Related papers: The Pontryagin Maximum Principle for Training Conv…

We derive the Pontryagin maximum principle and $Q$-functions for the relaxed control of noisy rough differential equations. Our main tool is the development of a novel differentiation procedure along `spike variation' perturbations of the…

Model predictive control offers a powerful framework for managing constrained systems, but its repeated online optimization can become computationally prohibitive. Multiparametric programming addresses this challenge by precomputing optimal…

Based on Pontryagin Maximum Principle (PMP), this paper establishes a generalized PMP aiming at control system with with extra input/output terms. The paper details the adaptive target and gives a proof of the generalized theorem.…

We derive a new margin-based regularization formulation, termed multi-margin regularization (MMR), for deep neural networks (DNNs). The MMR is inspired by principles that were applied in margin analysis of shallow linear classifiers, e.g.,…

In this paper, we propose a method to solve nonlinear optimal control problems (OCPs) with constrained control input in real-time using neural networks (NNs). We introduce what we have termed co-state Neural Network (CoNN) that learns the…

This study investigates the potential of hybrid metaheuristic algorithms to enhance the training of Probabilistic Neural Networks (PNNs) by leveraging the complementary strengths of multiple optimisation strategies. Traditional learning…

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA)…

We study dropout regularization in continuous-time models through the lens of random-batch methods -- a family of stochastic sampling schemes originally devised to reduce the computational cost of interacting particle systems. We construct…

The weight decay regularization term is widely used during training to constrain expressivity, avoid overfitting, and improve generalization. Historically, this concept was borrowed from the SVM maximum margin principle and extended to…

In this work, we introduce a stochastic maximum principle (SMP) approach for solving the reinforcement learning problem with the assumption that the unknowns in the environment can be parameterized based on physics knowledge. For the…

We propose a scalable, policy-centric framework for continuous-time multi-asset portfolio-consumption optimization under inequality constraints. Our method integrates neural policies with Pontryagin's Maximum Principle (PMP) and enforces…

We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…

Model-based reinforcement learning (MBRL) improves sample efficiency by leveraging learned dynamics models for policy optimization. However, the effectiveness of methods such as actor-critic is often limited by compounding model errors,…

Convolutional neural network (CNN) is one of the most frequently used deep learning techniques. Various forms of models have been proposed and im-proved for learning at CNN. When learning with CNN, it is necessary to determine the optimal…

Port-Hamiltonian neural networks have shown promising results in the identification of nonlinear dynamics of complex systems, as their combination of physical principles with data-driven learning allows for accurate modelling. However, due…

In this note we develop the theory of the quantum Pontryagin principle for continuous measurements and feedback. The analysis is carried out under the assumption of compatible events in the output channel. The plant is a quantum system,…

State-space models (SSMs) are effective architectures for sequential modeling, but a rigorous theoretical understanding of their training dynamics is still lacking. In this work, we formulate the training of SSMs as an ensemble optimal…

We study a continuous time stochastic optimal control problem under partial observations that are available only at discrete time instants. This hybrid setting, with continuous dynamics and intermittent noisy measurements, arises in…

We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…

Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that…