相关论文: Remarks on the Polyak-Lojasiewicz inequality and t…

Solutions of optimization problems, including policy optimization in reinforcement learning, typically rely upon some variant of gradient descent. There has been much recent work in the machine learning, control, and optimization…

The Polyak-Lojasiewicz inequality (PLI) in $\mathbb{R}^d$ is a natural condition for proving convergence of gradient descent algorithms. In the present paper, we study an analogue of PLI on the space of probability measures…

In 1963, Polyak proposed a simple condition that is sufficient to show a global linear convergence rate for gradient descent. This condition is a special case of the \L{}ojasiewicz inequality proposed in the same year, and it does not…

In this paper, we derive a new linear convergence rate for the gradient method with fixed step lengths for non-convex smooth optimization problems satisfying the Polyak-Lojasiewicz (PL) inequality. We establish that the PL inequality is a…

We study the linear convergence rates of the proximal gradient method for composite functions satisfying two classes of Polyak-{\L}ojasiewicz (PL) inequality: the PL inequality, the variant of PL inequality defined by the proximal map-based…

This paper develops a comprehensive convergence analysis for generic classes of descent algorithms in nonsmooth and nonconvex optimization under several conditions of the Polyak-\L ojasiewicz-Kurdyka (PLK) type. Along other results, we…

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…

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…

Policy gradients methods apply to complex, poorly understood, control problems by performing stochastic gradient descent over a parameterized class of polices. Unfortunately, even for simple control problems solvable by standard dynamic…

We make three contributions toward better understanding policy gradient methods in the tabular setting. First, we show that with the true gradient, policy gradient with a softmax parametrization converges at a $O(1/t)$ rate, with constants…

Although the optimization objectives for learning neural networks are highly non-convex, gradient-based methods have been wildly successful at learning neural networks in practice. This juxtaposition has led to a number of recent studies on…

From the perspective of control theory, the gradient descent optimization methods can be regarded as a dynamic system where various control techniques can be designed to enhance the performance of the optimization method. In this paper, we…

We consider minimization problems with the well-known Polya-Lojasievich condition and Lipshitz-continuous gradient. Such problem occurs in different places in machine learning and related fields. Furthermore, we assume that a gradient is…

We explore reinforcement learning methods for finding the optimal policy in the linear quadratic regulator (LQR) problem. In particular, we consider the convergence of policy gradient methods in the setting of known and unknown parameters.…

The {\L}ojasiewicz inequality characterizes objective-value convergence along gradient flows and, in special cases, yields exponential decay of the cost. However, such results do not directly give rates of convergence in the state. In this…

While the techniques in optimal control theory are often model-based, the policy optimization (PO) approach directly optimizes the performance metric of interest. Even though it has been an essential approach for reinforcement learning…

The paper presents a review of the state-of-the-art of subgradient and accelerated methods of convex optimization, including in the presence of disturbances and access to various information about the objective function (function value,…

Due to its applications in many different places in machine learning and other connected engineering applications, the problem of minimization of a smooth function that satisfies the Polyak-{\L}ojasiewicz condition receives much attention…

Quadratically regularized optimal transport (QOT) is an alternative to entropic regularization that yields sparse couplings and avoids numerical instabilities due to exponential scaling. From an optimization viewpoint, the dual QOT…

With the outstanding performance of policy gradient (PG) method in the reinforcement learning field, the convergence theory of it has aroused more and more interest recently. Meanwhile, the significant importance and abundant theoretical…