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…
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48 results for “stochastic variance-reduced”
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…
New algorithm improves convergence of AUC maximization.
problem Optimizing AUC for imbalanced classes with stochastic methods.
method Variance Reduced Stochastic Proximal Algorithm for AUC Maximization (VRSPAM).
result VRSPAM converges faster than previous methods.
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…
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…
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 …
We analyze distributed algorithms for minimizing losses with large, disjoint data.
problem Distributed implementation of stochastic variance reduced methods for large, disjoint data.
method General framework for distributing stochastic variance reduced methods in a master/slave model.
result Linear convergence of distributed algorithms for minimizing strongly convex losses.
A Stochastic Variance Reduced Gradient using Barzilai-Borwein Techniques as Second Order Informationmath.OC
Improved SVRG method using BB techniques for faster convergence.
problem Improving the convergence speed of stochastic variance reduction methods.
method Incorporates Barzilai-Borwein (BB) techniques as second-order information into SVRG.
result Proves linear convergence of the proposed method and its variants.
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 methods solve graph sparsity optimization problems faster.
problem Complex graph sparsity optimization problems in disease outbreak monitoring and social network analysis.
method Stochastic variance-reduced gradient-based methods GraphSVRG-IHT and GraphSCSG-IHT.
result Our methods achieve linear convergence speed.
Improved Optimization of Finite Sums with Minibatch Stochastic Variance Reduced Proximal Iterationsmath.OC
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-…
Study variance-reduced method for estimating fixed points in Banach spaces.
problem Estimating fixed points of contractive operators in Banach spaces with noisy evaluations.
method Variance-reduced stochastic approximation scheme in Banach spaces.
result Establish non-asymptotic bounds for operator defect and estimation error.
Memory-efficient algorithm reduces variance in off-policy RL.
problem High variance in off-policy policy optimization.
method Memory-efficient, stochastically variance-reduced algorithm using off-policy samples.
result Empirically validated effectiveness of the proposed algorithm.
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…
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…
Unified analysis of stochastic gradient methods for convex and smooth optimization.
problem Minimizing composite convex and smooth functions.
method Unified convergence analysis of various stochastic gradient methods.
result Unified convergence rates for a variety of methods including proximal SGD, variance reduced methods, quantization, and coordinate descent.
Stochastic Variance-Reduced Cubic regularization (SVRC) algorithms have received increasing attention due to its improved gradient/Hessian complexities (i.e., number of queries to stochastic gradient/Hessian oracles) to find local minima for nonconvex finite-sum optimization. However, it is unclear whether existing SVR…
New scheme adapts batch size for faster variance-reduced algorithms.
problem Slowness of variance-reduced algorithms due to large batch size.
method Eliminates backtracking line search, adapts batch size via history stochastic gradients.
result Significantly reduces overall complexity for SVRG and SARAH/SPIDER.
Improved robustness in optimization methods using second-order information.
problem Scalability and sensitivity to mini-batch size in optimization methods.
method Mini-Batch Stochastic Variance-Reduced Newton () algorithm incorporating partial second-order information.
result Achieves a fast linear convergence rate independent of mini-batch size for large data sizes.
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 …
A new method reduces the complexity of decentralized optimization.
problem Decentralized stochastic non-convex optimization over a network.
method GT-HSGD, a hybrid variance-reduced method.
result Achieves an oracle complexity of O(n^(-1)ε^(-3)) for small ε.
A new hybrid algorithm reduces stochastic gradient evaluations for nonconvex optimization.
problem Solving stochastic composite nonconvex optimization problems efficiently.
method Proposes a new hybrid variance-reduced proximal gradient method with a stochastic gradient estimator.
result Achieves optimal stochastic oracle complexity bound with one less gradient evaluation.
New algorithm reduces noise in GAN training, improving stability and efficiency.
problem Stochastic gradient noise hinders GAN convergence.
method Stochastic variance-reduced extragradient (SVRE) optimization algorithm.
result SVRE improves GAN training stability and efficiency compared to standard methods.
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…
Improved SVRPG analysis for faster convergence in reinforcement learning.
problem Finding faster convergence in reinforcement learning algorithms.
method Improved convergence analysis of SVRPG method, focusing on variance reduction and epoch length/batch size parameters.
result Improved convergence to ε-approximate stationary point with reduced sample complexity.
