arXiv subjects

Viktor Bengs

Publications and source records attributed to Viktor Bengs.

At least 19 recordsLinked to original sources

arXiv2026

Calibrated Preference Learning: The Case of Label Ranking

Calibration, the alignment of predicted probabilities with true outcome frequencies, is essential for reliable decision-making. While extensively studied for classification and regression, calibration has not been formally addressed for probabilistic label ranking, where the goal is to predict a distribution over orderings of a label set. Naively treating rankings as classes ignores their structure and fails to capture important modalities such as pairwise and top-k predictions. We formalize calibration for label ranking and develop a hierarchy of notions covering full rankings, sub-rankings, and top-k rankings. We prove that full-rank calibration implies the others but not conversely, and sub-ranking and top-k calibration are incomparable. Empirically, we find popular label ranking models are often poorly calibrated, with substantial differences between sub-ranking and top-k metrics. Applying our framework to RLHF reward models, we find that calibration correlates strongly but not perfectly with benchmark accuracy, suggesting it captures a meaningful quality dimension beyond top-1 accuracy. These findings motivate future work on understanding the downstream effects of miscalibration and developing methods to correct it.

cs.LG↗

arXiv2026

Linear-LLM-SCM: Benchmarking LLMs for Coefficient Elicitation in Linear-Gaussian Causal Models

Large language models (LLMs) have shown potential in identifying qualitative causal relations, but their ability to perform quantitative causal reasoning---estimating effect sizes that parametrize functional relationships---remains underexplored in continuous domains. We introduce Linear-LLM-SCM, a plug-and-play framework for evaluating LLMs on Linear Gaussian structural causal model parametrization when a directed acyclic graph (DAG) is given. The framework decomposes a DAG into local parent-child sets and prompts an LLM to produce a regression-style structural equation per node, which is aggregated and compared against available ground-truth parameters. Our experiments with seven real-world DAGs effect ground truth illustrate limitations of LLMs as quantitative causal parameterizers. Across most models, we observe variability in coefficient estimates and sensitivity to structural perturbations. We open-sourced the framework to further encourage the community to work on studies toward the use of LLM for causal effect elicitation in safety-critical domain, e.g., healthcare.

cs.LG↗

arXiv2025

Co-Exploration and Co-Exploitation via Shared Structure in Multi-Task Bandits

We propose a novel Bayesian framework for efficient exploration in contextual multi-task multi-armed bandit settings, where the context is only observed partially and dependencies between reward distributions are induced by latent context variables. In order to exploit these structural dependencies, our approach integrates observations across all tasks and learns a global joint distribution, while still allowing personalised inference for new tasks. In this regard, we identify two key sources of epistemic uncertainty, namely structural uncertainty in the latent reward dependencies across arms and tasks, and user-specific uncertainty due to incomplete context and limited interaction history. To put our method into practice, we represent the joint distribution over tasks and rewards using a particle-based approximation of a log-density Gaussian process. This representation enables flexible, data-driven discovery of both inter-arm and inter-task dependencies without prior assumptions on the latent variables. Empirically, we demonstrate that our method outperforms baselines such as hierarchical model bandits, especially in settings with model misspecification or complex latent heterogeneity.

cs.LG↗

arXiv2025

A comparative analysis of rank aggregation methods for the partial label ranking problem

The label ranking problem is a supervised learning scenario in which the learner predicts a total order of the class labels for a given input instance. Recently, research has increasingly focused on the partial label ranking problem, a generalization of the label ranking problem that allows ties in the predicted orders. So far, most existing learning approaches for the partial label ranking problem rely on approximation algorithms for rank aggregation in the final prediction step. This paper explores several alternative aggregation methods for this critical step, including scoring-based and non-parametric probabilistic-based rank aggregation approaches. To enhance their suitability for the more general partial label ranking problem, the investigated methods are extended to increase the likelihood of producing ties. Experimental evaluations on standard benchmarks demonstrate that scoring-based variants consistently outperform the current state-of-the-art method in handling incomplete information. In contrast, non-parametric probabilistic-based variants fail to achieve competitive performance.

cs.LG↗

arXiv2025

A calibration test for evaluating set-based epistemic uncertainty representations

The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of constructing these credal sets is via ensembling or specialized supervised learning methods, where the epistemic uncertainty can be quantified through measures such as the set size or the disagreement among members. In principle, these sets should contain the true data-generating distribution. As a necessary condition for this validity, we adopt the strongest notion of calibration as a proxy. Concretely, we propose a novel statistical test to determine whether there is a convex combination of the set's predictions that is calibrated in distribution. In contrast to previous methods, our framework allows the convex combination to be instance dependent, recognizing that different ensemble members may be better calibrated in different regions of the input space. Moreover, we learn this combination via proper scoring rules, which inherently optimize for calibration. Building on differentiable, kernel-based estimators of calibration errors, we introduce a nonparametric testing procedure and demonstrate the benefits of capturing instance-level variability on of synthetic and real-world experiments.

cs.LG↗

arXiv2024

Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?

