Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (…
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48 results for “mean-square convergence”
A Lyapunov Theory for Finite-Sample Guarantees of Asynchronous Q-Learning and TD-Learning Variantscs.LG
Unified framework for finite-sample RL algorithms using Lyapunov theory.
problem Finite-sample convergence guarantees of asynchronous RL algorithms.
method Reformulate RL algorithms as Markovian SA, develop Lyapunov analysis.
result Mean-square error bounds and convergence for various RL algorithms.
Double Q-learning has the same mean-squared error as Q-learning under certain conditions.
problem Comparing the mean-squared error of Double Q-learning and Q-learning.
method Theoretical analysis based on Lyapunov equations for both tabular and linear function approximation settings.
result The asymptotic mean-squared error of Double Q-learning is exactly equal to that of Q-learning under specific conditions.
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably dominates its conventional counterpart in terms of mean square deviations. We es…
New methods for estimating complex causal effects in econometrics.
problem Estimating causal parameters in short panel data models using nested nonparametric instrumental variable regression.
method Introducing techniques to limit ill-posedness in nested NPIV, providing explicit mean square rates and efficient inference.
result Explicit mean square rates for nested NPIV and efficient inference for causal parameters.
Paper analyzes convergence of two time-scale stochastic approximation using martingale approach.
problem Analyzing convergence of two time-scale stochastic approximation algorithms.
method Uses martingale approach to establish convergence conditions and rates.
result Establishes different rates of convergence for fast and slow subsystems.
Mirror Langevin Algorithm converges with zero bias.
problem Achieving convergence with zero bias in discrete-time sampling.
method Discretization of Mirror Langevin Diffusion and mean-square analysis.
result Mirror Langevin Algorithm converges with zero bias.
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention as been paid to proving lower error bounds for the SGD method. It is the key cont…
Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size (bandwidth) is still an open important issue especially for learning with small sample s…
Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. Th…
Previous studies have shown that deep neural networks (DNNs) with common settings often capture target functions from low to high frequency, which is called Frequency Principle (F-Principle). It has also been shown that F-Principle can provide an understanding to the often observed good generalization ability of DNNs. …
We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l1-l2 norm regularizer. By systematically treating the non-differentiable regulariz…
Layer normalization (LayerNorm) has been successfully applied to various deep neural networks to help stabilize training and boost model convergence because of its capability in handling re-centering and re-scaling of both inputs and weight matrix. However, the computational overhead introduced by LayerNorm makes these…
Enhances RL for jump processes using MSBVE algorithm.
problem Challenges in continuous-time RL with jumps and noise.
method Introduces MSBVE algorithm to minimize quadratic variation error.
result MSBVE algorithm outperforms MSTDE in jump processes.
Paper optimizes diffusion models for denoising tasks with theoretical guarantees.
problem Lack of theoretical understanding of MSE optimality in diffusion models.
method Inspired by MSE-optimal CME, proposes a novel denoising strategy for diffusion models.
result Demonstrates polynomial-time convergence to the CME under mild conditions.
This work analyzes -learning with adaptive stepsizes for finite-time convergence.
problem Finite-time convergence analysis for average-reward -learning with adaptive stepsizes.
method Adaptive stepsizes as local clocks, time-inhomogeneous Markovian reformulation, almost-sure time-varying bounds, conditioning arguments, and Markov chain concentration inequalities.
result Convergence rates of for mean-square and pointwise mean-square convergence.
Paper analyzes kNN estimator for KL divergence, proving its optimality.
problem Estimating KL divergence from identical samples.
method kNN estimator based on nearest neighbor distances.
result kNN method is asymptotically rate optimal for KL divergence estimation.
I unravel the basic long run dynamics of the broker call money market, which is the pile of cash that funds margin loans to retail clients (read: continuous time Kelly gamblers). Call money is assumed to supply itself perfectly inelastically, and to continuously reinvest all principal and interest. I show that the rela…
Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distri…
Temporal-difference learning (TD), coupled with neural networks, is among the most fundamental building blocks of deep reinforcement learning. However, due to the nonlinearity in value function approximation, such a coupling leads to nonconvexity and even divergence in optimization. As a result, the global convergence …
Bayesian PINN improves estimation of PDE solutions from noisy data.
problem Estimating solutions of PDEs from noisy measurements.
method Bayesian approach to Physics-informed neural networks (PINNs) for inverse problems.
result Convergence rate of Bayesian posterior mean error in PDE solutions.
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or O(n*log(n)) for constructing a classifier, where n is the number of sampling instances.…
Paper improves Gumbel-Softmax estimator variance reduction.
problem Challenges in gradient estimation for models with discrete latent variables.
method Rao-Blackwellization applied to straight-through Gumbel-Softmax estimator.
result Reduces mean squared error and variance of Gumbel-Softmax estimator.
This study explains gradient flow dynamics in neural networks for small initialisation.
problem Understanding the training dynamics of neural networks for small initialisation.
method Analysis of gradient flow dynamics for one-hidden layer ReLU networks with orthogonal inputs.
result Gradient flow converges to zero loss and characterizes implicit bias towards minimum variation norm.
Approximate Survey Propagation for Statistical Inferencecond-mat.dis-nn
Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this algorithm as the approximate survey propagation (ASP) and derive it for a class of low-…
Unified framework for PE and TD methods in continuous time and space.
problem Policy evaluation and TD learning in continuous settings.
method Martingale characterization for designing PE algorithms.
result Convergent time-discretized algorithms converge to continuous-time counterparts.
