arXiv subjects

Tobias Windisch

Publications and source records attributed to Tobias Windisch.

12 recordsLinked to original sources

arXiv2026

Trajectory-Level Data Augmentation for Offline Reinforcement Learning

We propose a data augmentation method for offline reinforcement learning, motivated by active positioning problems. Particularly, our approach enables the training of off-policy models from a limited number of suboptimal trajectories. We introduce a trajectory-based augmentation technique that exploits task structure and the geometric relationship between rewards, value functions, and mathematical properties of logging policies. During data collection, our augmentation supports suboptimal logging policies, leading to higher data quality and improved offline reinforcement learning performance. We provide theoretical justification for these strategies and validate them empirically across positioning tasks of varying dimensionality and under partial observability.

cs.LG↗

arXiv2025

SAT-sampling for statistical significance testing in sparse contingency tables

Exact conditional tests for contingency tables require sampling from fibers with fixed margins. Classical Markov basis MCMC is general but often impractical: computing full Markov bases that connect all fibers of a given constraint matrix can be infeasible and the resulting chains may converge slowly, especially in sparse settings or in presence of structural zeros. We introduce a SAT-based alternative that encodes fibers as Boolean circuits which allows modern SAT samplers to generate tables randomly. We analyze the sampling bias that SAT samplers may introduce, provide diagnostics, and propose practical mitigation. We propose hybrid MCMC schemes that combine SAT proposals with local moves to ensure correct stationary distributions which do not necessarily require connectivity via local moves which is particularly beneficial in presence of structural zeros. Across benchmarks, including small and involved tables with many structural zeros where pure Markov-basis methods underperform, our methods deliver reliable conditional p-values and often outperform samplers that rely on precomputed Markov bases.

stat.ME↗

arXiv2025

Nonlinear Causal Discovery for Grouped Data

Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social science, and industrial manufacturing, the causal units of interest are groups of variables rather than individual scalar measurements. Motivated by these applications, we extend nonlinear additive noise models to handle random vectors, establishing a two-step approach for causal graph learning: First, infer the causal order among random vectors. Second, perform model selection to identify the best graph consistent with this order. We introduce effective and novel solutions for both steps in the vector case, demonstrating strong performance in simulations. Finally, we apply our method to real-world assembly line data with partial knowledge of causal ordering among variable groups.

stat.ML↗

arXiv2025

LineFlow: A Framework to Learn Active Control of Production Lines

Many production lines require active control mechanisms, such as adaptive routing, worker reallocation, and rescheduling, to maintain optimal performance. However, designing these control systems is challenging for various reasons, and while reinforcement learning (RL) has shown promise in addressing these challenges, a standardized and general framework is still lacking. In this work, we introduce LineFlow, an extensible, open-source Python framework for simulating production lines of arbitrary complexity and training RL agents to control them. To demonstrate the capabilities and to validate the underlying theoretical assumptions of LineFlow, we formulate core subproblems of active line control in ways that facilitate mathematical analysis. For each problem, we provide optimal solutions for comparison. We benchmark state-of-the-art RL algorithms and show that the learned policies approach optimal performance in well-understood scenarios. However, for more complex, industrial-scale production lines, RL still faces significant challenges, highlighting the need for further research in areas such as reward shaping, curriculum learning, and hierarchical control.

cs.LG↗

arXiv2025

Active Alignments of Lens Systems with Reinforcement Learning

Aligning a lens system relative to an imager is a critical challenge in camera manufacturing. While optimal alignment can be mathematically computed under ideal conditions, real-world deviations caused by manufacturing tolerances often render this approach impractical. Measuring these tolerances can be costly or even infeasible, and neglecting them may result in suboptimal alignments. We propose a reinforcement learning (RL) approach that learns exclusively in the pixel space of the sensor output, eliminating the need to develop expert-designed alignment concepts. We conduct an extensive benchmark study and show that our approach surpasses other methods in speed, precision, and robustness. We further introduce relign, a realistic, freely explorable, open-source simulation utilizing physically based rendering that models optical systems with non-deterministic manufacturing tolerances and noise in robotic alignment movement. It provides an interface to popular machine learning frameworks, enabling seamless experimentation and development. Our work highlights the potential of RL in a manufacturing environment to enhance efficiency of optical alignments while minimizing the need for manual intervention.

