Related papers: On the Effectiveness of Richardson Extrapolation i…
We consider a regularized expected reward optimization problem in the non-oblivious setting that covers many existing problems in reinforcement learning (RL). In order to solve such an optimization problem, we apply and analyze the…
In the era of deep learning, understanding over-fitting phenomenon becomes increasingly important. It is observed that carefully designed deep neural networks achieve small testing error even when the training error is close to zero. One…
The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
Understanding when and why interpolating methods generalize well has recently been a topic of interest in statistical learning theory. However, systematically connecting interpolating methods to achievable notions of optimality has only…
This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…
Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
We introduce a technique to estimate a linear operator by embedding it in a family $A_t$ of operators, $t\in(\sigma_0,\infty)$, with suitable curvature properties. One can then estimate the norm of each $A_t$ by bounds that hold in the…
Representation learning is a key technique in modern machine learning that enables models to identify meaningful patterns in complex data. However, different methods tend to extract distinct aspects of the data, and relying on a single…
Our goal is to enable robots to learn cost functions from user guidance. Often it is difficult or impossible for users to provide full demonstrations, so corrections have emerged as an easier guidance channel. However, when robots learn…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
We examine the necessity of interpolation in overparameterized models, that is, when achieving optimal predictive risk in machine learning problems requires (nearly) interpolating the training data. In particular, we consider simple…
Training advanced machine learning models demands massive datasets, resulting in prohibitive computational costs. To address this challenge, data pruning techniques identify and remove redundant training samples while preserving model…
In this work, we further investigate the application of the well-known Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for numerically solving initial-value…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…
Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial…
The presence of measurement error is a widespread issue which, when ignored, can render the results of an analysis unreliable. Numerous corrections for the effects of measurement error have been proposed and studied, often under the…