Related papers: Preconditioner on Matrix Lie Group for SGD
Deep neural networks (DNNs) are currently predominantly trained using first-order methods. Some of these methods (e.g., Adam, AdaGrad, and RMSprop, and their variants) incorporate a small amount of curvature information by using a diagonal…
Stochastic Gradient Descent (SGD) is arguably the most important single algorithm in modern machine learning. Although SGD with unbiased gradient estimators has been studied extensively over at least half a century, SGD variants relying on…
Stochastic gradient descent (SGD) is an estimation tool for large data employed in machine learning and statistics. Due to the Markovian nature of the SGD process, inference is a challenging problem. An underlying asymptotic normality of…
Stochastic Gradient Descent (SGD) has become the method of choice for solving a broad range of machine learning problems. However, some of its learning properties are still not fully understood. We consider least squares learning in…
Linear programming relaxations are central to {\sc map} inference in discrete Markov Random Fields. The ability to properly solve the Lagrangian dual is a critical component of such methods. In this paper, we study the benefit of using…
While second order optimizers such as natural gradient descent (NGD) often speed up optimization, their effect on generalization has been called into question. This work presents a more nuanced view on how the \textit{implicit bias} of…
Stochastic gradient descent (SGD) is central to simulation optimization, stochastic programming, and online M-estimation, where sampling effort is a decision variable. We study the mini-batch gradient noise as a sampling-design object.…
We present a unified framework for analyzing local SGD methods in the convex and strongly convex regimes for distributed/federated training of supervised machine learning models. We recover several known methods as a special case of our…
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…
In this paper we propose an efficiently preconditioned Newton method for the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices. A sequence of preconditioners based on the BFGS update formula is…
In several experimental reports on nonconvex optimization problems in machine learning, stochastic gradient descent (SGD) was observed to prefer minimizers with flat basins in comparison to more deterministic methods, yet there is very…
Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…
We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods…
Geometry-aware optimizers such as Newton and natural gradient can improve conditioning in deep learning, but scalable variants such as K-FAC, Shampoo, and related preconditioners usually impose structural approximations early, often…
While classical forms of stochastic gradient descent algorithm treat the different coordinates in the same way, a framework allowing for adaptive (non uniform) coordinate sampling is developed to leverage structure in data. In a non-convex…
The gradient descent (GD) method -- is a fundamental and likely the most popular optimization algorithm in machine learning (ML), with a history traced back to a paper in 1847 (Cauchy, 1847). It was studied under various assumptions,…
Adam is the de facto optimization algorithm for several deep learning applications, but an understanding of its implicit bias and how it differs from other algorithms, particularly standard first-order methods such as (stochastic) gradient…
Gradient-based algorithms are one of the methods of choice for the optimisation of Markov Decision Processes. In this article we will present a novel approximate Newton algorithm for the optimisation of such models. The algorithm has…
We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied to address the constraints in optimization problems, such as…
We propose a gradient preconditioning method that makes reward-guided generation with one-step generative models both efficient and reliable. Test-time noise optimization can unlock substantially better reward-guided generations from…