Study shows a linear quadratic regulator's imitation learning converges globally.
problem Global convergence of imitation learning for linear quadratic regulators.
method Analyzed alternating gradient algorithm and established Q-linear rate of convergence.
result Established a unique saddle point for globally optimal policy and reward function.
Newton's method converges linearly for stable Hessians, even with approximations.
problem Finding global linear convergence for functions without strong convexity or Lipschitz gradients.
method Global linear convergence of Newton's method for stable Hessians, using approximate Hessians and subproblems.
result Global linear convergence rate for a broad class of functions, superior to first-order methods.
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.
Paper proposes a quasi-Newton method for nonlinear equations with global convergence guarantees.
problem Solving smooth and monotone nonlinear equations efficiently and globally.
method Hybrid proximal extragradient framework combined with online learning for Jacobian approximation.
result First global convergence results showing quasi-Newton method's advantage over extragradient method.
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.
Wide neural networks converge linearly to zero loss with feature learning.
problem Optimizing wide neural networks with feature learning guarantees.
method Gradient flow analysis for wide shallow and multi-layer NNs.
result Training loss converges linearly to zero for wide NNs under GF, demonstrating feature learning and better generalization.
Paper improves a method for fast global and local convergence in optimization.
problem Slow global convergence in optimization methods with noisy Hessian estimates.
method Stochastic Newton Proximal Extragradient method using HPE framework.
result Faster global linear rate and superlinear convergence in fewer iterations.
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.
This paper extends the convergence rate of DEQs with ReLU to any general activation.
problem Proving global convergence rate for DEQs with general activations.
method Developed a novel population Gram matrix and new form of dual activation with Hermite polynomial expansion.
result Gradient descent converges to a globally optimal solution at a linear rate for DEQs with general activations.
Single-timescale actor-critic finds globally optimal policy.
problem Finding globally optimal policy in reinforcement learning.
method Simultaneous actor and critic updates with linear or deep neural network approximations.
result Actor sequence converges to globally optimal policy at O(K−1/2) rate. Gradient EM converges globally for over-parameterized Gaussian mixtures.
problem Global convergence of gradient EM for Gaussian mixtures with more than 2 components.
method Likelihood-based convergence analysis framework.
result Gradient EM converges globally with a sublinear rate of O(1/√t).
Gradient descent converges linearly for deep linear networks under specific conditions.
problem Speed of convergence in gradient descent for deep linear neural networks.
method Analysis of gradient descent training for deep linear neural networks minimizing ℓ2 loss. result Gradient descent converges linearly under specific conditions on layer dimensions, initialization, and initial loss.
Actor-critic converges globally in LQR with ergodic cost.
problem Theoretical understanding of actor-critic algorithm's global convergence.
method Nonasymptotic convergence analysis of actor-critic in linear quadratic regulator (LQR) setting.
result Actor-critic finds globally optimal policy and value function at a linear rate.
Gradient descent solves non-convex neural networks with random initialization.
problem Gradient descent can solve non-convex neural networks with random initialization.
method Gradient descent, over-parameterized neural networks, random initialization, strong convexity-like property.
result Gradient descent converges to a globally optimal solution at a linear rate.
Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.
problem Finding optimal policies in nonlinear control systems with partial information.
method Policy gradient algorithm designed for nearly linear-quadratic regulators with small Lipschitz nonlinear components.
result Policy gradient algorithm converges to globally optimal policy with linear rate.
This paper studies GAIL's global convergence for general MDP and nonlinear rewards.
problem Understanding when GAIL algorithms achieve global convergence for general MDP and nonlinear rewards.
method Characterization of global convergence for various policy gradient algorithms applied to GAIL.
result First systematic theoretical study of GAIL for global convergence.
Gradient descent with preconditioning finds global optima in overparameterized nonconvex factorization.
problem Finding global optima in nonconvex Burer-Monteiro factorization.
method Preconditioned gradient descent for overparameterized nonconvex function minimization.
result Gradient descent with preconditioning achieves linear convergence in the overparameterized case.
AGDA and variance-reduced methods solve nonconvex-nonconcave minimax problems globally and faster.
problem Solving nonconvex-nonconcave minimax problems in machine learning.
method Global convergence of AGDA and variance-reduced algorithms.
result AGDA and variance-reduced methods achieve global convergence and faster rates.
This work shows linear convergence for two-layer neural networks in mean-field regime.
problem Optimizing two-layer neural networks in the mean-field regime.
method Mean-field analysis and continuous-time noisy gradient descent.
result Establishes linear convergence rate for two-layer neural networks.
Many statistical M-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite gradient methods for solving such problems, working within a high-dimensional framewor…
Improved DANE algorithm for faster convergence in distributed machine learning.
problem Challenges in convergence of DANE algorithm for general convex functions.
method Introducing variants of DANE with backtracking line search and heavy-ball method.
result Proved global and local convergence rates for quadratic and non-quadratic strongly convex functions.
New algorithms prove fast convergence in complex min-max problems.
problem Proving fast convergence in nonconvex min-max optimization.
method Hamiltonian Gradient Descent (HGD) and Consensus Optimization (CO) algorithms.
result HGD and CO achieve linear convergence in various settings.
AGGLIO optimizes non-convex functions with local convexity guarantees.
problem Optimizing non-convex functions with local convexity.
method Stage-wise, graduated optimization technique for locally convex functions.
result Global convergence to the global optimum for non-convex and locally convex objectives.
GAIL with neural networks converges to global optima and has a known rate.
problem Uncertainty about GAIL with neural networks achieving global optimality.
method Gradient-based alternating updates algorithm.
result Established sublinear convergence to globally optimal solution.
While convergence of the Alternating Direction Method of Multipliers (ADMM) on convex problems is well studied, convergence on nonconvex problems is only partially understood. In this paper, we consider the Gaussian phase retrieval problem, formulated as a linear constrained optimization problem with a biconvex objecti…
New algorithm improves convergence of gradient boosting trees.
problem Global convergence of Newton boosting in tabular machine learning.
method Introduces Gradient Regularized Newton Descent for GBDTs, proving linear convergence for smooth, strongly convex losses and O(k21) rate for general convex losses. result Achieves globally convergent second-order GBDT algorithm with rate matching first-order boosting.
New quasi-Newton method guarantees global superlinear convergence.
problem Global convergence and superlinear convergence of quasi-Newton methods.
method Hybrid proximal extragradient method with online learning for Hessian approximation.
result First globally convergent quasi-Newton method with explicit superlinear convergence rate.
FedAvg converges linearly to global minimum in federated learning with partial participation.
problem Challenges in federated learning with partial client participation.
method Federated averaging (FedAvg) method for over-parameterized neural networks.
result FedAvg converges to global minimum at a linear rate after t iterations.
Paper analyzes convergence of Adam-type RL algorithms under Markovian sampling.
problem Theoretical convergence analysis of Adam-type RL algorithms.
method Develops techniques for analyzing convergence under Markovian sampling.
result PG-AMSGrad and TD-AMSGrad converge to stationary points or global optima at specified rates.
New convergence rates for SGD under heavy-tailed noise with infinite variance.
problem Convergence analysis of SGD under heavy-tailed noise with infinite variance.
method Identifying a condition on the Hessian and providing a convergence rate for the distance to the global optimum.
result SGD can converge to the global optimum under heavy-tailed noise with infinite variance.
Self-attention optimizers converge to optimal weights, revealing bias patterns.
problem Understanding the implicit bias in self-attention mechanisms.
method Analysis of gradient-based optimization in self-attention layers.
result Adaptive step-size strategies can accelerate convergence to optimal weights.
Stochastic second-order methods converge fast under interpolation conditions.
problem Minimizing smooth and strongly-convex functions efficiently.
method Regularized subsampled Newton method (R-SSN) and stochastic BFGS algorithms.
result R-SSN achieves global linear convergence and quadratic rate in a local neighbourhood.
