Related papers: Deep Learning Theory Review: An Optimal Control an…

Deep neural networks can achieve great successes when presented with large data sets and sufficient computational resources. However, their ability to learn new concepts quickly is limited. Meta-learning is one approach to address this…

When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more…

Artificial neural networks often struggle with catastrophic forgetting when learning multiple tasks sequentially, as training on new tasks degrades the performance on previously learned tasks. Recent theoretical work has addressed this…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

Optimization of deep neural networks (DNNs) has been a driving force in the advancement of modern machine learning and artificial intelligence. With DNNs characterized by a prolonged sequence of nonlinear propagation, determining their…

The connection between control algorithms for Markov decision processes and optimization algorithms has been implicitly and explicitly exploited since the introduction of dynamic programming algorithm by Bellman in the 1950s. Recently, this…

Sophisticated multilayer neural networks have achieved state of the art results on multiple supervised tasks. However, successful applications of such multilayer networks to control have so far been limited largely to the perception portion…

Controlling continuous-time dynamical systems is generally a two step process: first, identify or model the system dynamics with differential equations, then, minimize the control objectives to achieve optimal control function and optimal…

Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

Deep learning achieves remarkable generalization capability with overwhelming number of model parameters. Theoretical understanding of deep learning generalization receives recent attention yet remains not fully explored. This paper…

Deep learning is formulated as a discrete-time optimal control problem. This allows one to characterize necessary conditions for optimality and develop training algorithms that do not rely on gradients with respect to the trainable…

Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…

We develop an optimization framework centered around a core idea: once a (parametric) policy is specified, control authority is transferred to the policy, resulting in an autonomous dynamical system. Thus we should be able to optimize…

This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic…

Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs…

Learning-based control aims to construct models of a system to use for planning or trajectory optimization, e.g. in model-based reinforcement learning. In order to obtain guarantees of safety in this context, uncertainty must be accurately…

Meta-learning is a branch of machine learning which aims to quickly adapt models, such as neural networks, to perform new tasks by learning an underlying structure across related tasks. In essence, models are being trained to learn new…

Connections between Deep Neural Networks (DNNs) training and optimal control theory has attracted considerable attention as a principled tool of algorithmic design. Differential Dynamic Programming (DDP) neural optimizer is a recently…