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.

168,695 papers · 148 categories

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48 results for “Linear Stochastic Approximation”

A Diffusion Approximation for Temporal-Difference Learning with Linear Features under Markovian Noisestat.ML

Stochastic differential equation approximation for linear TD(0) under Markovian noise

problem Temporal-difference learning with linear function approximation

method Stochastic differential equation approximation

result Explains the constant-stepsize error floor

TD learning linear function approximation Markovian noise stochastic differential equation

2026-06-16abs ↗pdf ↗

Gaussian Approximation for Two-Timescale Linear Stochastic Approximationstat.ML

Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.

problem Non-asymptotic bounds for accuracy of normal approximation in linear two-timescale stochastic approximation algorithms.

method Established bounds for normal approximation in terms of convex distance, focusing on last iterate and Polyak-Ruppert averaging.

result Normal approximation rate for the last iterate improves with increased timescale separation, while it decreases in the averaged setting.

stochastic approximation two-timescale normal approximation convex distance timescale separation

2025-08-11abs ↗pdf ↗

Gaussian Approximation and Multiplier Bootstrap for Polyak-Ruppert Averaged Linear Stochastic Approximation with Applications to TD Learningstat.ML

Paper improves confidence intervals for LSA with multiplier bootstrap.

problem Improving confidence intervals for parameter estimation in LSA.

method Berry-Esseen bound for multivariate normal approximation and multiplier bootstrap.

result Valid confidence intervals for parameter estimation in LSA.

Berry-Esseen bound multiplier bootstrap linear stochastic approximation parameter estimation temporal difference learning

2024-05-26abs ↗pdf ↗

Global universal approximation with Brownian signaturesmath.PR

Universal approximation for stochastic processes using Brownian motion.

problem Approximating stochastic processes with linear functionals.

method Establishing

L^p

-type universal approximation theorems for rough path spaces.

result Linear functionals on the signature of time-extended Brownian motion can approximate any

p

-integrable stochastic process.

universal approximation rough paths stochastic processes Brownian motion signature

2025-12-18abs ↗pdf ↗

Bayesian Bandit Algorithms with Approximate Inference in Stochastic Linear Banditsstat.ML

Bayesian bandit algorithms with approximate inference improve regret bounds in stochastic linear bandits.

problem Theoretical justification for Bayesian bandit algorithms with approximate inference in stochastic linear bandits.

method Proposed a theoretical framework to analyze approximate inference impact and conducted frequentist regret analysis on LinTS and LinBUCB.

result LinTS and LinBUCB preserve their original regret upper bounds with larger constant terms in approximate inference settings.

Bayesian bandit stochastic linear bandits approximate inference regret analysis Thompson Sampling

2024-06-20abs ↗pdf ↗

Bridging Constraints and Stochasticity: A Fully First-Order Method for Stochastic Bilevel Optimization with Linear Constraintsmath.OC

First-order method solves stochastic bilevel optimization with linear constraints.

problem Stochastic bilevel optimization with linear constraints and noise.

method Developed a novel framework using gradient-based techniques and smoothed penalty functions.

result Achieved finite-time convergence guarantees for

(δ, ε)

-Goldstein stationary points.

stochastic bilevel optimization linear constraints finite-time convergence first-order methods hypergradient approximations

2025-11-13abs ↗pdf ↗

Global universality via discrete-time signaturesmath.PR

Global approximation for piecewise linear paths via signatures.

problem Global approximation theorems for piecewise linear paths.

method Using signatures of piecewise linear paths and their density in

L^p

-norms.

result Linear functionals of signatures are dense in

L^p

-norms under an integrability condition.

approximation theory piecewise linear paths signatures Brownian motion random ODEs

2026-03-10abs ↗pdf ↗

Universal approximation property of neural stochastic differential equationsmath.PR

Neural networks can approximate complex stochastic equations well.

problem Approximating general stochastic differential equations.

method Identified neural network classes approximating continuous functions.

result Neural stochastic differential equations can approximate general stochastic differential equations arbitrarily well.

neural networks stochastic differential equations approximation Itô diffusion quantitative error estimates

2025-03-20abs ↗pdf ↗

Regret Bounds for Stochastic Shortest Path Problems with Linear Function Approximationcs.LG

Algorithm reduces regret in SSP problems with LFA.

problem Finding shortest paths in stochastic environments with linear approximations.

method Uses linear function approximation and stationary policies to minimize regret.

result Achieves sublinear regret under minimal assumptions.

regret bounds stochastic shortest path linear function approximation stationary policies

2021-05-04abs ↗pdf ↗

Improved Central Limit Theorem and Bootstrap Approximations for Linear Stochastic Approximationstat.ML

Paper improves CLT and bootstrap approximations for LSA with decreasing step size.

problem Improving normal approximation and bootstrap methods for LSA with decreasing step sizes.

method Refined Berry-Esseen bounds and multiplier bootstrap procedure for LSA.

result Approximation rates up to

1/\sqrt{n}

for LSA rescaled error distribution.