Trustworthy ML systems should not only return accurate predictions, but also a reliable representation of their uncertainty. Bayesian methods are commonly used to quantify both aleatoric and epistemic uncertainty, but alternative approaches, such as evidential deep learning methods, have become popular in recent years. The latter group of methods in essence extends empirical risk minimization (ERM) for predicting second-order probability distributions over outcomes, from which measures of epistemic (and aleatoric) uncertainty can be extracted. This paper presents novel theoretical insights of evidential deep learning, highlighting the difficulties in optimizing second-order loss functions and interpreting the resulting epistemic uncertainty measures. With a systematic setup that covers a wide range of approaches for classification, regression and counts, it provides novel insights into issues of identifiability and convergence in second-order loss minimization, and the relative (rather than absolute) nature of epistemic uncertainty measures.

cs.AI↗

arXiv2024

Approximating the Shapley Value without Marginal Contributions

The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is due to axiomatic properties that only the Shapley value satisfies, which, however, comes at the expense of an exact computation growing exponentially with the number of agents. Accordingly, a number of works are devoted to the efficient approximation of the Shapley value, most of them revolve around the notion of an agent's marginal contribution. In this paper, we propose with SVARM and Stratified SVARM two parameter-free and domain-independent approximation algorithms based on a representation of the Shapley value detached from the notion of marginal contribution. We prove unmatched theoretical guarantees regarding their approximation quality and provide empirical results including synthetic games as well as common explainability use cases comparing ourselves with state-of-the-art methods.

cs.LG↗

arXiv2023

A Survey of Reinforcement Learning from Human Feedback

Reinforcement learning from human feedback (RLHF) is a variant of reinforcement learning (RL) that learns from human feedback instead of relying on an engineered reward function. Building on prior work on the related setting of preference-based reinforcement learning (PbRL), it stands at the intersection of artificial intelligence and human-computer interaction. This positioning provides a promising approach to enhance the performance and adaptability of intelligent systems while also improving the alignment of their objectives with human values. The success in training large language models (LLMs) has impressively demonstrated this potential in recent years, where RLHF has played a decisive role in directing the model's capabilities towards human objectives. This article provides an overview of the fundamentals of RLHF, exploring how RL agents interact with human feedback. While recent focus has been on RLHF for LLMs, our survey covers the technique across multiple domains. We provide our most comprehensive coverage in control and robotics, where many fundamental techniques originate, alongside a dedicated LLM section. We examine the core principles that underpin RLHF, how algorithms and human feedback work together, and the main research trends in the field. Our goal is to give researchers and practitioners a clear understanding of this rapidly growing field.

cs.LG↗

arXiv2023

Second-Order Uncertainty Quantification: A Distance-Based Approach

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

cs.LG↗

arXiv2023

Identifying Copeland Winners in Dueling Bandits with Indifferences

We consider the task of identifying the Copeland winner(s) in a dueling bandits problem with ternary feedback. This is an underexplored but practically relevant variant of the conventional dueling bandits problem, in which, in addition to strict preference between two arms, one may observe feedback in the form of an indifference. We provide a lower bound on the sample complexity for any learning algorithm finding the Copeland winner(s) with a fixed error probability. Moreover, we propose POCOWISTA, an algorithm with a sample complexity that almost matches this lower bound, and which shows excellent empirical performance, even for the conventional dueling bandits problem. For the case where the preference probabilities satisfy a specific type of stochastic transitivity, we provide a refined version with an improved worst case sample complexity.

cs.LG↗

arXiv2023

On the Calibration of Probabilistic Classifier Sets

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes error, and epistemic uncertainty via the size of the set. In this paper, we extend the notion of calibration, which is commonly used to evaluate the validity of the aleatoric uncertainty representation of a single probabilistic classifier, to assess the validity of an epistemic uncertainty representation obtained by sets of probabilistic classifiers. Broadly speaking, we call a set of probabilistic classifiers calibrated if one can find a calibrated convex combination of these classifiers. To evaluate this notion of calibration, we propose a novel nonparametric calibration test that generalizes an existing test for single probabilistic classifiers to the case of sets of probabilistic classifiers. Making use of this test, we empirically show that ensembles of deep neural networks are often not well calibrated.

