Related papers: Symmetric Discrete Optimal Control and Deep Learni…

Drifting is a complicated task for autonomous vehicle control. Most traditional methods in this area are based on motion equations derived by the understanding of vehicle dynamics, which is difficult to be modeled precisely. We propose a…

Control systems are at the core of every real-world robot. They are deployed in an ever-increasing number of applications, ranging from autonomous racing and search-and-rescue missions to industrial inspections and space exploration. To…

Deep learning has provided new ways of manipulating, processing and analyzing data. It sometimes may achieve results comparable to, or surpassing human expert performance, and has become a source of inspiration in the era of artificial…

We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate…

In this paper, we present the combined learning-and-control (CLC) approach, which is a new way to solve optimal control problems with unknown dynamics by unifying model-based control and data-driven learning. The key idea is simple: we…

Privacy concerns in distributed learning often lead clients to return intentionally altered gradient information. We consider the problem of learning convex and $L$-smooth functions under adversarial gradient perturbation, where a client's…

We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…

This paper is addressed to studying the exact controllability for stochastic transport equations by two controls: one is a boundary control imposed on the drift term and the other is an internal control imposed on the diffusion term. By…

Spacecraft trajectory design is a global search problem, where previous work has revealed specific solution structures that can be captured with data-driven methods. This paper explores two global search problems in the circular restricted…

This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application…

One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization…

We consider left-invariant optimal control problems on connected Lie groups such that generic stabilizer of the coadjoint action is connected and has dimension not more than 1. We introduce a construction for symmetries of the exponential…

We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first contribution, we introduce a modified problem, whose optimal control is under some…

Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…

The present study investigates a linear-quadratic Dirichlet control problem governed by a non-coercive elliptic equation posed on a possibly non-convex polygonal domain. Tikhonov regularization is carried out in an energy seminorm. The…

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…

We discuss a dynamical systems perspective on discrete optimization. Departing from the fact that many combinatorial optimization problems can be reformulated as finding low energy spin configurations in corresponding Ising models, we…

In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…