Related papers: A stochastic gradient method for a class of nonlin…
In this paper we apply the stochastic variance reduced gradient (SVRG) method, which is a popular variance reduction method in optimization for accelerating the stochastic gradient method, to solve large scale linear ill-posed systems in…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
We develop a distributed stochastic gradient descent algorithm for solving non-convex optimization problems under the assumption that the local objective functions are twice continuously differentiable with Lipschitz continuous gradients…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
We consider nonconvex-concave minimax optimization problems of the form $\min_{\bf x}\max_{\bf y\in{\mathcal Y}} f({\bf x},{\bf y})$, where $f$ is strongly-concave in $\bf y$ but possibly nonconvex in $\bf x$ and ${\mathcal Y}$ is a convex…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…
Despite its popularity in the reinforcement learning community, a provably convergent policy gradient method for continuous space-time control problems with nonlinear state dynamics has been elusive. This paper proposes proximal gradient…
We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…
We study statistical inverse learning in the context of nonlinear inverse problems under random design. Specifically, we address a class of nonlinear problems by employing gradient descent (GD) and stochastic gradient descent (SGD) with…
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
Distributionally Robust Optimization (DRO), as a popular method to train robust models against distribution shift between training and test sets, has received tremendous attention in recent years. In this paper, we propose and analyze…
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…
Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform…
We consider a class of stochastic optimal control problems for discrete-time stochastic linear systems which seek for control policies that will steer the probability distribution of the terminal state of the system close to a desired…