On-device research index

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.

168,742 papers · 148 categories

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48 results for “rate function”

Function-Space Learning Ratesstat.ML

Develops methods to measure and set function-space learning rates in neural networks.

problem Measuring and optimizing changes in neural network output functions.

method Efficient methods to measure and set function-space learning rates, requiring minimal computational overhead.

result Demonstrates FLeRM (Function-space Learning Rate Matching) for hyperparameter transfer across model scales.

neural networks learning rates function space hyperparameter transfer optimization

2025-02-24abs ↗pdf ↗

A coding theorem for the rate-distortion-perception functioncs.IT

New coding theorem shows achievable rate matches theoretical limit.

problem Unknown existence of encoders and decoders for RDPF.

method Used stochastic, variable-length codes to prove RDPF achievable.

result Achievable rate matches theoretical rate-distortion-perception function.

rate-distortion-perception function stochastic codes variable-length codes lossy compression realism

2021-04-28abs ↗pdf ↗

Equivalence of Convergence Rates of Posterior Distributions and Bayes Estimators for Functions and Nonparametric Functionalsmath.ST

Bayesian method with Gaussian process priors achieves optimal convergence rates for regression function and its derivatives.

problem Estimating the regression function and its derivatives in nonparametric regression.

method Bayesian approach with Gaussian process priors, focusing on convergence rates and plug-in property.

result Equivalence of convergence rates of posterior distributions and Bayes estimators for regression function and its derivatives.

Bayesian methods Gaussian processes nonparametric regression posterior contraction Bayes estimators

2020-11-27abs ↗pdf ↗

Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Codingcs.IT

Estimates rate-distortion function for large datasets using neural networks.

problem Designing lossy data compression schemes and comparing them with theoretical limits.

method Re-formulate rate-distortion objective and solve using neural networks.

result NERD accurately estimates the rate-distortion function for real-world datasets.

rate-distortion function deep neural networks operational source coding Blahut-Arimoto algorithm image datasets

2022-04-04abs ↗pdf ↗

Minimax learning rates for estimating binary classifiers under margin conditionsstat.ML

Study minimax rates for binary classifier estimation with margin conditions.

problem Estimating binary classifiers with geometric margin conditions.

method Derive lower bounds for worst-case learning rates over various function classes.

result Identify optimal rates close to

\mathcal{O}(n^{-1})

for different function classes.

minimax rates binary classifiers margin conditions Barron-regular functions Hölder-continuous functions

2025-05-15abs ↗pdf ↗

Continuum-Armed Bandits: A Function Space Perspectivestat.ML

This paper studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.

problem Optimizing an unknown function with limited evaluations.

method Studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.

result Minimax rates over Besov spaces are identical to those over the smallest Hölder space into which Besov spaces embed.

continuum-armed bandits Besov smoothness minimax rates optimization function space perspective

2020-10-15abs ↗pdf ↗

LALR: Theoretical and Experimental validation of Lipschitz Adaptive Learning Rate in Regression and Neural Networkscs.LG

LALR adapts learning rate for faster convergence in regression and neural nets.

problem Finding optimal learning rates for faster convergence in regression and neural networks.

method Lipschitz continuity theory applied to Mean Absolute Error and Quantile loss functions.

result Adaptive learning rate policy enables up to 20x faster convergence.

Lipschitz continuity adaptive learning rate Mean Absolute Error Quantile loss regression

2020-05-19abs ↗pdf ↗

Time consistent portfolio strategies for a general utility functionq-fin.PM

Study optimal portfolio strategies with time-varying discount rates.

problem Optimizing portfolio decisions with a non-constant discount rate.

method Introduced subgame perfect strategies to handle time inconsistency, using fixed point iteration to find the utility-weighted discount rate.

result Subgame perfect strategies are equivalent to optimal strategies under certain utility function assumptions.

portfolio management time inconsistency subgame perfect utility function discount rate

2026-02-20abs ↗pdf ↗

Learning-Rate-Free Learning by D-Adaptationcs.LG

D-Adaptation automatically sets optimal learning rates without manual tuning.

problem Optimizing learning rates for efficient convergence in machine learning.

method D-Adaptation, which asymptotically achieves optimal learning rates without back-tracking or additional evaluations.

result D-Adaptation automatically matches hand-tuned learning rates across diverse problems.

learning rate optimization machine learning convex functions convergence

2023-01-18abs ↗pdf ↗

Non-asymptotic approximations of neural networks by Gaussian processesmath.PR

Wide neural networks can be closely approximated by Gaussian processes, with rates depending on the activation function's properties.