Central Limit Theorem Bootstrap Linear Stochastic Approximation Decreasing Step Size Gaussian Distribution

2025-10-14abs ↗pdf ↗

On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentrationstat.ML

Study on stochastic approximation with Polyak-Ruppert averaging for linear systems.

problem Understanding the asymptotic and non-asymptotic properties of stochastic approximation procedures.

method Detailed analysis of linear stochastic approximation with Polyak-Ruppert averaging, focusing on asymptotic and non-asymptotic properties.

result Proves CLT and non-asymptotic concentration inequality for averaged iterates, providing refined understanding of linear stochastic approximation.

stochastic approximation linear systems Polyak-Ruppert averaging central limit theorem non-asymptotic concentration

2020-04-09abs ↗pdf ↗

Exponential Concentration in Stochastic Approximationstat.ML

Stochastic approximation algorithms show exponential progress bounds.

problem Analyzing the convergence of stochastic approximation algorithms.

method Developed geometric ergodicity proofs to establish exponential concentration bounds.

result Proved faster convergence rates for specific algorithms.

stochastic approximation concentration bounds geometric ergodicity Markov chains stochastic gradient descent

2022-08-15abs ↗pdf ↗

Statistical inference for Linear Stochastic Approximation with Markovian Noisestat.ML

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

\mathcal{O}(n^{-1/4})

convergence rates and guarantees consistent inference.

Linear Stochastic Approximation Markovian Noise Berry-Esseen Bounds Bootstrap Confidence Intervals Convergence Rates

2025-05-25abs ↗pdf ↗

Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysismath.DS

The paper introduces Causal Neural Operators to approximate operators in stochastic analysis.

problem Leveraging temporal structure in non-linear operators for deep learning models.

method Designing a deep learning model framework for infinite-dimensional linear metric spaces.

result Causal Neural Operators can uniformly approximate Hölder or smooth trace class operators.

Causal Neural Operators Stochastic Analysis Deep Learning Banach Spaces Temporal Structure

2022-10-24abs ↗pdf ↗

A Stochastic Approximation for Fully Nonlinear Free Boundary Parabolic Problemsmath.NA

We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.

2011-09-27abs ↗pdf ↗

Finite-Time Decoupled Convergence in Nonlinear Two-Time-Scale Stochastic Approximationmath.OC

We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.

problem Achieving decoupled convergence in nonlinear two-time-scale stochastic approximation.

method Nested local linearity assumption, suitable step size selection, convergence analysis of matrix cross term, fourth-order moment convergence rates.

result Finite-time decoupled convergence rates can be achieved in nonlinear two-time-scale stochastic approximation with proper step size selection.

stochastic approximation two-time-scale decoupled convergence local linearity step size

2024-01-08abs ↗pdf ↗

Instance-optimal stochastic convex optimization: Can we improve upon sample-average and robust stochastic approximation?math.OC

Improved stochastic optimization outperforms standard methods.

problem Optimizing smooth, strongly convex functions with noisy data.

method Variance reduction strategy called VISOR.

result VISOR achieves optimal sample complexity and oracle complexity.

stochastic optimization variance reduction stochastic approximation convex optimization generalized linear models

2026-03-26abs ↗pdf ↗

Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximationstat.ML

Paper develops Gaussian approximations and bootstrap for federated LSA with trade-off bounds.

problem Analyzing convergence rates and trade-offs in federated linear stochastic approximation.

method Established Berry-Esseen-type bounds for federated LSA, developed multiplier bootstrap for inference.

result First federated Gaussian approximations with explicit trade-off terms and non-asymptotic validity guarantees.

federated learning stochastic approximation Gaussian approximation bootstrap convergence rates

2026-05-19abs ↗pdf ↗

High-dimensional Limit of SGD for Diagonal Linear Networksmath.OC

SGD on diagonal linear networks approximates to SDE in high dimensions.

problem Understanding optimization and generalization in neural models.

