arXiv research

Paper establishes lower bounds for finite-sum optimization problems using novel construction methods.

We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than o…

Novel analysis of EFP for finite-sum problems in neural networks.

New lower bounds for gradient methods in strongly convex finite-sum optimization.

We study the conditions under which one is able to efficiently apply variance-reduction and acceleration schemes on finite sum optimization problems. First, we show that, perhaps surprisingly, the finite sum structure by itself, is not sufficient for obtaining a complexity bound of $\tilde{\cO}((n+L/μ)\ln(1/ε))$ for $L…

Finite-sum optimization problems are ubiquitous in machine learning, and are commonly solved using first-order methods which rely on gradient computations. Recently, there has been growing interest in \emph{second-order} methods, which rely on both gradients and Hessians. In principle, second-order methods can require …

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike SVRG, our method can be directly applied to non-strongly and strongly convex prob…

Paper proposes a faster SPIDER-EM variant for large-scale nonconvex optimization.

Study on Nesterov's method in stochastic settings, revealing divergence under certain conditions.

A thesis submitted for the degree of Doctor of Philosophy of The Australian National University. In this work we introduce several new optimisation methods for problems in machine learning. Our algorithms broadly fall into two categories: optimisation of finite sums and of graph structured objectives. The finite sum pr…

New method solves root-finding problems with faster convergence.

Smooth finite-sum optimization has been widely studied in both convex and nonconvex settings. However, existing lower bounds for finite-sum optimization are mostly limited to the setting where each component function is (strongly) convex, while the lower bounds for nonconvex finite-sum optimization remain largely unsol…

Two new Frank-Wolfe algorithms improve convergence for constrained optimization.

Optimal SGD rates achieved with shuffling, covering non-convex and convex cases.

New method reduces complexity of minimizing convex finite sums without needing individual function indices.

Paper develops probabilistic bounds for a stochastic gradient algorithm in non-convex problems.

Lower bounds for higher-order methods in non-convex optimization.

Freya PAGE optimizes nonconvex optimization with heterogeneous, asynchronous workers.

Novel Newton method for large-scale kernel methods using random features.

In this paper, we consider a class of finite-sum convex optimization problems defined over a distributed multiagent network with $m$ agents connected to a central server. In particular, the objective function consists of the average of $m$ ($\ge 1$) smooth components associated with each network agent together with a s…

Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for example by data augmentation. In such cases, the objective is no longer a finite su…

We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic composite gradient method that employs an incremental variance-reduced estimator…

SignSVRG improves SignSGD by reducing variance, achieving similar convergence rates.

A new decentralized method solves minimax problems with reduced communication and sample complexity.

A new algorithm improves convergence rates for convex optimization problems.

PAGE is a simple gradient estimator for nonconvex optimization problems.

New algorithms solve non-convex optimization problems efficiently.

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,…

DESTRESS optimizes decentralized nonconvex optimization with optimal IFO complexity and efficient communication.

Techniques for reducing the variance of gradient estimates used in stochastic programming algorithms for convex finite-sum problems have received a great deal of attention in recent years. By leveraging dissipativity theory from control, we provide a new perspective on two important variance-reduction algorithms: SVRG …

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)…

Nesterov's momentum trick is famously known for accelerating gradient descent, and has been proven useful in building fast iterative algorithms. However, in the stochastic setting, counterexamples exist and prevent Nesterov's momentum from providing similar acceleration, even if the underlying problem is convex and fin…

The height function of various surfaces decomposes into finite sums of scaled and translated versions of itself.

Unified framework for decentralized optimization combining gradient tracking and variance reduction.

SVRN accelerates Newton methods by reducing variance and improving performance.

The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function $F(w)=\frac{1}{n} \sum_{i=1}^n f_i(w)$ has been proven to be at least $Ω(\sqrt{n}/ε)$ for $n \leq …

Accelerates optimization in asynchronous systems with sparse updates.

The paper analyzes the variance of different shuffling methods in stochastic gradient descent.

New algorithms find near-stationary points in convex optimization.

Paper analyzes complexity of solving nonconvex-strongly-concave problems.

Improved variance reduction for Riemannian non-convex optimization with adaptive batch size.

Stochastic Gradient Descent underperforms on some problems, contrary to expectations.

SMG combines shuffling and momentum for non-convex optimization.

Independent component analysis (ICA) is a widespread data exploration technique, where observed signals are modeled as linear mixtures of independent components. From a machine learning point of view, it amounts to a matrix factorization problem with a statistical independence criterion. Infomax is one of the most used…

In this paper, we consider a class of finite-sum convex optimization problems whose objective function is given by the summation of $m$ ($\ge 1$) smooth components together with some other relatively simple terms. We first introduce a deterministic primal-dual gradient (PDG) method that can achieve the optimal black-bo…

Avare improves optimization and sampling with adaptive importance sampling.

We propose two algorithms that can find local minima faster than the state-of-the-art algorithms in both finite-sum and general stochastic nonconvex optimization. At the core of the proposed algorithms is $\text{One-epoch-SNVRG}^+$ using stochastic nested variance reduction (Zhou et al., 2018a), which outperforms the s…

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-…