problem Approximating the behavior of wide neural networks using Gaussian processes.

method Established convergence rates for the central limit theorem in an infinite-dimensional functional space, using a transportation distance metric.

result Explicit convergence rates for neural networks approximated by Gaussian processes, varying based on the activation function's properties.

neural networks Gaussian processes approximation theory transportation distance activation functions

2021-02-17abs ↗pdf ↗

On the inability of Gaussian process regression to optimally learn compositional functionsstat.ML

Gaussian processes struggle with compositional functions, but deep Gaussian processes can outperform.

problem Gaussian process regression struggles with compositional functions.

method We study information-theoretic lower bounds for posterior contraction rates in Gaussian process regression for a continuous regression model.

result Posterior based on any mean-zero Gaussian process can only recover the truth at a rate strictly slower than the minimax rate for generalized additive functions.

Gaussian process regression compositional functions minimax rate information-theoretic lower bounds

2022-05-16abs ↗pdf ↗

A Constrained BA Algorithm for Rate-Distortion and Distortion-Rate Functionscs.IT

Modified BA algorithm computes RD and DR functions efficiently.

problem Computing rate-distortion and distortion-rate functions.

method A novel modification of the BA algorithm using Newton's method for root-finding.

result The modified algorithm converges to RD and DR function solutions with rate

O(1/n)

and provides

\varepsilon

-approximations.

Blahut-Arimoto algorithm rate-distortion function distortion-rate function Newton's method one-dimensional root-finding

2023-05-04abs ↗pdf ↗

Nuisance Function Tuning and Sample Splitting for Optimally Estimating a Doubly Robust Functionalmath.ST

Optimally estimates a functional using nuisance function tuning and sample splitting.

problem Estimating optimal rates for a doubly robust functional.

method Combines nuisance function tuning and sample splitting strategies.

result Shows optimal rates of convergence for various estimators.

doubly robust functional estimation nuisance function sample splitting optimal rates

2022-12-30abs ↗pdf ↗

Multivariate Smoothing via the Fourier Integral Theorem and Fourier Kernelmath.ST

The paper introduces new estimators for multivariate functions using Fourier methods.

problem Estimating multivariate functions like densities and regression functions.

method Monte Carlo estimators based on the Fourier integral theorem.

result Established rates of convergence for new estimators, often superior to existing methods.

Fourier integral theorem Monte Carlo methods multivariate functions rates of convergence

2020-12-28abs ↗pdf ↗

Sharp Bounds on the Approximation Rates, Metric Entropy, and

n

-widths of Shallow Neural Networksstat.ML

Sharp bounds on neural network approximation rates and widths.

problem Estimating approximation rates, metric entropy, and n-widths of shallow neural networks.

method Introducing smoothly parameterized dictionaries and providing upper and lower bounds.

result Sharp bounds on approximation rates, metric entropy, and n-widths for neural networks with various activation functions.

shallow neural networks metric entropy n-widths approximation rates smoothly parameterized dictionaries

2021-01-29abs ↗pdf ↗

Sharp Lower Bounds on the Approximation Rate of Shallow Neural Networksstat.ML

Sharp lower bounds on shallow neural networks' approximation rates are derived.

problem The efficiency of shallow neural networks in approximating functions.

method Lower bounding the

L^2

-metric entropy and Kolmogorov

n

-widths of the convex hull of neural network basis functions.

result Sharp lower bounds on the approximation rates for shallow neural networks are provided.

shallow neural networks approximation rates metric entropy Kolmogorov n-widths convex hull

2021-06-28abs ↗pdf ↗

Automatic, Dynamic, and Nearly Optimal Learning Rate Specification by Local Quadratic Approximationstat.ML

A new method automatically and dynamically sets learning rates in deep learning.

problem Determining the appropriate learning rate in deep learning tasks is challenging and often subjective.

method Local Quadratic Approximation (LQA) to automatically and dynamically set learning rates.

result The proposed method leads to nearly optimal learning rates in a computationally efficient way.

learning rate deep learning optimization gradient-based local quadratic approximation

2020-04-07abs ↗pdf ↗

Closing the convergence gap of SGD without replacementcs.LG

Paper closes convergence gap for SGD without replacement.

problem Establishing convergence rate for SGD without replacement.

method Analyzes convergence rates for strongly convex and smooth functions.

result Achieves a rate of O(1/T^2 + n^2/T^3) for quadratic sums.

