Related papers: Stochastic Gradient Estimation for Higher-order Di…
High-resolution representations are important for vision-based robotic grasping problems. Existing works generally encode the input images into low-resolution representations via sub-networks and then recover high-resolution…
Importance sampling has been successfully used to accelerate stochastic optimization in many convex problems. However, the lack of an efficient way to calculate the importance still hinders its application to Deep Learning. In this paper,…
This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable…
Stochastic gradient descent (SGD) gives an optimal convergence rate when minimizing convex stochastic objectives $f(x)$. However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when $f(x)$ is…
Variational Optimization forms a differentiable upper bound on an objective. We show that approaches such as Natural Evolution Strategies and Gaussian Perturbation, are special cases of Variational Optimization in which the expectations are…
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…
Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…
First-order methods for stochastic optimization have undeniable relevance, in part due to their pivotal role in machine learning. Variance reduction for these algorithms has become an important research topic. In contrast to common…
We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent…
Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to $\mathcal{O}(d^{k})$ scaling of the derivative tensor size and the…
In this paper, we propose several novel deep learning methods for object saliency detection based on the powerful convolutional neural networks. In our approach, we use a gradient descent method to iteratively modify an input image based on…
An appealing property of the natural gradient is that it is invariant to arbitrary differentiable reparameterizations of the model. However, this invariance property requires infinitesimal steps and is lost in practical implementations with…
Sketching is a dimensionality reduction technique where one compresses a matrix by linear combinations that are chosen at random. A line of work has shown how to sketch the Hessian to speed up each iteration in a second order method, but…
We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an…
We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
We propose a fast second-order method that can be used as a drop-in replacement for current deep learning solvers. Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
Any gradient descent optimization requires to choose a learning rate. With deeper and deeper models, tuning that learning rate can easily become tedious and does not necessarily lead to an ideal convergence. We propose a variation of the…
Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…