Related papers: Further extensions on the successive approximation…

In this paper, we consider a chain of distributed systems governed by a degenerate parabolic equation, which satisfies a weak H\"{o}rmander type condition, with a control distributed over an open subdomain. In particular, we consider two…

Reinforcement learning algorithms describe how an agent can learn an optimal action policy in a sequential decision process, through repeated experience. In a given environment, the agent policy provides him some running and terminal…

In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…

This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…

Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…

Recent advances in robot learning have enabled robots to become increasingly better at mastering a predefined set of tasks. On the other hand, as humans, we have the ability to learn a growing set of tasks over our lifetime. Continual robot…

We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves…

This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal…

The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…

This paper studies continuous-time optimal contracting in a hierarchy problem which generalises the model of Sung (2015). The hierarchy is modeled by a series of interlinked principal-agent problems, leading to a sequence of Stackelberg…

Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…

This paper develops a comprehensive extension of the $\Lambda$-set framework for optimal control, introducing second-order $\Lambda$-sets and generalizing the theory to non-smooth, hybrid, and stochastic hybrid systems. We first establish…

Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…

The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For…

Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic…

Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal…

We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…