Stochastic Gradient Descent SGD without replacement Convergence rate Strongly convex Smooth functions

2020-02-24abs ↗pdf ↗

Do firms share the same functional form of their growth rate distribution? A new statistical testphysics.data-an

We introduce a new statistical test of the hypothesis that a balanced panel of firms have the same growth rate distribution or, more generally, that they share the same functional form of growth rate distribution. We applied the test to European Union and US publicly quoted manufacturing firms data, considering functio…

2011-03-11abs ↗pdf ↗

Optimal rates of approximation by shallow ReLU

^k

neural networks and applications to nonparametric regressionstat.ML

Optimal rates for shallow ReLU networks in nonparametric regression.

problem Approximating smooth and non-smooth functions with shallow ReLU networks.

method Analysis of shallow ReLU

^k

neural networks, using variation norms and deep learning theory.

result Optimal approximation rates for shallow ReLU networks in nonparametric regression.

ReLU networks nonparametric regression shallow neural networks convolutional neural networks Hölder functions

2023-04-04abs ↗pdf ↗

Finite Sample Analysis of Minimax Offline Reinforcement Learning: Completeness, Fast Rates and First-Order Efficiencycs.LG

The paper analyzes reinforcement learning methods for estimating weights and quality functions with fast convergence rates.

problem Estimating weights and quality functions in reinforcement learning with function approximation.

method The paper uses minimax methods for estimating marginal importance weights and q-functions.

result The minimax approach enables fast rates of convergence for weights and quality functions, achieving first-order efficiency.

reinforcement learning minimax methods off-policy evaluation function approximation fast rates

2021-02-05abs ↗pdf ↗

Minimax Analysis for Inverse Risk in Nonparametric Planer Invertible Regressionmath.ST

Study on estimating invertible functions with minimax analysis.

problem Minimizing risk of estimating invertible functions on a plane.

method Introduce two types of

L^2

-risks, derive lower and upper rates for minimax values, develop an asymptotically almost everywhere invertible estimator.

result Invertibility does not reduce the complexity of the estimation problem in terms of the rate.

minimax analysis inverse risk nonparametric regression invertible functions bi-Lipschitz functions

2021-12-01abs ↗pdf ↗

Short-Rate-Dependent Volatility Modelsq-fin.MF

Study provides explicit pricing formula for options with volatility dependent on short rate.

problem Pricing European options with volatility dependent on short rate.

method Developed a class of models with explicit pricing formula using characteristic functions.

result Explicit pricing formula for European options is derived.

volatility models short rate European options characteristic function

2026-01-31abs ↗pdf ↗

Kernel-based estimation for partially functional linear model: Minimax rates and randomized sketchesmath.ST

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.

kernel-based estimation partially functional linear model minimax rates randomized sketches high dimensional setting

2021-10-18abs ↗pdf ↗

A Theory of Nonparametric Covariance Function Estimation for Discretely Observed Datamath.ST

Study nonparametric covariance function estimation for noisy data.

problem Estimating covariance function from discrete noisy data in high dimensions.

method Adaptive learning-based estimators, including deep learning.

result Established oracle inequality and convergence rates for deep learning estimators.

covariance function nonparametric estimation discrete data deep learning oracle inequality

2026-03-24abs ↗pdf ↗

On Learning Rates and Schrödinger Operatorscs.LG

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.

learning rate stochastic gradient descent Schrödinger operator nonconvex optimization convex optimization

2020-04-15abs ↗pdf ↗

A note on

L^1

-Convergence of the Empiric Minimizer for unbounded functions with fast growthmath.ST

Study shows convergence rate for empirical minimizer of unbounded functions with fast growth.

problem Convergence rate of empirical minimizer for unbounded functions with fast growth.

method Analyzes

L^1

-distance convergence rate of the empiric minimizer for coercive functions sampled with noise.

result Convergence rate is bounded above by

a_n n^{-1/q}

, where

q

is the dimension and

a_n = o(n^\varepsilon)

for every

\varepsilon > 0

Convergence rate Empirical minimizer Unbounded functions Fast growth Coercive functions

2023-03-08abs ↗pdf ↗

On time-consistent equilibrium stopping under aggregation of diverse discount ratesq-fin.MF

Study optimal stopping for group with diverse discount rates using an attitude function.

problem Optimal stopping for a group with diverse discount rates under an aggregation preference.

method Develop iterative approach using consistent planning for time-consistent equilibria.

result Characterize all time-consistent mild equilibria as fixed points of an operator.

optimal stopping diverse discount rates aggregation preference attitude function time-consistent equilibrium

