Related papers: Mirror Descent for Deterministic Optimal Control
We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and…
In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…
The paper considers the problem of constructing program control for an object described by a system with a quasidifferentiable right-hand side. The control aim is to bring the system from a given initial position to a given final state in…
We propose a Model Predictive Control (MPC) with a single-step prediction horizon to approximate the solution of infinite horizon optimal control problems with the expected sum of convex stage costs for constrained linear uncertain systems.…
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and…
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…
In this paper, we consider a class of stochastic control problems for stochastic differential equations with random coefficients. The control domain need not to be convex but the control process is not allowed to enter in diffusion term.…
We consider the following class of online optimization problems with functional constraints. Assume, that a finite set of convex Lipschitz-continuous non-smooth functionals are given on a closed set of $n$-dimensional vector space. The…
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…
The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general nonlinear cost functional, and an option to directly control the nonlocal terms of the…
Value iteration-type methods have been extensively studied for computing a nearly optimal value function in reinforcement learning (RL). Under a generative sampling model, these methods can achieve sharper sample complexity than policy…
Network utility maximization is the most important problem in network traffic management. Given the growth of modern communication networks, we consider the utility maximization problem in a network with a large number of connections…
This paper studies bandit convex optimization in non-stationary environments with two-point feedback, using dynamic regret as the performance measure. We propose an algorithm based on bandit mirror descent that extends naturally to…
This work addresses distributed optimization, where a network of agents wants to minimize a global strongly convex objective function. The global function can be written as a sum of local convex functions, each of which is associated with…
Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the…
In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost…
We investigate an optimal control problem for a diffusion whose drift and running cost are merely measurable in the state variable. Such low regularity rules out the use of Pontryagin's maximum principle and also invalidates the standard…