arXiv:2409.18010v3 Announce Type: replace-cross 
Abstract: In this paper we propose an end-to-end algorithm for indirect data-driven control for bilinear systems with stability guarantees. We consider the case where the collected i.i.d. data is affected by probabilistic noise with possibly unbounded support and leverage tools from statistical learning theory to derive finite sample identification error bounds. To this end, we solve the bilinear identification problem by solving a set of linear and affine identification problems, by a particular choice of a control input during the data collection phase. We provide a priori as well as data-dependent finite sample identification error bounds on the individual matrices as well as ellipsoidal bounds, both of which are structurally suitable for control. Further, we integrate the structure of the derived identification error bounds in a robust controller design to obtain an exponentially stable closed-loop. By means of an extensive numerical study we showcase the interplay between the controller design and the derived identification error bounds. Moreover, we note appealing connections of our results to indirect data-driven control of general nonlinear systems through Koopman operator theory and discuss how our results may be applied in this setup.

تم تطوير خوارزمية جديدة من البداية إلى النهاية للتحكم غير المباشر القائم على البيانات للأنظمة الثنائية، مما يضمن الاستقرار حتى في وجود ضوضاء احتمالية. هذه الخطوة مهمة لأنها تستفيد من نظرية التعلم الإحصائي لتوفير حدود خطأ التعريف لعينة محدودة، مما يجعلها حلاً واعدًا للأنظمة المعقدة. يمكن أن تؤدي نتائج هذا البحث إلى تحسين موثوقية وكفاءة التطبيقات المختلفة في الهندسة والتكنولوجيا.

Se ha desarrollado un nuevo algoritmo de extremo a extremo para el control indirecto basado en datos de sistemas bilineales, asegurando estabilidad incluso en presencia de ruido probabilístico. Este avance es significativo ya que aprovecha la teoría del aprendizaje estadístico para proporcionar límites de error de identificación de muestras finitas, convirtiéndolo en una solución prometedora para sistemas de control complejos. Las implicaciones de esta investigación podrían mejorar la fiabilidad y eficiencia de diversas aplicaciones en ingeniería y tecnología.

Un nouvel algorithme de bout en bout a été développé pour le contrôle indirect basé sur les données des systèmes bilinéaires, garantissant la stabilité même en présence de bruit probabiliste. Cette avancée est significative car elle s'appuie sur la théorie de l'apprentissage statistique pour fournir des bornes d'erreur d'identification à échantillons finis, ce qui en fait une solution prometteuse pour des systèmes de contrôle complexes. Les implications de cette recherche pourraient améliorer la fiabilité et l'efficacité de diverses applications en ingénierie et en technologie.

A new end-to-end algorithm has been developed for indirect data-driven control of bilinear systems, ensuring stability even in the presence of probabilistic noise. This advancement is significant as it leverages statistical learning theory to provide finite sample identification error bounds, making it a promising solution for complex control systems. The implications of this research could enhance the reliability and efficiency of various applications in engineering and technology.

End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data

arXiv:2601.08100v1 Announce Type: new 
Abstract: Understanding the generalization behavior of deep neural networks remains a fundamental challenge in modern statistical learning theory. Among existing approaches, PAC-Bayesian norm-based bounds have demonstrated particular promise due to their data-dependent nature and their ability to capture algorithmic and geometric properties of learned models. However, most existing results rely on isotropic Gaussian posteriors, heavy use of spectral-norm concentration for weight perturbations, and largely architecture-agnostic analyses, which together limit both the tightness and practical relevance of the resulting bounds. To address these limitations, in this work, we propose a unified framework for PAC-Bayesian norm-based generalization by reformulating the derivation of generalization bounds as a stochastic optimization problem over anisotropic Gaussian posteriors. The key to our approach is a sensitivity matrix that quantifies the network outputs with respect to structured weight perturbations, enabling the explicit incorporation of heterogeneous parameter sensitivities and architectural structures. By imposing different structural assumptions on this sensitivity matrix, we derive a family of generalization bounds that recover several existing PAC-Bayesian results as special cases, while yielding bounds that are comparable to or tighter than state-of-the-art approaches. Such a unified framework provides a principled and flexible way for geometry-/structure-aware and interpretable generalization analysis in deep learning.

تشير دراسة جديدة إلى إطار موحد لـ PAC-Bayes للحدود العامة المعتمدة على المعايير، حيث تتناول التحديات المتعلقة بفهم سلوك التعميم في الشبكات العصبية العميقة. تعيد هذه الدراسة صياغة اشتقاق هذه الحدود كمشكلة تحسين عشوائي على توزيعات غاوسية غير متساوية، بهدف تعزيز الصلة العملية للنتائج.

Un nuevo estudio propone un marco PAC-Bayes unificado para los límites de generalización basados en normas, abordando los desafíos de comprender el comportamiento de generalización de las redes neuronales profundas. La investigación reformula la derivación de estos límites como un problema de optimización estocástica sobre posteriors gaussianos anisotrópicos, con el objetivo de mejorar la relevancia práctica de los resultados.

Une nouvelle étude propose un cadre PAC-Bayésien unifié pour les bornes de généralisation basées sur les normes, abordant les défis de la compréhension du comportement de généralisation des réseaux de neurones profonds. La recherche reformule la dérivation de ces bornes comme un problème d'optimisation stochastique sur des postérieurs gaussiens anisotropes, visant à améliorer la pertinence pratique des résultats.

A new study proposes a unified PAC-Bayesian framework for norm-based generalization bounds, addressing the challenges of understanding deep neural networks' generalization behavior. The research reformulates the derivation of these bounds as a stochastic optimization problem over anisotropic Gaussian posteriors, aiming to enhance the practical relevance of the results.

End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data

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