Related papers: Linear Convergence of Generalized Mirror Descent w…
This paper is concerned with convergence analysis for the mirror descent (MD) method, a well-known algorithm in convex optimization. An analysis framework via integral quadratic constraints (IQCs) is constructed to analyze the convergence…
We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates…
Communication delays and synchronization are major bottlenecks for parallel computing, and tolerating asynchrony is therefore crucial for accelerating parallel computation. Motivated by optimization problems that do not satisfy convexity…
In this note, we establish a new exact worst-case linear convergence rate of the proximal gradient method in terms of the proximal gradient norm, which complements the recent results in [1] and implies a refined descent lemma.descent lemma.…
We present and analyze a novel regularized form of the gradient clipping algorithm, proving that it converges to global minima of the loss surface of deep neural networks under the squared loss, provided that the layers are of sufficient…
In this paper we consider online mirror descent (OMD) algorithms, a class of scalable online learning algorithms exploiting data geometric structures through mirror maps. Necessary and sufficient conditions are presented in terms of the…
Nonconvex and nonsmooth optimization problems are important and challenging for statistics and machine learning. In this paper, we propose Projected Proximal Gradient Descent (PPGD) which solves a class of nonconvex and nonsmooth…
In this paper, we study decentralized online stochastic non-convex optimization over a network of nodes. Integrating a technique called gradient tracking in decentralized stochastic gradient descent, we show that the resulting algorithm,…
In this paper, we present a new policy gradient (PG) methods, namely the block policy mirror descent (BPMD) method for solving a class of regularized reinforcement learning (RL) problems with (strongly)-convex regularizers. Compared to the…
Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…
We consider the problem of optimising the expected value of a loss functional over a nonlinear model class of functions, assuming that we have only access to realisations of the gradient of the loss. This is a classical task in statistics,…
Stochastic gradient descent (SGD) is a foundational algorithm for large-scale statistical learning and stochastic optimization. However, statistical inference based on SGD iterates remains challenging when stochastic gradients have infinite…
We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient algorithm is the classical method for solving such a problem…
We provide theoretical guarantees for convergence of discrete-time policy mirror descent with inexact advantage functions updated using temporal difference (TD) learning for entropy regularised MDPs in Polish state and action spaces. We…
We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
It is well known that mirror descent may diverge or cycle on merely monotone variational inequalities. In this paper, we propose \emph{Target Mirror Descent} (TMD), a unified framework that stabilizes monotone flows via a target point…
We study the statistical and computational complexities of the Polyak step size gradient descent algorithm under generalized smoothness and Lojasiewicz conditions of the population loss function, namely, the limit of the empirical loss…
We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…
We consider off-policy temporal-difference (TD) learning methods for policy evaluation in Markov decision processes with finite spaces and discounted reward criteria, and we present a collection of convergence results for several…