相关论文: Worst Exponential Decay Rate for Degenerate Gradie…

In this paper we extend the adaptive gradient descent (AdaGrad) algorithm to the optimal distributed control of parabolic partial differential equations with uncertain parameters. This stochastic optimization method achieves an improved…

This paper studies the design of feedback controllers to steer a switching linear time-invariant dynamical system towards the solution trajectory of a time-varying convex optimization problem. We propose two types of controllers: (i) a…

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Minimax optimal convergence rates for classes of stochastic convex optimization problems are well characterized, where the majority of results utilize iterate averaged stochastic gradient descent (SGD) with polynomially decaying step sizes.…

We study an asymptotic behaviour of the principal eigenvalue for an elliptic operator with large advection which is given by a gradient of a potential function. It is shown that the principal eigenvalue decays exponentially under the…

We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In the case of multiplicative noise, existence of optimal controls and necessary conditions for optimality are derived. In…

We prove exponential decay for the solution of the Schr{\"o}dinger equation on a dissipative waveguide. The absorption is effective everywhere on the boundary but the geometric control condition is not satisfied. The proof relies on…

In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of the solution of a gradient flow. We show through a simple…

Consider a discrete-time Linear Quadratic Regulator (LQR) problem solved using policy gradient descent when the system matrices are unknown. The gradient is transmitted across a noisy channel over a finite time horizon using analog…

In recent years, more attention has been paid prominently to accelerated degradation testing in order to characterize accurate estimation of reliability properties for systems that are designed to work properly for years of even decades.…

Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…

Gradient descent (GD) and stochastic gradient descent (SGD) have been widely used in a large number of application domains. Therefore, understanding the dynamics of GD and improving its convergence speed is still of great importance. This…

In this work we study a distributed optimal output consensus problem for heterogeneous linear multi-agent systems where the agents aim to reach consensus with the purpose of minimizing the sum of private convex costs. Based on output…

We consider the continuous-time Linear-Quadratic-Regulator (LQR) problem in terms of optimizing a real-valued matrix function over the set of feedback gains. The results developed are in parallel to those in Bu et al. [1] for discrete-time…

Strong stability, defined by bounds that decay not only over time but also with the number of impulses, has been established as a requirement to ensure robustness properties for impulsive systems with respect to inputs or disturbances. Most…

We investigate a well-known phenomenon of variational approaches in image processing, where typically the best image quality is achieved when the gradient flow process is stopped before converging to a stationary point. This paradox…

We are concerned with flow enhanced mixing of passive scalars in the presence of diffusion. Under the assumption that the velocity gradient is suitably integrable, we provide upper bounds on the exponential rates of enhanced dissipation.…

We establish new, optimal gradient continuity estimates for solutions to a class of 2nd order partial differential equations, $\mathscr{L}(X, \nabla u, D^2 u) = f$, whose diffusion properties (ellipticity) degenerate along the \textit{a…

Three-dimensional control is considered in the flow past a backward-facing step (BFS). The BFS flow at Reynolds number $Re=500$ (defined with the step height and the maximum inlet velocity) is two-dimensional and linearly stable but…

We consider policy gradient methods for stochastic optimal control problem in continuous time. In particular, we analyze the gradient flow for the control, viewed as a continuous time limit of the policy gradient method. We prove the global…