2023-02-15abs ↗pdf ↗

Adaptive multi-fidelity optimization with fast learning ratesstat.ML

Paper optimizes multi-fidelity function with fast learning rates.

problem Optimizing a locally smooth function with limited budget and varying fidelity approximations.

method Kometo algorithm that achieves simple regret rates without knowing function smoothness or fidelity assumptions.

result Kometo algorithm outperforms previous methods empirically.

multi-fidelity optimization fast learning rates simple regret locally smooth function fidelity approximations

2026-04-17abs ↗pdf ↗

Classification with unknown class-conditional label noise on non-compact feature spacesstat.ML

We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite sample rates, previous approaches to classification with unknown class-conditiona…

2019-02-14abs ↗pdf ↗

On the Outsized Importance of Learning Rates in Local Update Methodscs.LG

Local update methods' performance depends on learning rates, affecting convergence rates and alignment with true loss.

problem The performance of local update methods in federated learning and meta-learning is sensitive to learning rates.

method Proved that local update methods perform SGD on a surrogate loss function, characterized the surrogate loss, and derived convergence rates.

result Proper learning rate tuning is crucial for near-optimal behavior in communication-limited settings.

learning rates local update methods federated learning meta-learning convergence rates

2020-07-02abs ↗pdf ↗

On averaging the best samples in evolutionary computationcs.NE

The paper improves evolutionary computation by optimizing selection rates.

problem Choosing the right selection rate in evolutionary computation.

method The paper proves mathematically that a selection rate of μ/λ leads to better progress rates and provides a theoretical basis for this.

result The theoretical selection rate μ/λ leads to a better progress rate of order O(λ^-1) compared to O(λ^-2/d).

evolutionary computation selection rate simple regret progress rate sphere function

2020-04-24abs ↗pdf ↗

Nonparametric regression with modified ReLU networksstat.ML

Modified ReLU networks improve regression estimation rates.

problem Regression estimation with smooth functions.

method Using modified ReLU neural networks with specific weight modifications.

result Empirical risk minimizers achieve minimax rate of prediction.

ReLU networks Regression Minimax rate Smooth functions

2022-07-17abs ↗pdf ↗

Adaptive estimation of a function from its Exponential Radon Transform in presence of noisemath.ST

Adapts to estimate functions from noisy ERT data.

problem Estimating functions from noisy Exponential Radon Transform data.

method Locally adaptive kernel type estimator for functions of varying smoothness.

result Achieves minimax optimal rate up to a log(n) factor for Sobolev functions.

Exponential Radon Transform Adaptive Estimation Kernel Estimator Minimax Rate Sobolev Regularity

2020-11-13abs ↗pdf ↗

Good regularity creates large learning rate implicit biases: edge of stability, balancing, and catapultcs.LG

Large learning rates lead to various implicit biases in nonconvex optimization.

problem Understanding the conditions under which large learning rates yield edge of stability, balancing, and catapult phenomena.

method Developed a global convergence theory for nonconvex functions without globally Lipschitz continuous gradient, focusing on functions with good regularity.

result These implicit biases are more likely to occur in functions with good regularity, and large learning rates favor flatter regions.

large learning rates nonconvex optimization edge of stability balancing catapult

2023-10-26abs ↗pdf ↗

SignSVRG: fixing SignSGD via variance reductionmath.OC

SignSVRG improves SignSGD by reducing variance, achieving similar convergence rates.

problem Minimizing finite sums of convex and Lipschitz functions.

method Incorporates variance reduction techniques into SignSGD.

result Achieves convergence rates of

\mathcal{O}(1 / \sqrt{T})

for expected norm of the gradient and

\mathcal{O}(1/T)

for smooth convex functions.

Variance Reduction SignSGD Convergence Rates Finite Sums Convex Functions

2023-05-22abs ↗pdf ↗

Suboptimality of Penalized Empirical Risk Minimization in Classificationmath.ST

Let $\cF$ be a set of $M$ classification procedures with values in $[-1,1]$ . Given a loss function, we want to construct a procedure which mimics at the best possible rate the best procedure in $\cF$. This fastest rate is called optimal rate of aggregation. Considering a continuous scale of loss functions with various …

2007-03-27abs ↗pdf ↗

Scalable Frank-Wolfe on Generalized Self-concordant Functions via Simple Stepsmath.OC

Improved Frank-Wolfe algorithm for generalized self-concordant functions converges quickly.

problem Efficiently solving learning problems with generalized self-concordant objectives.

method Simple Frank-Wolfe variant with open-loop step size strategy

γ_t = 2/(t+2)

result Achieves

\mathcal{O}(1/t)

convergence rate for primal and Frank-Wolfe gaps.

