulation objectives. We formulate a knowledge-gradient-based acquisition function to jointly optimize the first- and second-stage variables, establish a guarantee of asymptotic consistency, and provide a computationally efficient approximation. We demonstrate comparable empirical results to an alternative we formulate with fewer approximations, which alternates its focus between the two variable types, and superior empirical results over the state of the art and the standard, naïve, two-step benchmark.

stat.ML↗

arXiv2024

Bayesian Optimization of Bilevel Problems

Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics, engineering, and machine learning. This paper focuses on bilevel optimization where both upper-level and lower-level functions are black boxes and expensive to evaluate. We propose a Bayesian Optimization framework that models the upper and lower-level functions as Gaussian processes over the combined space of upper and lower-level decisions, allowing us to exploit knowledge transfer between different sub-problems. Additionally, we propose a novel acquisition function for this model. Our experimental results demonstrate that the proposed algorithm is highly sample-efficient and outperforms existing methods in finding high-quality solutions.

cs.LG↗

arXiv2024

EDOLAB: An Open-Source Platform for Education and Experimentation with Evolutionary Dynamic Optimization Algorithms

Many real-world optimization problems exhibit dynamic characteristics, posing significant challenges for traditional optimization techniques. Evolutionary Dynamic Optimization Algorithms (EDOAs) are designed to address these challenges effectively. However, in existing literature, the reported results for a given EDOA can vary significantly. This inconsistency often arises because the source codes for many EDOAs, which are typically complex, have not been made publicly available, leading to error-prone re-implementations. To support researchers in conducting experiments and comparing their algorithms with various EDOAs, we have developed an open-source MATLAB platform called the Evolutionary Dynamic Optimization LABoratory (EDOLAB). This platform not only facilitates research but also includes an educational module designed for instructional purposes. The education module allows users to observe: a) a 2-dimensional problem space and its morphological changes following each environmental change, b) the behaviors of individuals over time, and c) how the EDOA responds to environmental changes and tracks the moving optimum. The current version of EDOLAB features 25 EDOAs and four fully parametric benchmark generators. The MATLAB source code for EDOLAB is publicly available and can be accessed from [https://github.com/Danial-Yazdani/EDOLAB-MATLAB].

cs.NE↗

arXiv2024

Competition on Dynamic Optimization Problems Generated by Generalized Moving Peaks Benchmark (GMPB)

The Generalized Moving Peaks Benchmark (GMPB) is a tool for generating continuous dynamic optimization problem instances with controllable dynamic and morphological characteristics. GMPB has been used in recent Competitions on Dynamic Optimization at prestigious conferences, such as the IEEE Congress on Evolutionary Computation (CEC). This dynamic benchmark generator can create a wide variety of landscapes, ranging from simple unimodal to highly complex multimodal configurations and from symmetric to asymmetric forms. It also supports diverse surface textures, from smooth to highly irregular, and can generate varying levels of variable interaction and conditioning. This document provides an overview of GMPB, emphasizing how its parameters can be adjusted to produce landscapes with customizable characteristics. The MATLAB implementation of GMPB is available on the EDOLAB Platform.

cs.NE↗

arXiv2024

Identifying the Best Arm in the Presence of Global Environment Shifts

This paper formulates a new Best-Arm Identification problem in the non-stationary stochastic bandits setting, where the means of all arms are shifted in the same way due to a global influence of the environment. The aim is to identify the unique best arm across environmental change given a fixed total budget. While this setting can be regarded as a special case of Adversarial Bandits or Corrupted Bandits, we demonstrate that existing solutions tailored to those settings do not fully utilise the nature of this global influence, and thus, do not work well in practice (despite their theoretical guarantees). To overcome this issue, in this paper we develop a novel selection policy that is consistent and robust in dealing with global environmental shifts. We then propose an allocation policy, LinLUCB, which exploits information about global shifts across all arms in each environment. Empirical tests depict a significant improvement in our policies against other existing methods.