cs.RO↗

arXiv2024

A method to benchmark high-dimensional process drift detection

Process curves are multivariate finite time series data coming from manufacturing processes. This paper studies machine learning that detect drifts in process curve datasets. A theoretic framework to synthetically generate process curves in a controlled way is introduced in order to benchmark machine learning algorithms for process drift detection. An evaluation score, called the temporal area under the curve, is introduced, which allows to quantify how well machine learning models unveil curves belonging to drift segments. Finally, a benchmark study comparing popular machine learning approaches on synthetic data generated with the introduced framework is presented that shows that existing algorithms often struggle with datasets containing multiple drift segments.

stat.ML↗

arXiv2024

$\texttt{causalAssembly}$: Generating Realistic Production Data for Benchmarking Causal Discovery

Algorithms for causal discovery have recently undergone rapid advances and increasingly draw on flexible nonparametric methods to process complex data. With these advances comes a need for adequate empirical validation of the causal relationships learned by different algorithms. However, for most real data sources true causal relations remain unknown. This issue is further compounded by privacy concerns surrounding the release of suitable high-quality data. To help address these challenges, we gather a complex dataset comprising measurements from an assembly line in a manufacturing context. This line consists of numerous physical processes for which we are able to provide ground truth causal relationships on the basis of a detailed study of the underlying physics. We use the assembly line data and associated ground truth information to build a system for generation of semisynthetic manufacturing data that supports benchmarking of causal discovery methods. To accomplish this, we employ distributional random forests in order to flexibly estimate and represent conditional distributions that may be combined into joint distributions that strictly adhere to a causal model over the observed variables. The estimated conditionals and tools for data generation are made available in our Python library $\texttt{causalAssembly}$. Using the library, we showcase how to benchmark several well-known causal discovery algorithms.

stat.ML↗

arXiv2017

Parity binomial edge ideals

Parity binomial edge ideals of simple undirected graphs are introduced. Unlike binomial edge ideals, they do not have square-free Gröbner bases and are radical if only if the graph is bipartite or the characteristic of the ground field is not two. The minimal primes are determined and shown to encode combinatorics of even and odd walks in the graph. A mesoprimary decomposition is determined and shown to be a primary decomposition in characteristic two.

math.AC↗

arXiv2016

Rapid mixing and Markov bases

The mixing behaviour of random walks on lattice points of polytopes using Markov bases is examined. It is shown that under a dilation of the underlying polytope, these random walks do not mix rapidly when a fixed Markov basis is used. We also show that this phenomenon does not disappear after adding more moves to the Markov basis. Avoiding rejections by sampling applicable moves does also not lead to an asymptotic improvement. As a way out, a method of how to adapt Markov bases in order to achieve the fastest mixing behaviour is introduced.

math.CO↗

arXiv2016

Heat-bath random walks with Markov bases

Graphs on lattice points are studied whose edges come from a finite set of allowed moves of arbitrary length. We show that the diameter of these graphs on fibers of a fixed integer matrix can be bounded from above by a constant. We then study the mixing behaviour of heat-bath random walks on these graphs. We also state explicit conditions on the set of moves so that the heat-bath random walk, a generalization of the Glauber dynamics, is an expander in fixed dimension.

math.CO↗

arXiv2016

The fiber dimension of a graph

Graphs on integer points of polytopes whose edges come from a set of allowed differences are studied. It is shown that any simple graph can be embedded in that way. The minimal dimension of such a representation is the fiber dimension of the given graph. The fiber dimension is determined for various classes of graphs and an upper bound in terms of the chromatic number is stated.

math.CO↗

arXiv2015

On the Connectivity of Fiber Graphs

We consider the connectivity of fiber graphs with respect to Gröbner basis and Graver basis moves. First, we present a sequence of fiber graphs using moves from a Gröbner basis and prove that their edge-connectivity is lowest possible and can have an arbitrarily large distance from the minimal degree. We then show that graph-theoretic properties of fiber graphs do not depend on the size of the right-hand side. This provides a counterexample to a conjecture of Engström on the node-connectivity of fiber graphs. Our main result shows that the edge-connectivity in all fiber graphs of this counterexample is best possible if we use moves from Graver basis instead.

math.CO↗