Frank-Wolfe algorithm self-concordant functions convergence rate learning problems

2021-05-28abs ↗pdf ↗

Discordance Minimization-based Imputation Algorithms for Missing Values in Rating Datastat.ML

The study proposes algorithms to minimize rating discordance in missing data.

problem Missing ratings in combined rating lists.

method Optimization models and algorithms that minimize total rating discordance.

result The proposed methods outperform state-of-the-art imputation methods in accuracy.

rating data missing values discordance minimization imputation algorithms quadratic function

2023-11-07abs ↗pdf ↗

Adapting to Function Difficulty and Growth Conditions in Private Optimizationcs.LG

New algorithms optimize private convex optimization with faster rates for functions with κ-growth.

problem Optimizing private convex functions with varying difficulty and growth conditions.

method Adapts inverse sensitivity mechanism and localization techniques to achieve faster rates without knowing growth constant.

result Achieves faster privacy rates

({\sqrt{d}}/{n\varepsilon})^{ fracκ{κ- 1}}

for functions with κ-growth.

private optimization convex optimization growth conditions κ-growth privacy rates

2021-08-05abs ↗pdf ↗

Convergence rates of efficient global optimization algorithmsstat.ML

Efficient global optimization is the problem of minimizing an unknown function f, using as few evaluations f(x) as possible. It can be considered as a continuum-armed bandit problem, with noiseless data and simple regret. Expected improvement is perhaps the most popular method for solving this problem; the algorithm pe…

2011-01-18abs ↗pdf ↗

Optimal rates for first-order stochastic convex optimization under Tsybakov noise conditioncs.LG

We focus on the problem of minimizing a convex function $f$ over a convex set $S$ given $T$ queries to a stochastic first order oracle. We argue that the complexity of convex minimization is only determined by the rate of growth of the function around its minimizer $x^*_{f,S}$ , as quantified by a Tsybakov-like noise co…

2012-07-12abs ↗pdf ↗

Online Nonparametric Regression with General Loss Functionsstat.ML

This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the curvature of the loss function and the sequential complexities of the class. Above this…

2015-01-26abs ↗pdf ↗

Sum-Rate-Distortion Function for Indirect Multiterminal Source Coding in Federated Learningcs.IT

This paper studies communication efficiency in federated learning by optimizing the sum-rate-distortion function for indirect multiterminal source coding.

problem Indirect multiterminal source coding in federated learning where edge devices send noisy gradients to the server.

method Analyzes the rate region for the quadratic vector Gaussian CEO problem under unbiased estimator and derives an explicit formula for the sum-rate-distortion function.

result Derives an explicit formula for the sum-rate-distortion function in the special case of identical gradients over edge devices.

federated learning multiterminal source coding CEO problem gradient variance sum-rate-distortion function

2021-01-21abs ↗pdf ↗

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approachmath.OC

SGD and stochastic gradient descent converge at optimal rates for certain non-convex functions.

problem Optimal convergence rates for non-convex functions under gradient noise.

method Geometric interpretation of the PL-condition to analyze convergence rates.

result Convergence rates of SGD and stochastic gradient descent match those of strongly convex quadratics.

SGD stochastic gradient descent convergence rates non-convex functions PL-condition

2026-05-14abs ↗pdf ↗

Neural Continuous-Time Markov Modelsstat.ML

Neural models learn continuous-time Markov chain transition rates from data.

problem Learning transition rates for complex stochastic systems.

method Neural networks to model nonlinear transition rates from observed data.

result Neural models outperform traditional methods in accuracy.

neural networks continuous-time Markov chains stochastic systems transition rates covariates

2022-12-11abs ↗pdf ↗

Refined Convergence Rates for Maximum Likelihood Estimation under Finite Mixture Modelsmath.ST

Improved convergence rates for MLE in mixture models using penalized log-likelihood.

problem Convergence rates for MLE in finite mixture models.

method Penalizing log-likelihood to discourage vanishing mixing weights, using Wasserstein distance and new loss functions.

result Improved convergence rates for some mixture components, faster than traditional methods.

MLE finite mixture models convergence rates Wasserstein distance penalized log-likelihood

2022-02-17abs ↗pdf ↗

Acceleration and Averaging in Stochastic Mirror Descent Dynamicsmath.OC

We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a stochastic variant in which the gradient is contaminated by noise, and study the resultin…

2017-07-19abs ↗pdf ↗