method High-dimensional analysis of SGD on diagonal linear networks, approximated by SDE.

result SGD dynamics in high dimensions converge exponentially to zero risk.

stochastic gradient descent diagonal linear networks high-dimensional limit stochastic differential equation exponential convergence

2026-05-16abs ↗pdf ↗

A Diffusion Analysis of Policy Gradient for Stochastic Banditsstat.ML

Study on policy gradient for stochastic bandits using diffusion approximation.

problem Improving policy gradient methods for stochastic bandits with optimal regret bounds.

method Continuous-time diffusion approximation of policy gradient with learning rate analysis.

result Proved optimal regret bound of

O(k \log(k) \log(n) / η)

for

η= O(Δ^2/\log(n))

policy gradient stochastic bandits diffusion approximation regret analysis learning rate

2026-03-10abs ↗pdf ↗

A Convergent Linear Regression Method for Forward-Backward Stochastic Differential Equations with Jumpsq-fin.CP

In this paper, we introduce a large class of convergent numerical methods, based on (linear) basis function regression technique, to approximate the solution to a forward-backward stochastic differential equation with jumps (FBSDEJ hereafter). Numerical experiment shows good applicability of the proposed method.

2018-05-15abs ↗pdf ↗

An Analysis of Quantile Temporal-Difference Learningcs.LG

Quantile Temporal-Difference learning proved convergent with proof.

problem Lack of theoretical understanding of QTD despite empirical success.

method Proof of convergence using stochastic approximation and non-smooth analysis.

result QTD converges to fixed points with probability 1.

Quantile Temporal-Difference Reinforcement Learning Convergence Stochastic Approximation Non-Smooth Analysis

2023-01-11abs ↗pdf ↗

Stochastic Neural Networks with Monotonic Activation Functionsstat.ML

We propose a Laplace approximation that creates a stochastic unit from any smooth monotonic activation function, using only Gaussian noise. This paper investigates the application of this stochastic approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences.…

2016-01-01abs ↗pdf ↗

Approximation Theory Based Methods for RKHS Banditscs.LG

New algorithms tackle RKHS bandits with reduced complexity and improved performance.

problem Adversarial and stochastic RKHS bandit problems with high computational complexity.

method Combining approximation theory with misspecified linear bandit methods.

result First general algorithm for adversarial RKHS bandit problem.

approximation theory RKHS bandits misspecified linear bandit stochastic bandits adversarial bandits

2020-10-23abs ↗pdf ↗

Optimal and instance-dependent guarantees for Markovian linear stochastic approximationmath.OC

Study optimal and instance-dependent guarantees for solving linear equations with Markovian data.

problem Approximately solving linear fixed point equations with Markovian data.

method Non-asymptotic bounds and instance-dependent characterizations for stochastic approximation.

result Instance-optimality of the averaged SA estimator and matching upper and lower bounds.

stochastic approximation Markov chains linear fixed point TD(λ)autoregressive models

2021-12-23abs ↗pdf ↗

Universal approximation with signatures of non-geometric rough pathsmath.PR

The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.

problem Approximating functionals of non-geometric rough paths.

method Extending rough paths with time and quadratic variation terms, proving uniform approximation.

result Linear functionals of extended signatures uniformly approximate continuous functionals.

rough paths universal approximation non-geometric quadratic variation semimartingales

2026-02-05abs ↗pdf ↗

Finite-time High-probability Bounds for Polyak-Ruppert Averaged Iterates of Linear Stochastic Approximationstat.ML

The paper offers precise bounds for averaged LSA iterates in linear systems.

problem Computing approximate solutions of linear systems with noisy observations.

method Finite-time analysis of LSA algorithms with Polyak-Ruppert averaging.

result Sharp high-probability bounds for averaged LSA iterates.

linear stochastic approximation polyak-rupeert averaging finite-time analysis high-probability bounds linear systems

2022-07-10abs ↗pdf ↗

Learning Stochastic Shortest Path with Linear Function Approximationcs.LG

New algorithm learns optimal path in reinforcement learning with linear approximations.

problem Optimal path learning in reinforcement learning with linear approximations.

method Proposes novel algorithm with Hoeffding-type and Bernstein-type confidence sets.

result Achieves near-optimal regret guarantee for linear mixture SSP.

reinforcement learning stochastic shortest path linear function approximation regret minimization confidence sets

2021-10-25abs ↗pdf ↗

Linear Noise Approximation Assisted Bayesian Inference on Mechanistic Model of Partially Observed Stochastic Reaction Networkstat.ML

Paper develops efficient Bayesian inference for enzymatic SRNs with LNA metamodel.

problem Bayesian inference for nonlinear SDE-based mechanistic models with partial observations and measurement errors.

method Interpretable Bayesian updating LNA metamodel and efficient posterior sampling.

result Proposed approach demonstrates promising performance in empirical studies.

