Related papers: A Progressive Batching L-BFGS Method for Machine L…

Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of…

We explore the usage of the Levenberg-Marquardt (LM) algorithm for regression (non-linear least squares) and classification (generalized Gauss-Newton methods) tasks in neural networks. We compare the performance of the LM method with other…

Mini-batch stochastic gradient methods (SGD) are state of the art for distributed training of deep neural networks. Drastic increases in the mini-batch sizes have lead to key efficiency and scalability gains in recent years. However,…

We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the…

Stochastic gradient methods for minimizing nonconvex composite objective functions typically rely on the Lipschitz smoothness of the differentiable part, but this assumption fails in many important problem classes like quadratic inverse…

Batch Normalization (BN) has become a cornerstone of deep learning across diverse architectures, appearing to help optimization as well as generalization. While the idea makes intuitive sense, theoretical analysis of its effectiveness has…

This paper concerns exact linesearch quasi-Newton methods for minimizing a quadratic function whose Hessian is positive definite. We show that by interpreting the method of conjugate gradients as a particular exact linesearch quasi-Newton…

We study here a fixed mini-batch gradient decent (FMGD) algorithm to solve optimization problems with massive datasets. In FMGD, the whole sample is split into multiple non-overlapping partitions. Once the partitions are formed, they are…

In this paper, we studied a buffered mini-batch gradient descent (BMGD) algorithm for training complex model on massive datasets. The algorithm studied here is designed for fast training on a GPU-CPU system, which contains two steps: the…

Iterative code generation with Large Language Models (LLMs) can be viewed as an optimization process guided by textual feedback. However, existing LLM self-correction methods predominantly operate in a stateless, trial-and-error manner akin…

Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple…

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true…

Boosting is a popular ensemble algorithm that generates more powerful learners by linearly combining base models from a simpler hypothesis class. In this work, we investigate the problem of adapting batch gradient boosting for minimizing…

In this paper, we propose a quasi Newton method to solve the robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty set. Here the robust counterpart of an uncertain multiobjective…

In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…

It is well-known by now that the BFGS method is an effective method for minimizing nonsmooth functions. However, despite its popularity, theoretical convergence results are almost non-existent. One of the difficulties when analyzing the…

In this paper, we present a global complexity analysis of the classical BFGS method with inexact line search, as applied to minimizing a strongly convex function with Lipschitz continuous gradient and Hessian. We consider a variety of…

We present PrecisionBatching, a quantized inference algorithm for speeding up neural network execution on traditional hardware platforms at low bitwidths without the need for retraining or recalibration. PrecisionBatching decomposes a…

This paper considers an explicit continuation method and the trust-region updating strategy for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the…

Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard…