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.

168,657 papers · 148 categories

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48 results for “Linear Approximation”

Improving the Linearized Laplace Approximation via Quadratic Approximationsstat.ML

QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.

problem Overconfident out-of-distribution predictions from DNNs.

method Proposes Quadratic Laplace Approximation (QLA) to improve Bayesian uncertainty quantification.

result QLA yields modest yet consistent uncertainty estimation improvements over Linearized Laplace Approximation (LLA) on five regression datasets.

Bayesian uncertainty Deep neural networks Quadratic approximation Laplace approximation Prediction

2026-02-03abs ↗pdf ↗

Linear Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximationcs.LG

Entropy-regularized NPG converges linearly with linear function approximation.

problem Analyzing convergence of entropy-regularized NPG with function approximation.

method Established finite-time convergence analyses with entropy regularization and linear function approximation.

result Entropy-regularized NPG achieves linear convergence up to a function approximation error.

entropy regularization natural policy gradient linear function approximation reinforcement learning convergence analysis

2021-06-08abs ↗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 ↗

A Finite Sample Analysis of Distributional TD Learning with Linear Function Approximationstat.ML

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.

distributional reinforcement learning temporal difference learning linear function approximation return distribution Markov decision process

2025-02-20abs ↗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 ↗

Accelerated Distributional Temporal Difference Learning with Linear Function Approximationstat.ML

New algorithms improve distributional TD learning with linear approximations.

problem Estimating return distributions in reinforcement learning.

method Fine-grained analysis of linear-categorical Bellman equation, variance reduction techniques.

result Tight sample complexity bounds for distributional TD learning with linear approximations.

reinforcement learning temporal difference learning distributional reinforcement linear function approximation variance reduction

2025-11-16abs ↗pdf ↗

On the Rate of Gaussian Approximation for Linear Regression Problemsstat.ML

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

d

and design matrix.

result Rate of normal approximation is

\sqrt{\log{n}/n}

for large

n

Gaussian approximation linear regression online learning rate of convergence dimensionality

2025-09-17abs ↗pdf ↗

In-Context Learning of Linear Dynamical Systems with Transformers: Approximation Bounds and Depth-Separationcs.LG

Transformers can learn noisy linear systems with depth and IID data.

problem Learning noisy linear dynamical systems with transformers.

method Theoretical analysis of multi-layer and single-layer transformers with respect to

L^2

-testing loss.

result Single-layer transformers have a non-diminishing lower bound on approximation error, suggesting depth separation.

transformers linear dynamical systems approximation bounds depth-separation IID data

2025-02-12abs ↗pdf ↗

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 ↗

Approximate is Good Enough: Probabilistic Variants of Dimensional and Margin Complexitycs.LG

New probabilistic complexity measures for linear and kernel methods.

problem Limitations of linear and kernel methods in machine learning.

method Introducing approximate notions of dimensional and margin complexity.

result Approximate complexity measures are both sufficient and necessary for learning.

machine learning dimensional complexity margin complexity linear predictors kernel methods

2020-03-09abs ↗pdf ↗

Piecewise-Linear Approximation for Feature Subset Selection in a Sequential Logit Modelstat.ME

This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between …

2015-10-19abs ↗pdf ↗

Reparameterization invariance in approximate Bayesian inferencecs.LG

The paper addresses the invariance issue in Bayesian neural networks using linearized Laplace approximation.

problem Bayesian neural networks fail to maintain invariance under reparameterization, leading to different posterior densities for identical functions.

method Developed a geometric view of reparameterizations and a Riemannian diffusion process to extend reparameterization invariance to neural network predictive.

result Empirically improved posterior fit through approximate posterior sampling.

Bayesian neural networks reparameterization invariance linearized Laplace approximation Riemannian diffusion posterior sampling

2024-06-05abs ↗pdf ↗

State spaces of multifactor approximations of nonnegative Volterra processesmath.PR

State spaces of multifactor approximations of nonnegative Volterra processes are linear transformations of the nonnegative orthant.

problem Characterizing state spaces of multifactor approximations of nonnegative Volterra processes.

method Explicit linear transformation of the nonnegative orthant.

result State spaces of multifactor approximations of nonnegative Volterra processes are given by explicit linear transformation of the nonnegative orthant.

Volterra processes Markovian processes state spaces multifactor approximations nonnegative orthant

2024-12-23abs ↗pdf ↗

Asymptotic Singular Value Distribution of Linear Convolutional Layerscs.LG

Improved singular value approximation for convolutional layers.

problem Improving accuracy of singular value approximation for linear convolutional layers.

method Developed a new spectral density matrix method for singular value approximation with improved accuracy and reduced computational complexity.

result Obtained moderate improvement in singular value distribution compared to circular approximation.

convolutional neural networks singular value distribution spectral density matrix spectral norm linear transformation

2020-06-12abs ↗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 ↗

Parallel Layer Normalization for Universal Approximationcs.LG

PLN-Nets with two linear layers and parallel LN achieve universal approximation.

problem Limitations of standard neural network architectures in universal approximation.

method Introduced PLN-Nets combining two linear layers with parallel LN.

result PLN-Nets achieve universal approximation, while standard LN has limited power.

Layer Normalization Universal Approximation Neural Networks Parallel LN Linear Layers

2025-05-19abs ↗pdf ↗

Target Network and Truncation Overcome The Deadly Triad in

Q

-Learningcs.LG

New methods stabilize Q-learning with linear approximations.

problem Stabilizing

Q

-learning with linear function approximation.

method Target network and truncation.

result Provably stable

Q

-learning with linear function approximation.

Q-learning target network truncation linear function approximation finite-sample guarantees

2022-03-05abs ↗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 ↗

Logarithmic Regret for Reinforcement Learning with Linear Function Approximationcs.LG

Logarithmic regret achieved in RL with linear function approximation.

problem Achieving logarithmic regret in reinforcement learning with linear function approximation.

method LSVI-UCB for linear MDP assumption, UCRL-VTR for linear mixture MDP assumption.

result Logarithmic regret bounds established for RL with linear function approximation.

reinforcement learning logarithmic regret linear function approximation linear MDP UCRL-VTR

2020-11-23abs ↗pdf ↗

An analysis of linear regression and neural networks approximation for the pricing of swing optionsq-fin.MF

This paper compares linear regression and neural networks for pricing swing options.

problem Pricing swing options using approximation methods.

method Linear regression and neural networks for approximating the continuation value and swing price.

result The approximation methods converge to the actual swing price as the number of functions or Monte Carlo samples increases.

swing options pricing linear regression neural networks approximation

2023-07-10abs ↗pdf ↗

Nearly Minimax Optimal Regret for Learning Infinite-horizon Average-reward MDPs with Linear Function Approximationcs.LG

UCRL2-VTR achieves nearly optimal regret for learning MDPs with linear function approximation.

problem Learning infinite-horizon average-reward MDPs with linear function approximation.

method UCRL2-VTR algorithm with Bernstein-type bonus.

result Achieves a regret of

ilde{O}(d\sqrt{DT})

with matching lower bound.

reinforcement learning MDP average-reward linear function approximation UCRL2-VTR

2021-02-15abs ↗pdf ↗

Provably Correct Optimization and Exploration with Non-linear Policiescs.LG

ENIAC method optimizes and explores complex RL problems with non-linear policies.

problem Theoretical understanding of non-linear policies in RL with strategic exploration.

method ENIAC, an actor-critic method for non-linear function approximation.

result ENIAC finds near-optimal policies in polynomial exploration rounds under bounded eluder dimension.

Reinforcement Learning Policy Optimization Non-linear Function Approximation Strategic Exploration Actor-Critic

2021-03-22abs ↗pdf ↗

Provably Efficient Reinforcement Learning with Linear Function Approximationcs.LG

Modern Reinforcement Learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of function approximation raises a fundamental set of challenges involving computational …

2019-07-11abs ↗pdf ↗

Converting MLPs into Polynomials in Closed Formcs.LG

Closed-form polynomial approximations replace MLPs in transformers, enabling new interpretability methods.

problem Replacing MLPs with polynomial approximations for transformer models.

method Theoretical derivation of closed-form least-squares approximations of MLPs and GLUs using polynomial functions.

result Polynomial approximations explain over 95% of MLP and GLU outputs' variance, enabling interpretability.

transformers MLP polynomial approximation interpretability SVD

2025-02-03abs ↗pdf ↗

Planning to avoid ambiguous states through Gaussian approximations to non-linear sensors in active inference agentseess.SY

Agents learn state ambiguity from non-linear sensor data using Gaussian approximations.

problem Learning state representation from non-linear sensor data.

method Second-order Taylor approximation of Gaussian distribution for non-linear measurement functions.

result Induces a preference for states based on inferability from observations.

active inference robot navigation state ambiguity Gaussian approximation Taylor expansion

2024-09-03abs ↗pdf ↗

Value Function Approximation in Noisy Environments Using Locally Smoothed Regularized Approximate Linear Programscs.LG

Recently, Petrik et al. demonstrated that L1Regularized Approximate Linear Programming (RALP) could produce value functions and policies which compared favorably to established linear value function approximation techniques like LSPI. RALP's success primarily stems from the ability to solve the feature selection and va…