cs.LG↗

arXiv2024

Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overview

Hyperparameter optimization constitutes a large part of typical modern machine learning workflows. This arises from the fact that machine learning methods and corresponding preprocessing steps often only yield optimal performance when hyperparameters are properly tuned. But in many applications, we are not only interested in optimizing ML pipelines solely for predictive accuracy; additional metrics or constraints must be considered when determining an optimal configuration, resulting in a multi-objective optimization problem. This is often neglected in practice, due to a lack of knowledge and readily available software implementations for multi-objective hyperparameter optimization. In this work, we introduce the reader to the basics of multi-objective hyperparameter optimization and motivate its usefulness in applied ML. Furthermore, we provide an extensive survey of existing optimization strategies, both from the domain of evolutionary algorithms and Bayesian optimization. We illustrate the utility of MOO in several specific ML applications, considering objectives such as operating conditions, prediction time, sparseness, fairness, interpretability and robustness.

cs.LG↗

arXiv2024

Clustering in Dynamic Environments: A Framework for Benchmark Dataset Generation With Heterogeneous Changes

Clustering in dynamic environments is of increasing importance, with broad applications ranging from real-time data analysis and online unsupervised learning to dynamic facility location problems. While meta-heuristics have shown promising effectiveness in static clustering tasks, their application for tracking optimal clustering solutions or robust clustering over time in dynamic environments remains largely underexplored. This is partly due to a lack of dynamic datasets with diverse, controllable, and realistic dynamic characteristics, hindering systematic performance evaluations of clustering algorithms in various dynamic scenarios. This deficiency leads to a gap in our understanding and capability to effectively design algorithms for clustering in dynamic environments. To bridge this gap, this paper introduces the Dynamic Dataset Generator (DDG). DDG features multiple dynamic Gaussian components integrated with a range of heterogeneous, local, and global changes. These changes vary in spatial and temporal severity, patterns, and domain of influence, providing a comprehensive tool for simulating a wide range of dynamic scenarios.

cs.LG↗

arXiv2024

Bi-objective Ranking and Selection Using Stochastic Kriging

We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto optimal solutions among a finite set of candidates for which the two objective outcomes have been observed with uncertainty (e.g., after running a multiobjective stochastic simulation optimization procedure). When identifying these solutions, the noise perturbing the observed performance may lead to two types of errors: solutions that are truly Pareto-optimal can be wrongly considered dominated, and solutions that are truly dominated can be wrongly considered Pareto-optimal. We propose a novel Bayesian bi-objective ranking and selection method that sequentially allocates extra samples to competitive solutions, in view of reducing the misclassification errors when identifying the solutions with the best expected performance. The approach uses stochastic kriging to build reliable predictive distributions of the objective outcomes, and exploits this information to decide how to resample. Experimental results show that the proposed method outperforms the standard allocation method, as well as a well-known the state-of-the-art algorithm. Moreover, we show that the other competing algorithms also benefit from the use of stochastic kriging information; yet, the proposed method remains superior.

stat.ML↗

arXiv2023

BOP-Elites, a Bayesian Optimisation Approach to Quality Diversity Search with Black-Box descriptor functions

Quality Diversity (QD) algorithms such as MAP-Elites are a class of optimisation techniques that attempt to find many high performing points that all behave differently according to a user-defined behavioural metric. In this paper we propose the Bayesian Optimisation of Elites (BOP-Elites) algorithm. Designed for problems with expensive black-box fitness and behaviour functions, it is able to return a QD solution-set with excellent final performance already after a relatively small number of samples. BOP-Elites models both fitness and behavioural descriptors with Gaussian Process (GP) surrogate models and uses Bayesian Optimisation (BO) strategies for choosing points to evaluate in order to solve the quality-diversity problem. In addition, BOP-Elites produces high quality surrogate models which can be used after convergence to predict solutions with any behaviour in a continuous range. An empirical comparison shows that BOP-Elites significantly outperforms other state-of-the-art algorithms without the need for problem-specific parameter tuning.

math.OC↗

arXiv2023

Generating a Graph Colouring Heuristic with Deep Q-Learning and Graph Neural Networks

The graph colouring problem consists of assigning labels, or colours, to the vertices of a graph such that no two adjacent vertices share the same colour. In this work we investigate whether deep reinforcement learning can be used to discover a competitive construction heuristic for graph colouring. Our proposed approach, ReLCol, uses deep Q-learning together with a graph neural network for feature extraction, and employs a novel way of parameterising the graph that results in improved performance. Using standard benchmark graphs with varied topologies, we empirically evaluate the benefits and limitations of the heuristic learned by ReLCol relative to existing construction algorithms, and demonstrate that reinforcement learning is a promising direction for further research on the graph colouring problem.

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