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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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141281422562 · Jun 202019922001200920172026
48 results for linear rate

Paper studies Gaussian approximation in linear regression with rates derived.

problem Gaussian approximation in online linear regression.
method Derives rates for constant learning rate settings, analyzes dependence on dd and design matrix.
result Rate of normal approximation is logn/n\sqrt{\log{n}/n} for large nn.

The paper analyzes how learning rate affects SGD and provides insights into optimal rates.

problem Understanding the impact of learning rate on stochastic gradient descent.
method Developed a learning-rate-dependent stochastic differential equation (lr-dependent SDE) to analyze SGD.
result Established a linear rate of convergence for SGD and found the optimal linear rate by analyzing the spectrum of the Witten-Laplacian.

We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure or G-mean, and constrained training problems where the classifier needs to sati…

2019-09-06abs ↗pdf ↗

We consider the problem of learning a non-negative linear classifier with a 11-norm of at most kk, and a fixed threshold, under the hinge-loss. This problem generalizes the problem of learning a kk-monotone disjunction. We prove that we can learn efficiently in this setting, at a rate which is linear in both kk and…

2012-12-13abs ↗pdf ↗

Gradient descent achieves exact linear convergence rate for symmetric matrix completion.

problem Low-rank symmetric matrix completion using gradient descent.
method Local analysis of gradient descent for symmetric matrices without additional assumptions.
result Closed-form expression of exact linear convergence rate matches practice.

New method for private linear regression under privacy constraints, achieving optimal rates.

problem Statistical complexity of private linear regression under unknown, ill-conditioned covariates.
method Information-Weighted Regression method
result Optimal convergence rates for both central and local privacy models.

Unified framework for robust linear predictions without distributional assumptions.

problem Robust linear predictions in the presence of outliers and model misspecification.
method Unified robust framework for linear prediction problems on Hilbert spaces, using Median of Means (MoM) approach.
result Achieves an error rate of \(O(\max\left\{|\mathcal{O}|^{1/2}n^{-1/2}, |\mathcal{I}|^{1/2}n^{-1} ight\}+ε)\) for misspecification level \(ε\), matching best-known rates.

Study on L2-boosting behavior as learning rate approaches zero.

problem Understanding the asymptotic behavior of L2-boosting algorithms with vanishing learning rates.
method Analyzes L2-boosting for regression with linear base learners, proving a deterministic limit and characterizing it as a solution to a linear differential equation.
result Proves the existence of a unique solution to the limit problem and analyzes the training and test error.

Paper revisits set membership estimation for linear systems with relaxed disturbance bounds.

problem Set membership estimation for linear systems with disturbances bounded by convex sets.
method Adopted block-martingale small-ball condition and random perturbed control policies to establish convergence rates.
result Established convergence rates for disturbances bounded by general convex sets.

Linear-Core Surrogates combine fast optimization and statistical efficiency in classification and structured prediction.

problem The trade-off between smoothness and margin-based losses in classification and structured prediction.
method Linear-Core (LC) Surrogates, a family of convex loss functions that stitch a linear core to a smooth tail.
result LC Surrogates achieve fast linear consistency rates while maintaining differentiability and strict HH-consistency bounds.

Paper analyzes TD(λλ) convergence rates for arbitrary features.

problem Convergence rates for linear TD(λλ) under arbitrary features.
method Developed a novel stochastic approximation result for arbitrary features.
result Established L2L^2 convergence rates for linear TD(λλ) without linearly independent features assumption.

PANDA improves linear discriminant analysis in high dimensions with minimal tuning.

problem Linear discriminant analysis in high-dimensional settings.
method PANDA: a tuning-insensitive method for linear discriminant analysis.
result PANDA achieves optimal convergence rates in estimation error and misclassification rate.

Active data collection improves convergence rates in operator learning.

problem Improving convergence rates in operator learning with linear target and stochastic input.
method Active data collection strategies with mean-zero stochastic process and continuous covariance kernels.
result Achieves arbitrarily fast error convergence rates with eigenvalue decay of covariance kernels.

Study identifies and validates a method for system identification of Markov jump linear systems.

problem System identification for autonomous Markov jump linear systems with complete state observations.
method Proposes switched least squares method for identification and derives rates of convergence.
result Data-independent rate of convergence is O(log(T)/T)\mathcal{O}\big(\sqrt{\log(T)/T} \big), showing strong consistency.

Improved SGD for robust linear and ReLU regression with adversarial corruptions.

problem Robust regression with adversarial corruptions in streaming data.
method Stochastic gradient descent (SGD-exp) with exponentially decaying step size.
result Nearly linear convergence to true parameter with up to 50% Massart corruption rate.

The paper analyzes how hyperparameters affect SGD with momentum's convergence rate.

problem The role of hyperparameters in SGD with momentum's convergence rate.
method Theoretical analysis using a hyperparameters-dependent stochastic differential equation (hp-dependent SDE).
result The optimal linear rate of convergence depends on both the learning rate and the momentum coefficient.

Study examines how data augmentation impacts optimization in linear regression.

problem Understanding how data augmentation schedules affect optimization in linear regression.
method Analyzed the effect of augmentation on optimization in linear regression with MSE loss, using classical convex optimization and recent work on implicit bias.
result Proved that under certain joint schedules for learning rate and augmentation scheme, augmented gradient descent converges and characterized the resulting minimum.

Linear Q-learning converges to a bounded set without divergence.

problem Proving linear Q-learning does not diverge and converges to a bounded set.
method No modifications to the original linear Q-learning algorithm, no Bellman completeness or near-optimality assumptions, only an ε-softmax behavior policy with adaptive temperature.
result First L2L^2 convergence rate of linear Q-learning iterates to a bounded set.

