arXiv research

Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizer. The existing convergence results assume uniform data sampling with replacement. However, it has been observed in …

In this paper, we propose a novel reinforcement- learning algorithm consisting in a stochastic variance-reduced version of policy gradient for solving Markov Decision Processes (MDPs). Stochastic variance-reduced gradient (SVRG) methods have proven to be very successful in supervised learning. However, their adaptation…

Memory-efficient algorithm reduces variance in off-policy RL.

New $Q$-learning method reduces variance and achieves optimal sample complexity.

This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear embedding and reinforcement learning. Although existing approaches such as stochastic gr…

Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms are usually slow to converge and achieve sub-linear convergence rates, due to t…

New scheme adapts batch size for faster variance-reduced algorithms.

Study variance-reduced method for estimating fixed points in Banach spaces.

AGDA and variance-reduced methods solve nonconvex-nonconcave minimax problems globally and faster.

Recent years have witnessed exciting progress in the study of stochastic variance reduced gradient methods (e.g., SVRG, SAGA), their accelerated variants (e.g, Katyusha) and their extensions in many different settings (e.g., online, sparse, asynchronous, distributed). Among them, accelerated methods enjoy improved conv…

Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Considering the stochastic learning in NMF, we specifically address the multiplicative update (MU) rule, which is the most popular, but which h…

New algorithms learn robust policies from shifted distributions.

Stochastic variance reduced methods have gained a lot of interest recently for empirical risk minimization due to its appealing run time complexity. When the data size is large and disjointly stored on different machines, it becomes imperative to distribute the implementation of such variance reduced methods. In this p…

Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients evaluated on mini-batches are used as a replacement. In order to reduce the high vari…

Develops variance-reduced methods for solving generalized equations.

A new method reduces variance in PG methods for RL, improving efficiency and convergence.

We study distributed optimization algorithms for minimizing the average of convex functions. The applications include empirical risk minimization problems in statistical machine learning where the datasets are large and have to be stored on different machines. We design a distributed stochastic variance reduced gradien…

New algorithm improves convergence of AUC maximization.

Improved robustness in optimization methods using second-order information.

New algorithm solves nonconvex-convex minimax problems efficiently.

We present novel minibatch stochastic optimization methods for empirical risk minimization problems, the methods efficiently leverage variance reduced first-order and sub-sampled higher-order information to accelerate the convergence speed. For quadratic objectives, we prove improved iteration complexity over state-of-…

As application demands for zeroth-order (gradient-free) optimization accelerate, the need for variance reduced and faster converging approaches is also intensifying. This paper addresses these challenges by presenting: a) a comprehensive theoretical analysis of variance reduced zeroth-order (ZO) optimization, b) a nove…

Improved SVRG method using BB techniques for faster convergence.

STORM-PG uses momentum for faster policy gradient updates.

New methods solve graph sparsity optimization problems faster.

Unified analysis of stochastic gradient methods for convex and smooth optimization.

Random features are improved by variance-reducing couplings, enhancing machine learning models.

We study Frank-Wolfe methods for nonconvex stochastic and finite-sum optimization problems. Frank-Wolfe methods (in the convex case) have gained tremendous recent interest in machine learning and optimization communities due to their projection-free property and their ability to exploit structured constraints. However,…

New variance-reduction methods solve stochastic composite inclusions.

VRCQ algorithm reduces variance in Q-learning for MDPs, achieving optimal sample complexity.

We revisit the stochastic variance-reduced policy gradient (SVRPG) method proposed by Papini et al. (2018) for reinforcement learning. We provide an improved convergence analysis of SVRPG and show that it can find an $ε$-approximate stationary point of the performance function within $O(1/ε^{5/3})$ trajectories. This s…

Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation of the control variates and leading to faster theoretical convergence close to …

New algorithm reduces optimization complexity in adaptive mirror descent.

We study the effect of the stochastic gradient noise on the training of generative adversarial networks (GANs) and show that it can prevent the convergence of standard game optimization methods, while the batch version converges. We address this issue with a novel stochastic variance-reduced extragradient (SVRE) optimi…

New method estimates optimal Q-values with better accuracy for specific problems.

Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g.\ SAG-ADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems. However, the best known convergence rate for general convex problems is O(1/T) as opp…

The alternating direction method of multipliers (ADMM) is a powerful optimization solver in machine learning. Recently, stochastic ADMM has been integrated with variance reduction methods for stochastic gradient, leading to SAG-ADMM and SDCA-ADMM that have fast convergence rates and low iteration complexities. However,…

Many machine learning, statistical inference, and portfolio optimization problems require minimization of a composition of expected value functions (CEVF). Of particular interest is the finite-sum versions of such compositional optimization problems (FS-CEVF). Compositional stochastic variance reduced gradient (C-SVRG)…

Paper proposes an efficient algorithm for learning sparse Bayesian networks from discrete high-dimensional data.

Efficient momentum-based methods for reinforcement learning with improved sample complexity.

The application of stochastic variance reduction to optimization has shown remarkable recent theoretical and practical success. The applicability of these techniques to the hard non-convex optimization problems encountered during training of modern deep neural networks is an open problem. We show that naive application…

With the purpose of examining biased updates in variance-reduced stochastic gradient methods, we introduce SVAG, a SAG/SAGA-like method with adjustable bias. SVAG is analyzed in a cocoercive root-finding setting, a setting which yields the same results as in the usual smooth convex optimization setting for the ordinary…

Improved TD learning reduces variance and bias errors.

The stochastic variance-reduced gradient method (SVRG) and its accelerated variant (Katyusha) have attracted enormous attention in the machine learning community in the last few years due to their superior theoretical properties and empirical behaviour on training supervised machine learning models via the empirical ri…

Recently it has been shown that the step sizes of a family of variance reduced gradient methods called the JacSketch methods depend on the expected smoothness constant. In particular, if this expected smoothness constant could be calculated a priori, then one could safely set much larger step sizes which would result i…

Recent advances in deep reinforcement learning have achieved human-level performance on a variety of real-world applications. However, the current algorithms still suffer from poor gradient estimation with excessive variance, resulting in unstable training and poor sample efficiency. In our paper, we proposed an innova…

We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence guarantees and optimal estimation accuracy in high dimensions. We further extend the …

State-of-the-art deep neural networks are known to be vulnerable to adversarial examples, formed by applying small but malicious perturbations to the original inputs. Moreover, the perturbations can \textit{transfer across models}: adversarial examples generated for a specific model will often mislead other unseen mode…