MAML with over-parameterized DNNs converges globally at a linear rate.
problem Few-shot learning with limited data.
method Model-agnostic meta-learning (MAML) with over-parameterized deep neural networks (DNNs).
result MAML with over-parameterized DNNs converges globally at a linear rate.
Paper addresses global convergence of MLR estimation under weak data conditions.
problem Learning mixed linear regression models with general data conditions.
method Two-step recursive identification algorithm using least squares and EM principles.
result Global convergence and optimal clustering performance established under general data conditions.
Adaptive-SGD method optimizes machine learning training with dynamic batch and step sizes.
problem Optimizing machine learning training with adaptive batch and step sizes.
method Adaptive-SGD method that dynamically adjusts batch size and step size based on local curvature and probability of descent directions.
result Adaptive-SGD achieves global linear convergence on self-concordant functions and compares favorably to fine-tuned methods.
The paper analyzes how over-parameterization affects GD convergence in matrix sensing problems.
problem Matrix sensing problem with over-parameterized gradient descent.
method Analyzes symmetric and asymmetric parameterizations, provides lower bounds and convergence rates.
result Over-parameterization slows down GD convergence, but asymmetric parameterization can speed up convergence.
Deep linear ResNets converge globally with certain transformations.
problem Global convergence of training deep linear ResNets.
method Gradient descent and stochastic gradient descent for training L-hidden-layer linear ResNets. result GD and SGD can converge to global minimum for deep linear ResNets with specific transformations.
Policy optimization converges to Nash equilibria in zero-sum LQ games.
problem Finding Nash equilibria in zero-sum linear quadratic games.
method Developed three projected nested-gradient methods to converge to NE.
result Policy optimization methods converge to Nash equilibria in zero-sum LQ games.
GBML with deep nets converges globally and generalizes well.
problem Theoretical guarantees for few-shot learning with deep nets.
method Proving global convergence and generalization bounds for GBML with over-parameterized DNNs.
result GBML with over-parameterized DNNs converges globally to the optimum at a linear rate and achieves good generalization.
EM algorithm converges globally for two-component mixed linear regression.
problem Global convergence of EM algorithm for mixed linear regression.
method Developed new theoretical analysis for EM algorithm convergence in mixed linear regression.
result EM algorithm converges globally for two-component mixed linear regression.
The Frank-Wolfe (FW) optimization algorithm has lately re-gained popularity thanks in particular to its ability to nicely handle the structured constraints appearing in machine learning applications. However, its convergence rate is known to be slow (sublinear) when the solution lies at the boundary. A simple less-know…
New method avoids spurious critical points for low-rank matrix recovery.
problem Low-rank matrix recovery problems on Riemannian manifold.
method Riemannian gradient descent with random initialization.
result Riemannian gradient descent avoids spurious critical points and converges nearly linearly.
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.
Proves convergence of mean curvature flow on cylinders with unique continuation.
problem Understanding the convergence and uniqueness of mean curvature flow on cylindrical surfaces.
method Proves convergence and provides unique continuation results for mean curvature flow on cylinders.
result Proves that rescaled mean curvature flow on cylinders converging super-exponentially must coincide with the cylinder itself.
DEQs converge to optimal solutions with mild over-parameterization.
problem Training over-parameterized deep equilibrium models.
method Solves equilibrium point directly, uses gradient descent, and analyzes convergence via linear rate.
result Gradient descent converges to a globally optimal solution at a linear rate for quadratic loss.
In 1963, Polyak proposed a simple condition that is sufficient to show a global linear convergence rate for gradient descent. This condition is a special case of the Łojasiewicz inequality proposed in the same year, and it does not require strong convexity (or even convexity). In this work, we show that this much-older…
Gradient descent converges to global optima in shallow overparameterized networks.
problem Understanding the level of overparameterization required for gradient descent to converge to a global optimum in shallow neural networks.
method Stochastic gradient descent starting from random initialization, focusing on shallow neural nets and smooth activations.
result Gradient descent converges geometrically to a nearby global optima as soon as the square-root of the number of parameters exceeds the size of the training data.
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these metho…