WSqD extends learning rate schedules for large model training without fixed horizons.

problem Fixed learning rate schedules limit training horizon extension.
method WSqD replaces constant stable phase with a shifted inverse-square-root base, retaining linear cooldown.
result WSqD achieves minimax-optimal convergence rate and horizon-independence.

Paper derives convergence rates and confidence intervals for LSA with Markovian noise.

problem Analyzing convergence rates and constructing confidence intervals for LSA with Markovian noise.
method Derives non-asymptotic Berry-Esseen bounds and multiplier block bootstrap procedure.
result Provides O(n1/4)\mathcal{O}(n^{-1/4}) convergence rates and guarantees consistent inference.

Study optimizes linear regression analysis for high-dimensional settings.

problem Understanding high-dimensional linear regression with interpolation and regularization.
method Localized uniform convergence analysis of optimistic rates for linear regression.
result Recover guarantees for ridge and LASSO regression under random designs.

Efficiently estimates linear models robust to corrupted data.

problem Learning linear models under adversarial corruption and minimal distributional assumptions.
method Develops a polynomial relaxation of independence to achieve optimal convergence rate.
result Achieves optimal convergence rate of ε22/kε^{2-2/k} for kk-hypercontractive distributions.

Paper develops a method for estimating PFLM with minimized rates in high dimensions.

problem Estimating PFLM with minimized rates in high dimensions.
method Least square approach with mixed regularizations of function-norm and ℓ1-norm.
result Established optimal minimax rates of estimation for PFLM.

AM converges super-linearly for solving mixed linear regression problems.

problem Learning linear regressors from unlabeled observations in multiple linear regression models.
method Alternating Minimization (AM) algorithm, which alternates between label estimation and regression solving.
result AM converges super-linearly in certain parameter regimes, requiring only O(log log(1/ε)) iterations to achieve an error of ε.

Study on distributional TD learning with linear approximations for better return estimation.

problem Estimating the return distribution of a policy in reinforcement learning.
method Finite-sample analysis of distributional TD learning with linear function approximation, using the linear-categorical Bellman equation and exponential stability arguments for products of random matrices.
result Sample complexity of linear distributional TD learning matches that of classic linear TD learning, indicating similar difficulty in estimating return distribution versus its expectation.

This paper closes the gap on matching pursuit's convergence rate.

problem Improving the understanding of matching pursuit's convergence rate.
method Constructing a worst case dictionary to analyze matching pursuit's performance.
result Sharp characterization of matching pursuit's convergence rate as nαn^{-α}, with α0.182α \approx 0.182.

Gradient descent converges linearly for overparameterized linear networks.

problem Convergence of gradient descent for overparameterized neural networks.
method Local Polyak-Lojasiewicz and Descent Lemma for overparameterized linear models.
result Gradient descent achieves linear convergence for two-layer linear networks under relaxed assumptions.

Two sweeps of the Brennan-Schwartz algorithm solve American options under negative rates.

problem Inability of the Brennan-Schwartz algorithm to solve American options under negative interest rates.
method Two sweeps of the Brennan-Schwartz algorithm in two directions.
result Recovery of the exact solution for American options under negative rates.

Guaranteed convergence for tensor factorization using Riemannian gradient descent.

problem Recovering tensor train format from linear measurements.
method Optimization over left-orthogonal TT format using Riemannian gradient descent on Stiefel manifold.
result RGD converges linearly to the ground-truth tensor with polynomial error growth in tensor order.

Study shows deep linear networks can converge to flatter minima at large learning rates.

problem Understanding the implicit bias of deep linear networks at large learning rates.
method Characterization of deep linear networks for binary classification using logistic loss in the large learning rate regime.
result Gradient descent iterates converge to a flatter minimum in the catapult phase for certain data separation conditions.

New insights into how large learning rates affect transformer training dynamics.

problem Understanding how large learning rates impact the training of transformer models.
method Analyzing a simplified linear transformer model with a two-factor product map.
result Large learning rates can lead to various training outcomes including cycles, chaos, or divergence.

Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for minimizing a smooth convex function over a linear space spanned by a set of atoms…

2019-04-28abs ↗pdf ↗

Stochastic gradient descent achieves polynomial convergence rates for noiseless linear models.

problem Convergence analysis of stochastic gradient descent in noiseless linear models.
method Fixed step-size stochastic gradient descent on least-square risk.
result Polynomial convergence rates depend on the regularities of the optimum and feature vectors.

Paper improves TD(0) convergence rate with LFA, i.i.d. samples, and averaging.

problem Improving convergence rate of TD(0) with linear function approximation.
method Polyak-Juditsky averaging, i.i.d. samples, strong mixing assumption.
result Established a new convergence rate for Mean-Square Error (MSE) of approximated function.

We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call non-linear affine processes. This is done as follows: given a set of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programm…

2018-06-07abs ↗pdf ↗

AdaLoss optimizes adaptive learning rates for efficient convergence in various models.

problem Efficiently optimizing adaptive learning rates for gradient descent methods.
method AdaLoss uses loss function information to dynamically adjust step sizes.
result AdaLoss achieves linear convergence in linear regression and robust global convergence in neural networks.

Unified framework for solving linear systems with improved convergence rates.

problem Efficiently solving linear systems with randomized batch-sampling methods.
method Developed a unified randomized batch-sampling Kaczmarz framework with concentration inequalities for analysis.
result Derived new expected linear convergence rate bounds that are tighter and more reflective of empirical behavior.