2012-10-16abs ↗pdf ↗

Improving variational methods via pairwise linear response identitiesstat.ML

Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing constraints on covariance, one can ensure consistency of linear response with the var…

2016-11-02abs ↗pdf ↗

Fast approximative estimation of conditional Shapley values when using a linear regression model or a polynomial regression modelstat.ME

Develops fast approximations for conditional Shapley values in linear and polynomial models.

problem Estimating conditional Shapley values using regression models is computationally expensive.

method A new approximative estimation method for conditional Shapley values using linear and polynomial regression models.

result Our method significantly reduces computation time compared to existing methods.

conditional Shapley values linear regression polynomial regression approximation computational efficiency

2025-04-25abs ↗pdf ↗

Pessimistic Nonlinear Least-Squares Value Iteration for Offline Reinforcement Learningcs.LG

Papers learn from data to make decisions without interacting, improving on previous methods.

problem Achieving optimal decision-making from offline data with non-linear function approximation.

method Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI) with three innovative components.

result Achieves minimax optimal instance-dependent regret for non-linear function approximation.

offline reinforcement learning non-linear function approximation value iteration regret bound minimax optimality

2023-10-02abs ↗pdf ↗

On Gaussian approximation for entropy-regularized Q-learning with function approximationstat.ML

The paper analyzes the convergence rates of Q-learning with entropy regularization and linear function approximation.

problem Analyzing the convergence rates of Q-learning with entropy regularization and linear function approximation.

method The paper derives rates of convergence using the high-dimensional central limit theorem, linearization of the soft Bellman recursion, and Gaussian approximation for the leading martingale term.

result The algorithm's last iterate satisfies high-order moment bounds, with a Gaussian approximation bound of order

n^{-1/4}

Q-learning entropy regularization linear function approximation convergence rates Gaussian approximation

2026-05-17abs ↗pdf ↗

Weighted universal approximation of differentiable maps on infinite-dimensional manifoldsmath.FA

Universal approximation theorem for differentiable maps on infinite-dimensional manifolds

problem Approximation of differentiable maps on infinite-dimensional manifolds

method Weighted universal approximation theorem

result Universal approximation theorem for differentiable maps

universal approximation differentiable maps infinite-dimensional manifolds

2026-06-08abs ↗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 ↗

Approximation of Nonlinear Functionals Using Deep ReLU Networksstat.ML

Study approximates nonlinear functionals using deep ReLU networks.

problem Approximating nonlinear continuous functionals with neural networks.

method Constructs continuous piecewise linear interpolation under simple triangulation, analyzes rates of approximation.

result Established rates of approximation for functional deep ReLU networks.

Deep ReLU networks Functional approximation Nonlinear functionals Rectified linear unit Triangulation

2023-04-10abs ↗pdf ↗

Nonstationary Reinforcement Learning with Linear Function Approximationcs.LG

New RL algorithm tackles nonstationary MDPs with linear approximations and varying rewards.

problem Nonstationary reinforcement learning with evolving reward and state transition functions.

method Developed a new algorithm LSVI-UCB-Restart with periodic restart, and parameter-free Ada-LSVI-UCB-Restart for unknown variation budgets.

result First minimax dynamic regret lower bound for nonstationary linear MDPs and linear MDPs lower bound.

reinforcement learning nonstationary linear function approximation dynamic regret optimistic algorithms

2020-10-08abs ↗pdf ↗

Gap-Dependent Bounds for Nearly Minimax Optimal Reinforcement Learning with Linear Function Approximationstat.ML

Improved gap-dependent bounds for reinforcement learning with linear approximations.

problem Achieving nearly minimax-optimal performance with linear function approximation.

method Developed and analyzed the LSVI-UCB++ algorithm and its concurrent variant.

result First gap-dependent regret bound for nearly minimax-optimal algorithm LSVI-UCB++.

reinforcement learning linear function approximation gap-dependent bounds LSVI-UCB++

2026-02-23abs ↗pdf ↗

Weighted universal approximation of differentiable maps on infinite-dimensional manifoldsmath.FA

Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.

problem Approximating differentiable maps on infinite-dimensional manifolds.

method Proves a weighted Nachbin theorem to establish universal approximation for differentiable maps, including derivatives.

result Linear functions of the signature can approximate path space functionals including their derivatives.

universal approximation differentiable maps infinite-dimensional manifolds derivatives weighted Nachbin theorem

2026-06-08abs ↗pdf ↗

Learning Infinite-horizon Average-reward MDPs with Linear Function Approximationcs.LG

New algorithms for learning MDPs with linear approximations in infinite-horizon settings.

problem Learning infinite-horizon average-reward MDPs with linear function approximation.

method Optimism principle, adversarial linear bandits, Natural Policy Gradient.

result Efficient algorithms with optimal or near-optimal regret bounds.