Bayesian inference LNA metamodel Stochastic reaction network Mechanistic model Digital twin

2024-05-05abs ↗pdf ↗

Optimal oracle inequalities for solving projected fixed-point equationscs.LG

Study optimizes solving fixed-point equations using subspace search.

problem Solving linear fixed point equations in Hilbert spaces.

method Linear stochastic approximation scheme with Polyak--Ruppert averaging.

result Established optimal approximation factor for temporal difference learning methods.

fixed-point equations Hilbert spaces stochastic approximation temporal difference learning policy evaluation

2020-12-09abs ↗pdf ↗

Sampling from Gaussian Process Posteriors using Stochastic Gradient Descentcs.LG

Stochastic gradient descent approximates Gaussian process posteriors efficiently.

problem Efficiently sampling from Gaussian process posteriors with limited computational resources.

method Developed stochastic gradient optimization objectives for sampling from Gaussian process posteriors.

result Stochastic gradient descent produces accurate predictive distributions, even in non-convergent cases.

Gaussian process Bayesian optimization Stochastic gradient descent Uncertainty quantification Sequential decision-making

2023-06-20abs ↗pdf ↗

Stochastic Modified Equations for Continuous Limit of Stochastic ADMMmath.OC

Unified analysis of stochastic ADMM variants via SME.

problem Analyzing and optimizing stochastic ADMM variants for machine learning.

method Unified mathematical framework of SME for continuous-time analysis.

result Dynamics of stochastic ADMM approximated by SDEs with small noise.

stochastic ADMM SME continuous limit machine learning empirical risk minimization

2020-03-07abs ↗pdf ↗

Sparse recovery by reduced variance stochastic approximationstat.ML

Paper develops a new algorithm for sparse signal recovery.

problem Sparse signal recovery from noisy observations.

method Iterative Stochastic Optimization using Stochastic Mirror Descent.

result Linear convergence during preliminary phase of the routine.

sparse recovery stochastic approximation signal processing median-of-means regression

2020-06-11abs ↗pdf ↗

Target Updates May Stabilize Linear Q-Learning: Periodic and Soft Dynamicsstat.ML

This paper analyzes how periodic and soft target updates stabilize linear Q-learning.

problem Theoretical explanation of stabilization mechanisms for linear Q-learning.

method Exact analysis using switched linear system dynamics and the joint spectral radius.

result Periodic and soft target updates can guarantee convergence to the exact projected Q-Bellman solution under specific conditions.

Q-learning linear function approximation stabilization periodic updates soft updates

2026-05-31abs ↗pdf ↗

Stochastic Mirror Descent for Large-Scale Sparse Recoverystat.ML

Paper uses Stochastic Mirror Descent for large-scale sparse recovery problems.

problem Statistical estimation of high-dimensional sparse parameters.

method Non-Euclidean Composite Stochastic Mirror Descent (CSMD) algorithm for solving penalized stochastic optimization problems.

result The proposed algorithm achieves optimal convergence in sparse Generalized Linear Regression problems.

Stochastic Mirror Descent Sparse Recovery High-Dimensional Statistics Generalized Linear Regression Sub-Gaussian Perturbations

2022-10-23abs ↗pdf ↗

Convergence in probability of numerical solutions of a highly non-linear delayed stochastic interest rate modelmath.PR

Study proves convergence of interest rate model approximations.

problem Investigating convergence of stochastic interest rate models.

method Developed analytical tools for true and truncated EM solutions, proving convergence in probability.

result True solution converges in probability to truncated EM solution as step size approaches zero.

stochastic interest rate model Euler-Maruyama approximation convergence in probability delayed stochastic model

2025-10-05abs ↗pdf ↗

Asymptotic Time-Uniform Inference for Parameters in Averaged Stochastic Approximationstat.ML

The paper develops time-uniform inference methods for stochastic approximation parameters.

problem Statistical inference for parameters in stochastic approximation problems.

method Analysis of averaged iterates convergence rates and construction of asymptotic confidence sequences.

result Valid asymptotic confidence sequences for parameters in stochastic approximation problems.

stochastic approximation asymptotic inference uniform coverage averaged iterates covariance estimation

2024-10-19abs ↗pdf ↗

Linear

Q

-Learning Does Not Diverge in

L^2

: Convergence Rates to a Bounded Setcs.LG

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

L^2

convergence rate of linear Q-learning iterates to a bounded set.