Improved bounds for non-linear SA with fast convergence.
problem Stochastic approximation with non-linear mappings and multiple time scales.
method Mean squared error bounds with rate for contractive mappings.
result First rate for non-linear two-time-scale SA without additional smoothness assumptions.
In this paper, we provide a unified analysis of temporal difference learning algorithms with linear function approximators by exploiting their connections to Markov jump linear systems (MJLS). We tailor the MJLS theory developed in the control community to characterize the exact behaviors of the first and second order …
Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a Markov factor graph model, this exploration process is called structure discover…
New convergence rates found for PnP methods using MMSE denoisers.
problem Asymptotic convergence of PnP methods with MMSE denoisers.
method Explicitly represented MMSE denoiser as an upper Moreau envelope, derived sublinear convergence rates.
result First sublinear convergence guarantee for PnP proximal gradient descent with MMSE denoiser.
ARISE models efficient markets without periodogram or Gaussianity assumptions.
problem Mimicking and learning long-term memory in efficient markets.
method ARISE process using aperiodic spectrum estimation and infinite-sum function of known processes.
result ARISE process has mean-square convergence, consistency, and asymptotic normality without periodogram and Gaussianity assumptions.
We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by th…
We study reinforcement learning under model misspecification, where we do not have access to the true environment but only to a reasonably close approximation to it. We address this problem by extending the framework of robust MDPs to the model-free Reinforcement Learning setting, where we do not have access to the mod…
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.
The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm is closely related to the Kalman filtering, and thus, the KLMS can be interpreted…
This paper introduces a class of k-nearest neighbor (-NN) estimators called bipartite plug-in (BPI) estimators for estimating integrals of non-linear functions of a probability density, such as Shannon entropy and Rényi entropy. The density is assumed to be smooth, have bounded support, and be uniformly bounded from…
We analyze two communication-efficient algorithms for distributed statistical optimization on large-scale data sets. The first algorithm is a standard averaging method that distributes the data samples evenly to $\nummac$ machines, performs separate minimization on each subset, and then averages the estimates. We p…
This study analyzes AdaGrad's stability and convergence in non-convex optimization.
problem Lack of theoretical analysis for AdaGrad in non-convex optimization.
method Novel stopping time-based techniques from probability theory.
result Established stability and derived convergence rates for AdaGrad.
Deep linear networks exhibit collapsing features and classifiers across datasets.
problem Understanding the collapse of features and classifiers in deep linear networks.
method Theoretical and empirical analysis of deep linear networks with MSE and CE losses.
result Deep linear networks exhibit NC properties, collapsing features and classifiers to orthogonal vectors.
In this paper, we study the online learning algorithm without explicit regularization terms. This algorithm is essentially a stochastic gradient descent scheme in a reproducing kernel Hilbert space (RKHS). The polynomially decaying step size in each iteration can play a role of regularization to ensure the generalizati…
Multilevel Monte Carlo in Sample Average Approximation: Convergence, Complexity and Applicationq-fin.CP
The paper improves Monte Carlo methods for optimization problems.
problem Efficiently solving optimization problems with biased Monte Carlo estimators.
method Introduces Multilevel Monte Carlo (MLMC) within Sample Average Approximation (SAA).
result Establishes uniform convergence and sample complexity for MLMC in SAA.
Paper studies a robust online learning algorithm for regression.
problem Develops a robust online learning algorithm for regression problems.
method Introduces an online learning algorithm with a robust loss function over RKHS.
result The algorithm achieves optimal convergence rates in mean square and RKHS.
Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.
problem Improving convergence of SGD in various settings.
method Develops a general weighted averaging scheme for SGD and establishes asymptotic normality.
result Establishes asymptotic normality and optimality of weighted averaged SGD solutions.
The paper proposes an efficient nested simulation design using likelihood ratio method.
problem Designing nested simulations with fixed outer scenarios and minimizing simulation effort.
method Proposes a bi-level optimization problem to decide inner replications and pooling strategies.
result Optimized design achieves $\cO(Γ^{-1})$ mean squared error of estimators.
Adaptive filtering algorithms operating in reproducing kernel Hilbert spaces have demonstrated superiority over their linear counterpart for nonlinear system identification. Unfortunately, an undesirable characteristic of these methods is that the order of the filters grows linearly with the number of input data. This …
Deep neural networks tackle high-dimensional nonparametric interaction models.
problem Estimating structured regression functions in high-dimensional data.
method Analyze order nonparametric interaction models in growing and high dimensions, introducing debiasing techniques.
result Debiased deep neural networks achieve optimal rates of convergence in both growing and high dimensions.
Estimates multiple linear systems on a graph with smoothness constraints.
problem Joint estimation of multiple linear systems under graph smoothness constraints.
method Proposes estimators for joint estimation of system matrices with error bounds.
result MSE converges to zero as increases, typically polynomially fast w.r.t .
This paper analyzes sampling from heavy-tailed distributions using discretized Itô diffusions.
problem Sampling from heavy-tailed distributions with finite variance.
method Mean-square analysis of discretized Itô diffusions with weighted Poincaré inequalities.
result Explicit iteration complexity for obtaining samples close to target distributions in Wasserstein-2 metric.