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…
STORM-PG uses momentum for faster policy gradient updates.
problem Improving policy gradient methods for reinforcement learning.
method Introduces STORM-PG, a SARAH-based algorithm with exponential moving average.
result Achieves sample complexity, matching best-known rate.
Improved training of large-scale neural networks with reduced variance noise.
problem Training large-scale neural networks with high variance noise.
method Stochastic variance reduced Nesterov's Accelerated Quasi-Newton method (SVR-NAQ).
result Improved performance compared to conventional methods on benchmark problems.
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.
problem Solving nonmonotone stochastic composite inclusions.
method Developed unbiased and biased variance-reduced estimators for FRBS method.
result Achieved best oracle complexities for finite-sum and expectation settings.
AGDA and variance-reduced methods solve nonconvex-nonconcave minimax problems globally and faster.
problem Solving nonconvex-nonconcave minimax problems in machine learning.
method Global convergence of AGDA and variance-reduced algorithms.
result AGDA and variance-reduced methods achieve global convergence and faster rates.
We propose a sample efficient stochastic variance-reduced cubic regularization (Lite-SVRC) algorithm for finding the local minimum efficiently in nonconvex optimization. The proposed algorithm achieves a lower sample complexity of Hessian matrix computation than existing cubic regularization based methods. At the heart…
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)…
In this paper, we propose a novel sufficient decrease technique for stochastic variance reduced gradient descent methods such as SVRG and SAGA. In order to make sufficient decrease for stochastic optimization, we design a new sufficient decrease criterion, which yields sufficient decrease versions of stochastic varianc…
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a compact manifold search space. To this e…
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions. This paper proposes a novel Riemannian extension of the Euclidean stochastic variance reduced gradient (R-SVRG) algorithm to a manifold search space.…
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…
Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization assumes convexity or strong convexity of each function. In this paper, we extend t…
VRSGT algorithm reduces orthogonality constraints in decentralized optimization.
problem Decentralized optimization with orthogonality constraints.
method VRSGT algorithm with variance reduction and orthogonal techniques.
result VRSGT achieves convergence rate of O(1 / k) for orthogonality constraints.
In this paper, we propose a novel sufficient decrease technique for variance reduced stochastic gradient descent methods such as SAG, SVRG and SAGA. In order to make sufficient decrease for stochastic optimization, we design a new sufficient decrease criterion, which yields sufficient decrease versions of variance redu…
Paper improves convergence rate of Langevin Dynamics algorithms.
problem Sampling problems and non-convex optimization in machine learning.
method Stochastic Variance Reduced Gradient Langevin Dynamics and Stochastic Recursive Gradient Langevin Dynamics with improved convergence rates.
result Proves convergence to objective distribution under weaker conditions.
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…
Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently…
Develops variance-reduced methods for solving generalized equations.
problem Solving a class of generalized equations, including minimization, minimax, and variational inequalities.
method Integrates accelerated operator splitting, fixed-point methods, and variance reduction techniques.
result Achieves both and convergence rates on the expected squared norm of the FBS residual.
Develops an accelerated algorithm for solving nonmonotone generalized equations.
problem Solving nonmonotone generalized equations with possibly non-accelerated schemes.
method Combines Nesterov's acceleration and variance-reduction techniques for a class of generalized equations.
result Achieves convergence rates, improving upon non-accelerated counterparts.
This work bounds the run-time of nonconvex optimization with early stopping.
problem Bounding the expected run-time of nonconvex optimization with early stopping.
method Derives conditions for well-defined early stopping based on validation function norms and bounds the expected number of iterations and gradient evaluations.
result Guarantees the validity of early stopping and provides bounds on the expected run-time for various optimization algorithms.
New algorithm reduces distributed optimization time with stochastic delays.
problem Optimizing distributed data with stochastic delays.
method Developed ADSAGA, a variant of SAGA for distributed-data settings with stochastic delays.
result ADSAGA converges in $ ilde{O}\left(\left(n + \sqrt{m}κ
ight)\log(1/ε)
ight)$ iterations under mean delay .