Q-learning linear function approximation convergence rate bounded set ε-softmax policy

2025-01-31abs ↗pdf ↗

Matrix Approximation of Bachelier Option Prices and Greeks under Stochastic Volatility modelsq-fin.PR

Matrix approximation method for Bachelier option pricing and Greeks under stochastic volatility models

problem Computing option prices and Greeks for stochastic volatility models

method Matrix approximation using elementary linear algebra

result Option prices and Greeks computed for infinitely many strikes with a finite number of expectations

matrix approximation Bachelier option pricing stochastic volatility Greeks SABR model

2026-06-24abs ↗pdf ↗

On the Stability of Random Matrix Product with Markovian Noise: Application to Linear Stochastic Approximation and TD Learningstat.ML

The paper analyzes stability of random matrix products with Markovian noise.

problem Analyzing stability of random matrix products with Markovian noise.

method Using a super-Lyapunov drift condition and controlled growth of matrix-valued functions, the paper provides an exponential stability result for the p-th moment of random matrix product.

result Finite-time p-th moment bounds for linear stochastic approximation and TD learning algorithms.

stability random matrix product Markov chain stochastic approximation TD learning

2021-01-30abs ↗pdf ↗

Pathwise Iteration for Backward SDEsmath.NA

We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., it…

2016-05-24abs ↗pdf ↗

SCAFFLSA: Taming Heterogeneity in Federated Linear Stochastic Approximation and TD Learningstat.ML

SCAFFLSA reduces communication complexity for federated learning with heterogeneous clients.

problem Quantifying and reducing communication complexity in federated learning with heterogeneous clients.

method Proposes SCAFFLSA, a variant of FedLSA using control variates to correct for client drift.

result SCAFFLSA achieves logarithmic communication complexity for statistically heterogeneous agents, scaling with the inverse of the desired accuracy.

federated learning heterogeneous clients communication complexity control variates temporal difference learning

2024-02-06abs ↗pdf ↗

Approximate Bayes learning of stochastic differential equationsphysics.data-an

We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and estimates are calculated directly from dense data sets using Gaussian process r…

2017-02-17abs ↗pdf ↗

A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEsmath.NA

New learning scheme solves high-dimensional semi-linear PDEs using sparse grids and Picard approximations.

problem Solving high-dimensional semi-linear parabolic PDEs.

method Probabilistic learning scheme based on Picard iteration with SGD, employing sparse grid approximation.

result Convergence proof and polynomial complexity in

ε^{-1}

for high-dimensional PDEs.

sparse grids Picard approximations semilinear PDEs machine learning stochastic gradient descent

2021-02-24abs ↗pdf ↗

Tight High Probability Bounds for Linear Stochastic Approximation with Fixed Stepsizestat.ML

The paper provides bounds for LSA with fixed stepsizes under random estimates.

problem Analyzing the performance of LSA algorithms with fixed stepsize.

method Non-asymptotic analysis based on new results about matrix moments and high probability bounds.

result Derives high probability bounds on LSA performance under weaker conditions than previous works.

linear stochastic approximation fixed stepsize high probability bounds matrix moments concentration inequalities

2021-06-02abs ↗pdf ↗

Finite-Time Analysis and Restarting Scheme for Linear Two-Time-Scale Stochastic Approximationcs.LG

Motivated by their broad applications in reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes for finding the solutions of a system of two equations. Our main focus is to characterize the finite-time complexity of this method under time-…

2019-12-23abs ↗pdf ↗

Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirementsq-fin.PR

New MKABSDEs help calculate initial margins in financial contracts.

problem Calculating initial margins in financial contracts with dependencies.

method Introduced MKABSDEs, provided existence and uniqueness, applied to CVaR, used deterministic and Monte-Carlo methods for numerical approximations.

result MKABSDEs provide a new way to solve for initial margins in financial contracts.

MKABSDEs initial margins financial contracts CVaR numerical approximations

2024-08-02abs ↗pdf ↗

Stochastic Conditional Gradient Methods: From Convex Minimization to Submodular Maximizationmath.OC

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their applicability remains limited when the problem dimension is large and the projecti…

2018-04-24abs ↗pdf ↗