相关论文: Sparsity in long-time control of neural ODEs

We consider the neural ODE perspective of supervised learning and study the impact of the final time $T$ (which may indicate the depth of a corresponding ResNet) in training. For the classical $L^2$--regularized empirical risk minimization…

We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical…

Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…

The performance of trained neural networks is robust to harsh levels of pruning. Coupled with the ever-growing size of deep learning models, this observation has motivated extensive research on learning sparse models. In this work, we focus…

Optimal control models have been successful in describing many aspects of human movement. The interpretation of such models regarding neuronal implementation of the human motor system is not clear. An important aspects of optimal control…

This paper studies the long-time behavior of optimal solutions for a class of linear-convex optimal control problems. We focus on a partial exponential turnpike property, established without imposing controllability or stabilizability…

We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural…

The training of ResNets and neural ODEs can be formulated and analyzed from the perspective of optimal control. This paper proposes a dissipative formulation of the training of ResNets and neural ODEs for classification problems by…

The \emph{turnpike property} in contemporary macroeconomics asserts that if an economic planner seeks to move an economy from one level of capital to another, then the most efficient path, as long as the planner has enough time, is to…

We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at…

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…

An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…

Recent literature has made much progress in understanding \emph{online LQR}: a modern learning-theoretic take on the classical control problem in which a learner attempts to optimally control an unknown linear dynamical system with fully…

Safety-critical cyber-physical systems require control strategies whose worst-case performance is robust against adversarial disturbances and modeling uncertainties. In this paper, we present a framework for approximate control and learning…

We consider the online convex optimization problem. In the setting of arbitrary sequences and finite set of parameters, we establish a new fast-rate quantile regret bound. Then we investigate the optimization into the L1-ball by…

A class of infinite horizon optimal control problems involving mixed quasi-norms of $L^p$-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The…

Sparse neural networks are highly desirable in deep learning in reducing its complexity. The goal of this paper is to study how choices of regularization parameters influence the sparsity level of learned neural networks. We first derive…

The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…

A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…