Convergence of Batch Updating Methods with Approximate Gradients and/or Noisy Measurements: Theory and Computational Results

2022-09-12 · Tadipatri Uday Kiran Reddy, M. Vidyasagar

In this paper, we present a unified and general framework for analyzing the batch updating approach to nonlinear, high-dimensional optimization. The framework encompasses all the currently used batch updating approaches, and is applicable to nonconvex as well as convex functions. Moreover, the framework permits the use of noise-corrupted gradients, as well as first-order approximations to the gradient (sometimes referred to as "gradient-free" approaches). By viewing the analysis of the iterations as a problem in the convergence of stochastic processes, we are able to establish a very general theorem, which includes most known convergence results for zeroth-order and first-order methods. The analysis of "second-order" or momentum-based methods is not a part of this paper, and will be studied elsewhere. However, numerical experiments indicate that momentum-based methods can fail if the true gradient is replaced by its first-order approximation. This requires further theoretical analysis.

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A Robust Multi-Batch L-BFGS Method for Machine Learning

2017-07-26 · Albert S. Berahas, Martin Takáč

This paper describes an implementation of the L-BFGS method designed to deal with two adversarial situations. The first occurs in distributed computing environments where some of the computational nodes devoted to the ev…

BIG-bench Machine Learning Binary Classification Distributed Computing

Improving Unlearning with Model Updates Probably Aligned with Gradients

2025-11-04 · Virgile Dine, Teddy Furon, Charly Faure arxiv

We formulate the machine unlearning problem as a general constrained optimization problem. It unifies the first-order methods from the approximate machine unlearning literature. This paper then introduces the concept of …

A Multi-Batch L-BFGS Method for Machine Learning

2016-05-19 · NeurIPS 2016 12 · Albert S. Berahas, Jorge Nocedal, Martin Takáč

The question of how to parallelize the stochastic gradient descent (SGD) method has received much attention in the literature. In this paper, we focus instead on batch methods that use a sizeable fraction of the training…

BIG-bench Machine Learning Distributed Computing

Convergence of the Stochastic Heavy Ball Method With Approximate Gradients and/or Block Updating

2023-03-28 · Uday Kiran Reddy Tadipatri, Mathukumalli Vidyasagar

In this paper, we establish the convergence of the stochastic Heavy Ball (SHB) algorithm under more general conditions than in the current literature. Specifically, (i) The stochastic gradient is permitted to be biased, …

Sample Efficient Reinforcement Learning with REINFORCE

2020-10-22 · Junzi Zhang, Jongho Kim, Brendan O'Donoghue, Stephen Boyd

Policy gradient methods are among the most effective methods for large-scale reinforcement learning, and their empirical success has prompted several works that develop the foundation of their global convergence theory. …

Policy Gradient Methods reinforcement-learning Reinforcement Learning Reinforcement Learning (RL)