Markov Decision Processes Linear Function Approximation Adversarial Linear Bandits Optimism Principle Natural Policy Gradient

2020-07-23abs ↗pdf ↗

Uniform-PAC Bounds for Reinforcement Learning with Linear Function Approximationcs.LG

New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.

problem RL with linear function approximation lacks uniform-PAC guarantees.

method FLUTE algorithm with minimax value function estimator and multi-level partition scheme.

result Uniform-PAC convergence to optimal policy with high probability.

reinforcement learning linear function approximation uniform-PAC minimax value function multi-level partition

2021-06-22abs ↗pdf ↗

SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecastingcs.LG

SKOLR uses linear RNNs to approximate Koopman operators for time-series forecasting.

problem Nonlinear dynamical system analysis and time-series forecasting with infinite-dimensional Koopman operators.

method Established a connection between Koopman operator approximation and linear RNNs, integrating learnable spectral decomposition and MLP.

result SKOLR delivers exceptional performance in various forecasting benchmarks and dynamical systems.

Koopman operator time-series forecasting Recurrent Neural Networks linear approximation spectral decomposition

2025-06-17abs ↗pdf ↗

Analytical Approximation for Non-linear FBSDEs with Perturbation Schemeq-fin.CP

In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily highe…

2011-06-01abs ↗pdf ↗

Nearly Minimax Optimal Offline Reinforcement Learning with Linear Function Approximation: Single-Agent MDP and Markov Gamecs.LG

New algorithm for offline RL with linear approx in MDPs and MGs, nearly optimal.

problem Offline RL with linear function approximation in MDPs and MGs.

method Pessimism-based algorithm with uncertainty decomposition via reference function.

result Nearly minimax optimal performance in offline RL for MDPs and MGs.

Offline RL Linear function approximation MDP MG Pessimism

2022-05-31abs ↗pdf ↗

State-Of-The-Art Algorithms For Low-Rank Dynamic Mode Decompositionstat.ML

Review of algorithms for linear system approximations.

problem Linear approximation of high-dimensional dynamical systems.

method State-of-the-art algorithms for low-rank DMD.

result Provides additional details for comprehensive understanding.

dynamic mode decomposition linear approximation high-dimensional systems state-of-the-art

2021-08-20abs ↗pdf ↗

Approximate Dynamic Programming with Neural Networks in Linear Discrete Action Spacescs.LG

Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we must often compute expected downstream values corresponding to current decision…

2019-02-26abs ↗pdf ↗

Non-linear reduced modeling of dynamical systems using kernel methods and low-rank approximationstat.ML

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS…

2017-10-30abs ↗pdf ↗

Efficient Planning in Large MDPs with Weak Linear Function Approximationcs.LG

Efficiently plans large MDPs with weak function approximations.

problem Planning in large MDPs with limited function approximation capabilities.

method Uses linear value function approximation with weak requirements and a generative oracle.

result Produces almost-optimal actions for any state with polynomial computation time.

Markov decision processes linear approximation weak function approximation generative oracle almost-optimal actions

2020-07-13abs ↗pdf ↗

On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysiscs.LG

Study on memory effects in RNNs learning temporal data.

problem Understanding memory effects in RNNs for temporal data learning.

method Mathematical analysis of continuous-time linear RNNs, focusing on approximation and optimization dynamics.

result Long-term memory requires a large number of neurons and slows down training.

Recurrent Neural Networks Temporal Data Memory Effects Approximation Theory Optimization Dynamics

2020-09-16abs ↗pdf ↗

Inject Machine Learning into Significance Test for Misspecified Linear Modelscs.LG

Paper presents a machine learning method to improve significance tests for misspecified linear models.

problem Misspecification of linear assumptions in social science models leads to inaccurate significance levels.

method Apply machine learning to fit ground truth function, calculate linear approximation, and adjust the estimator.

result The method significantly outperforms linear regression for non-linear ground truth functions.

machine learning significance test linear approximation misspecified models social science

2020-06-04abs ↗pdf ↗

High-probability sample complexities for policy evaluation with linear function approximationstat.ML

The paper analyzes the sample complexities for policy evaluation with linear function approximation.

problem Policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes.

method Investigates sample complexities for two policy evaluation algorithms: TD and TDC.

result Establishes high-probability sample complexity bounds for policy evaluation algorithms.

policy evaluation linear function approximation Markov decision processes temporal difference learning two-timescale linear TD

2023-05-30abs ↗pdf ↗