Characterizes problems solvable via linear convergence algorithms.
problem Optimization problems solvable with linear convergence.
method Riemannian gradient descent.
result Characterized problems solvable via linear convergence.
The Sinkhorn-Knopp derivatives converge with linear rate.
problem Optimal transport problem with entropic regularization.
method Iterative proportional fitting procedure.
result Derivatives converge with linear rate.
Policy gradient converges linearly with Hadamard parameterization in tabular settings.
problem Convergence of policy gradient methods under Hadamard parameterization.
method Studied convergence rate and established linear convergence after k0 iterations. result Algorithm converges linearly with rate $O( rac{1}{k})$ and faster locally after k0. 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.
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.
Policy gradient methods achieve linear convergence in simple MDPs.
problem Analyzing convergence rates of policy gradient methods in finite MDPs.
method Connections with policy iteration to show linear convergence with large step-sizes.
result Policy gradient methods succeed with large step-sizes and achieve linear rate of convergence.
Paper proves linear convergence of SCMS algorithm for directional data.
problem Identifying density ridges in directional data.
method Generalized SCMS algorithm to directional data, derived from SCGA with adaptive step size.
result Linear convergence of the proposed directional SCMS algorithm.
The paper improves convergence for linear systems using entropic mirror descent with Polyak stepsizes.
problem Convergence analysis for linear systems with unbounded domain.
method Entropic mirror descent with Polyak stepsizes, sublinear and linear convergence results.
result Generalized convergence result for arbitrary convex functions.
We consider linear slices of the space of Kleinian once-punctured torus groups; a linear slice is obtained by fixing the value of the trace of one of the generators. The linear slice for trace 2 is called the Maskit slice. We will show that if traces converge `horocyclically' to 2 then associated linear slices converge…
New analysis shows GMD can converge linearly under PL-like conditions.
problem Establishing linear convergence for generalized mirror descent.
method PL-based analysis for time-dependent mirrors, Taylor-series approach for stochastic GMD.
result Linear convergence of stochastic GMD under PL-like conditions.
Gradient descent achieves exact linear convergence rate for symmetric matrix completion.
problem Low-rank symmetric matrix completion using gradient descent.
method Local analysis of gradient descent for symmetric matrices without additional assumptions.
result Closed-form expression of exact linear convergence rate matches practice.
Study shows long-term solutions for complex equations on curved spaces.
problem Long-term behavior of solutions to fully non-linear parabolic equations on Hermitian manifolds.
method Used general assumptions and derived a Harnack inequality for the linearized equation.
result Proved the long-time existence and convergence of solutions.
New insights into continual learning for deep models, showing convergence issues but local linear solutions.
problem Challenges in continual learning for homogeneous deep models.
method Sequential projections onto task margin sets, leveraging nonconvex projection theory.
result Local linear convergence under certain conditions for homogeneous deep networks.
The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that EM enjoys global convergence for Gaussian Mixture Models. For Mixed Linear Regres…
New method for natural policy gradients converges linearly.
problem Improving natural policy gradient methods for better convergence.
method Fisher-Rao gradient flow applied to state-action distributions.
result Linear convergence rate with geometry-dependent factor.
This paper proves AdaGrad and Adam converge linearly under PL inequality.
problem Understanding the convergence of adaptive gradient methods.
method Unified approach proving AdaGrad and Adam converge linearly under PL inequality.
result AdaGrad and Adam converge linearly when the cost function is smooth and satisfies PL inequality.
Study shows directional convergence for neural networks under spherical symmetry.
problem Learning linear predictors with neural networks under spherically symmetric data.
method Analysis of gradient flow and gradient descent for two-layer and deep linear networks.
result Directional convergence guarantees with exact convergence rate for specific network architectures.
Stochastic gradient descent achieves polynomial convergence rates for noiseless linear models.
problem Convergence analysis of stochastic gradient descent in noiseless linear models.
method Fixed step-size stochastic gradient descent on least-square risk.
result Polynomial convergence rates depend on the regularities of the optimum and feature vectors.