stat.ML↗

arXiv2023

Iterative Deepening Hyperband

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the "right" budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

cs.LG↗

arXiv2023

On Second-Order Scoring Rules for Epistemic Uncertainty Quantification

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.

cs.LG↗

arXiv2022

AC-Band: A Combinatorial Bandit-Based Approach to Algorithm Configuration

We study the algorithm configuration (AC) problem, in which one seeks to find an optimal parameter configuration of a given target algorithm in an automated way. Recently, there has been significant progress in designing AC approaches that satisfy strong theoretical guarantees. However, a significant gap still remains between the practical performance of these approaches and state-of-the-art heuristic methods. To this end, we introduce AC-Band, a general approach for the AC problem based on multi-armed bandits that provides theoretical guarantees while exhibiting strong practical performance. We show that AC-Band requires significantly less computation time than other AC approaches providing theoretical guarantees while still yielding high-quality configurations.

cs.LG↗

arXiv2022

Multi-Armed Bandits with Censored Consumption of Resources

We consider a resource-aware variant of the classical multi-armed bandit problem: In each round, the learner selects an arm and determines a resource limit. It then observes a corresponding (random) reward, provided the (random) amount of consumed resources remains below the limit. Otherwise, the observation is censored, i.e., no reward is obtained. For this problem setting, we introduce a measure of regret, which incorporates the actual amount of allocated resources of each learning round as well as the optimality of realizable rewards. Thus, to minimize regret, the learner needs to set a resource limit and choose an arm in such a way that the chance to realize a high reward within the predefined resource limit is high, while the resource limit itself should be kept as low as possible. We propose a UCB-inspired online learning algorithm, which we analyze theoretically in terms of its regret upper bound. In a simulation study, we show that our learning algorithm outperforms straightforward extensions of standard multi-armed bandit algorithms.

cs.LG↗

arXiv2022

Finding Optimal Arms in Non-stochastic Combinatorial Bandits with Semi-bandit Feedback and Finite Budget

We consider the combinatorial bandits problem with semi-bandit feedback under finite sampling budget constraints, in which the learner can carry out its action only for a limited number of times specified by an overall budget. The action is to choose a set of arms, whereupon feedback for each arm in the chosen set is received. Unlike existing works, we study this problem in a non-stochastic setting with subset-dependent feedback, i.e., the semi-bandit feedback received could be generated by an oblivious adversary and also might depend on the chosen set of arms. In addition, we consider a general feedback scenario covering both the numerical-based as well as preference-based case and introduce a sound theoretical framework for this setting guaranteeing sensible notions of optimal arms, which a learner seeks to find. We suggest a generic algorithm suitable to cover the full spectrum of conceivable arm elimination strategies from aggressive to conservative. Theoretical questions about the sufficient and necessary budget of the algorithm to find the best arm are answered and complemented by deriving lower bounds for any learning algorithm for this problem scenario.

cs.LG↗

arXiv2022

Stochastic Contextual Dueling Bandits under Linear Stochastic Transitivity Models

We consider the regret minimization task in a dueling bandits problem with context information. In every round of the sequential decision problem, the learner makes a context-dependent selection of two choice alternatives (arms) to be compared with each other and receives feedback in the form of noisy preference information. We assume that the feedback process is determined by a linear stochastic transitivity model with contextualized utilities (CoLST), and the learner's task is to include the best arm (with highest latent context-dependent utility) in the duel. We propose a computationally efficient algorithm, $\texttt{CoLSTIM}$, which makes its choice based on imitating the feedback process using perturbed context-dependent utility estimates of the underlying CoLST model. If each arm is associated with a $d$-dimensional feature vector, we show that $\texttt{CoLSTIM}$ achieves a regret of order $\tilde O( \sqrt{dT})$ after $T$ learning rounds. Additionally, we also establish the optimality of $\texttt{CoLSTIM}$ by showing a lower bound for the weak regret that refines the existing average regret analysis. Our experiments demonstrate its superiority over state-of-art algorithms for special cases of CoLST models.

cs.LG↗

arXiv2022

Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

cs.LG↗