Related papers: An optimal scheduled learning rate for a randomize…

We develop a framework for analyzing the training and learning rate dynamics on a large class of high-dimensional optimization problems, which we call the high line, trained using one-pass stochastic gradient descent (SGD) with adaptive…

This paper investigates to what extent one can improve reinforcement learning algorithms. Our study is split in three parts. First, our analysis shows that the classical asymptotic convergence rate $O(1/\sqrt{N})$ is pessimistic and can be…

The classical Kaczmarz iteration and its randomized variants are popular tools for fast inversion of linear overdetermined systems. This method extends naturally to the setting of the phase retrieval problem via substituting at each…

In deep Reinforcement Learning (RL), the learning rate critically influences both stability and performance, yet its optimal value shifts during training as the environment and policy evolve. Standard decay schedulers assume monotonic…

We develop a stochastic approximation version of the classical Kaczmarz algorithm that is incremental in nature and takes as input noisy real time data. Our analysis shows that with probability one it mimics the behavior of the original…

For solving large consistent linear systems by iteration methods, inspired by the maximum residual Kaczmarz method and the randomized block Kaczmarz method, we propose the maximum residual block Kaczmarz method, which is designed to…

In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of $O(n^{-1/5})$ for…

Randomized block Kaczmraz method plays an important role in solving large-scale linear system. One of the key points of this type of methods is how to effectively select working rows. However, in most of the state-of-the-art randomized…

Due to the scarcity of high-quality data, large language models (LLMs) are often trained on mixtures of data with varying quality levels, even after sophisticated data curation. A natural approach to better leverage high-quality data is…

Randomized Kaczmarz methods form a family of linear system solvers which converge by repeatedly projecting their iterates onto randomly sampled equations. While effective in some contexts, such as highly over-determined least squares,…

We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…

In this paper, we analyze the convergence behavior of the randomized extended Kaczmarz (REK) method for all types of linear systems (consistent or inconsistent, overdetermined or underdetermined, full-rank or rank-deficient). The analysis…

$Q$-learning is one of the most fundamental reinforcement learning algorithms. It is widely believed that $Q$-learning with linear function approximation (i.e., linear $Q$-learning) suffers from possible divergence until the recent work…

We investigate the randomized Kaczmarz method that adaptively updates the stepsize using readily available information for solving inconsistent linear systems. A novel geometric interpretation is provided which shows that the proposed…

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…

Linear TD($\lambda$) is one of the most fundamental reinforcement learning algorithms for policy evaluation. Previously, convergence rates are typically established under the assumption of linearly independent features, which does not hold…

This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the…

We introduce a technique for tuning the learning rate scale factor of any base optimization algorithm and schedule automatically, which we call \textsc{mechanic}. Our method provides a practical realization of recent theoretical reductions…

We establish an improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers. Precisely, for the linear system $A\x = \b$, we show that there is a classical algorithm that…

Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…