Gradient descent converges linearly for overparameterized linear networks.
problem Convergence of gradient descent for overparameterized neural networks.
method Local Polyak-Lojasiewicz and Descent Lemma for overparameterized linear models.
result Gradient descent achieves linear convergence for two-layer linear networks under relaxed assumptions.
GD converges faster to flatter minima than gradient flow in shallow networks.
problem Understanding the dynamics of gradient descent in shallow linear networks.
method Analyzing the convergence rate and solution of gradient descent in depth-2 linear neural networks.
result GD converges linearly to flatter minima than gradient flow, even with large step sizes.
AdaLoss optimizes adaptive learning rates for efficient convergence in various models.
problem Efficiently optimizing adaptive learning rates for gradient descent methods.
method AdaLoss uses loss function information to dynamically adjust step sizes.
result AdaLoss achieves linear convergence in linear regression and robust global convergence in neural networks.
Online learning of linear operators between infinite-dimensional spaces is possible but with limitations.
problem Learning linear operators between infinite-dimensional Hilbert spaces in an online setting.
method Online learning approach for linear operators with bounded p-Schatten norm, proving impossibility for operator norm. result Separation between online learnability and uniform convergence for bounded linear operators.
FA algorithm provides convergence guarantees for deep linear networks.
problem Training efficiency and convergence of deep neural networks.
method Theoretical analysis of Feedback Alignment (FA) algorithm for deep linear networks.
result Certain initializations lead to implicit anti-regularization, affecting learning effectiveness.
We study the convergence of gradient descent (GD) and stochastic gradient descent (SGD) for training L-hidden-layer linear residual networks (ResNets). We prove that for training deep residual networks with certain linear transformations at input and output layers, which are fixed throughout training, both GD and SGD…
Improved SGD for robust linear and ReLU regression with adversarial corruptions.
problem Robust regression with adversarial corruptions in streaming data.
method Stochastic gradient descent (SGD-exp) with exponentially decaying step size.
result Nearly linear convergence to true parameter with up to 50% Massart corruption rate.
AM converges super-linearly for solving mixed linear regression problems.
problem Learning linear regressors from unlabeled observations in multiple linear regression models.
method Alternating Minimization (AM) algorithm, which alternates between label estimation and regression solving.
result AM converges super-linearly in certain parameter regimes, requiring only O(log log(1/ε)) iterations to achieve an error of ε.
Paper revisits set membership estimation for linear systems with relaxed disturbance bounds.
problem Set membership estimation for linear systems with disturbances bounded by convex sets.
method Adopted block-martingale small-ball condition and random perturbed control policies to establish convergence rates.
result Established convergence rates for disturbances bounded by general convex sets.
We show that gradient descent on full-width linear convolutional networks of depth L converges to a linear predictor related to the ℓ2/L bridge penalty in the frequency domain. This is in contrast to linearly fully connected networks, where gradient descent converges to the hard margin linear support vector m…
Paper proposes a pre-conditioning technique to speed up gradient-descent convergence in distributed linear least-squares problems.
problem Expediting convergence of gradient-descent method for ill-conditioned distributed linear least-squares problems.
method Iterative pre-conditioning technique to improve convergence rate of gradient-descent method.
result Pre-conditioned gradient-descent achieves superlinear convergence for unique solutions and improved linear convergence otherwise.
FedSARSA converges with heterogeneous agents, achieving linear speed-up.
problem Convergence analysis of Federated SARSA with heterogeneous agents.
method Linear function approximation, local training, multi-step error expansion.
result FedSARSA achieves linear speed-up with respect to the number of agents.
Unified framework for solving linear systems with improved convergence rates.
problem Efficiently solving linear systems with randomized batch-sampling methods.
method Developed a unified randomized batch-sampling Kaczmarz framework with concentration inequalities for analysis.
result Derived new expected linear convergence rate bounds that are tighter and more reflective of empirical behavior.
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 L2 convergence rate of linear Q-learning iterates to a bounded set. Paper analyzes EM algorithm's trajectory in 2MLR, revealing cycloid behavior.
problem Understanding the convergence and trajectory of EM algorithm in 2MLR.
method Explicit closed-form expressions for EM updates, recurrence relation derivation at population level.
result EM iterations lie on a cycloid trajectory, leading to theoretical estimate of convergence exponent.
Policy gradient methods find Nash equilibrium in noisy games.
problem Finding Nash equilibrium in noisy games.
method Policy gradient methods with noise added.
result Policy gradient methods converge to Nash equilibrium in noisy games.
Guaranteed convergence for tensor factorization using Riemannian gradient descent.
problem Recovering tensor train format from linear measurements.
method Optimization over left-orthogonal TT format using Riemannian gradient descent on Stiefel manifold.
result RGD converges linearly to the ground-truth tensor with polynomial error growth in tensor order.
Paper shows linear convergence of ISTA and FISTA for ill-conditioned images.
problem Solving linear inverse problems with sparse representation in signal and image processing.
method Revisits iterative shrinkage-thresholding algorithms (ISTA) and improves their convergence properties.
result Linear convergence of ISTA and FISTA for strongly convex smooth parts, even in ill-conditioned cases.
The MEM method uses data-driven priors for linear inverse problems, proving convergence and estimating differences.
problem Linear inverse problems with approximate priors.
method Maximum Entropy on the Mean (MEM) method with data-driven priors.
result Empirical mean convergence and estimates for prior differences based on epigraphical distance.
New insights show NAG and FISTA converge linearly without knowing strong convexity modulus.
problem Understanding linear convergence of NAG and FISTA without strong convexity modulus knowledge.
method High-resolution ODE framework, dynamically adapting kinetic energy coefficient.
result NAG and FISTA demonstrate linear convergence without requiring strong convexity modulus knowledge.
Paper analyzes TD(λ) convergence rates for arbitrary features.
problem Convergence rates for linear TD(λ) under arbitrary features. method Developed a novel stochastic approximation result for arbitrary features.
result Established L2 convergence rates for linear TD(λ) without linearly independent features assumption. This paper formalizes Q-learning and linear TD convergence using Lean 4.
problem Formalizing convergence properties of Q-learning and linear TD learning. method Formal verification using Lean 4 theorem prover and Mathlib library.
result Formalized almost sure convergence of Q-learning and linear TD learning. Study proves uniqueness of asymptotic limits for specific manifolds.
problem Proving uniqueness of asymptotic limits for Ricci-flat manifolds with linear volume growth.
method Established using natural curvature and cross section assumptions.
result Uniqueness and exponential convergence rate for complete noncollapsed Ricci-flat manifolds with linear volume growth.
Diffusion models converge linearly to complex data manifolds.
problem Sampling from high-dimensional complex data distributions.
method Score-matching generative models with novel integration scheme.
result Linear convergence in KL divergence to intrinsic dimension d. A new optimization algorithm improves convergence in unconstrained problems.
problem Unconstrained optimization problems.
method Element-wise relaxed scalar auxiliary variable (E-RSAV) algorithm.
result Improved convergence and alignment of modified and original energy.
New tensor recovery method uses Riemannian optimization on Segre manifold.
problem Recovering low-rank tensors from noisy measurements.
method Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN) algorithms over the Segre manifold.
result Proven convergence rates for RGD and RGN under mild noise assumptions.
The paper examines how deep linear neural networks behave as they become infinitely wide.
problem Understanding the behavior of deep linear neural networks as they approach infinite width.
method Analyzes the infinite-width limit of deep linear neural networks, proving convergence to deterministic models and providing precise laws for random weights.
result The training dynamics of deep linear neural networks converge to those of a deterministic model, and the weights' behavior is precisely described.
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is an iterative scheme born from the adaptation of proximal point algorithm to nois…
Paper proves EM algorithm convergence for mixtures of discrete and continuous parameters.
problem Nontrivial convergence analysis for EM algorithms with mixed-integer parameters.
method Introduces conditions for EM convergence in mixed-integer optimization.
result Proves convergence of EM-based sparse Bayesian learning algorithm.
Unified analysis of Federated Averaging and Nesterov FedAvg for linear speedup.
problem Understanding convergence of FL algorithms under non-i.i.d. data and partial participation.
method Systematic study of convergence guarantees for FedAvg and Nesterov FedAvg under different conditions.
result Unified analysis of linear speedup for FedAvg and Nesterov FedAvg in various settings.