Smooth convergence shown for curve diffusion flows.
problem Embeddedness and global existence of curves.
method Exponentially fast convergence established.
result Smooth convergence for curve diffusion flows.
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
Trend · papers per month
48 results for “global convergence”
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.
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.
Gradient descent proves global convergence for 4-layer matrix factorization.
problem Global convergence of gradient descent on four-layer matrix factorization under random initialization.
method New techniques to show saddle-avoidance properties and extend eigenvalue theories.
result Polynomial-time global convergence guarantee for randomly initialized gradient descent on four-layer matrix factorization.
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).
New framework for DNN training guarantees convergence to global minimum.
problem Training deep neural networks to converge to global minimum.
method Reformulated minimization problem with recursive algorithmic framework, using bounded style assumptions.
result Convergence to an ε-(global) minimum with O(1/ε^3) gradient computations.
Policy gradient methods with actor-critic schemes demonstrate tremendous empirical successes, especially when the actors and critics are parameterized by neural networks. However, it remains less clear whether such "neural" policy gradient methods converge to globally optimal policies and whether they even converge at …
Global convergence of multilayer neural networks proven for any depth.
problem Global convergence of multilayer neural networks in the mean field regime.
method Mean field limit framework, neuronal embedding, bidirectional diversity condition.
result Global convergence for multilayer networks of any depths, including correlated initializations.
Accelerates convergence in global non-convex optimization with reversible diffusion.
problem Global non-convex optimization challenges.
method Utilizes reversible diffusion processes with adaptive diffusion coefficients.
result Accelerated convergence with reduced discretization error.
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 …
SGD converges to global minimum for certain non-convex functions.
problem Theoretical challenges in optimizing non-convex functions in machine learning.
method Perturbed SGD on a broad class of non-convex functions.
result SGD converges to global minimum for certain non-convex functions.
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.
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.
This work studies the location estimation problem for a mixture of two rotation invariant log-concave densities. We demonstrate that Least Squares EM, a variant of the EM algorithm, converges to the true location parameter from a randomly initialized point. We establish the explicit convergence rates and sample complex…
Continuous-time distributed mirror descent with integral feedback converges to global optimum.
problem Distributed optimization of a global strongly convex function with local convex components.
method Continuous-time distributed mirror descent with integral feedback.
result Asymptotic convergence to global optimum with constant step-size.
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.
Study describes global existence and convergence of flows on surfaces and fibrations.
problem Global existence and convergence of flows on surfaces and fibrations.
method Complete description of Ricci-Yang-Mills flow and pluriclosed flow on bundles over Riemann surfaces.
result Equivalence of solutions to generalized Ricci flow and pluriclosed flow with symmetry.
SGD converges globally to logistic loss minima for two-layer nets.
problem Global convergence of SGD for logistic loss on two-layer neural nets.
method Demonstrates existence of Frobenius norm regularized logistic loss functions as Villani functions, proving convergence and exponential rate.
result SGD converges globally to the global minima of appropriately regularized logistic empirical risk of depth 2 nets.
RWR converges to global optimum in certain settings.
problem Proving convergence of RWR to optimal policy.
method Iterative learning with return-weighted log-likelihood.
result RWR converges to global optimum under certain conditions.
Paper proves global convergence of NCELM model.
problem Ensuring global convergence of NCELM model.
method Two-stage process: random base learners and NCL penalty term updates.
result Global convergence of NCELM proved using Banach theorem.
Wide neural networks with asymmetrical node scaling converge globally and learn features.
problem Global convergence and feature learning in over-parameterised shallow networks.
method Gradient-based optimisation of wide, shallow neural networks with asymmetrical node scaling.
result Gradient flow and gradient descent converge to a global minimum and learn features, unlike in the NTK parameterisation.
SGD methods fail to converge to global minimizers in deep neural networks with ReLU activation.
problem Failure of SGD methods to converge to global minimizers in deep neural networks.
method Stochastic Gradient Descent (SGD) and its variants like Adam, RMSProp, etc.
result SGD methods fail to converge to global minimizers with high probability in deep neural networks with ReLU activation.
EM algorithm converges to global max in latent Gaussian tree models.
problem Optimizing log-likelihood in latent Gaussian tree models.
method Analyzed the optimization landscape and convergence of EM algorithm.
result EM algorithm converges to global maximum in latent Gaussian tree models.
Gradient EM converges globally for over-parameterized Gaussian mixtures.
problem Recovering ground truth Gaussian mixtures with over-parameterized models.
method Gradient EM with over-parameterization, using Hermite polynomials and tensor decomposition.
result Gradient EM globally converges to ground truth with over-parameterization.
Paper develops NPG for risk-averse RL with ECRMs, proving global convergence.
problem Ensuring reliable performance in stochastic RL problems with risk-averse policies.
method Developed natural policy gradient updates for ECRMs-based RL problems, proving global optimality and iteration complexity.
result Global convergence of risk-averse NPG algorithm with ECRMs.
BCD algorithm finds global minima in neural networks.
problem Training deep neural networks to find global minima.
method Block coordinate descent with skip connections and non-negative projection.
result Proves convergence to global minima for strictly monotonic and ReLU activations.
Global convergence proved for three-layer neural networks in mean field regime.
problem Optimization efficiency of multilayer neural networks in the mean field regime.
method Developed a rigorous framework for mean field limit of three-layer networks using stochastic gradient descent and neuronal embedding.
result Global convergence guarantee for unregularized feedforward three-layer networks in the mean field regime.
Global Convergence and Generalization Bound of Gradient-Based Meta-Learning with Deep Neural Netscs.LG
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.
The paper investigates how activation functions impact the training of Neural ODEs, leading to global convergence.
problem Challenges in training Neural ODEs, particularly gradient computation accuracy and convergence analysis.
method Investigates the impact of activation functions on the training dynamics of Neural ODEs.
result Establishes global convergence of Neural ODEs under gradient descent in overparameterized regimes.
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 rate.
We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated.
New algorithm improves convergence for non-convex problems with boundaries.
problem Optimizing non-convex problems with constraints.
method Reflected Gradient Langevin Dynamics with probabilistic representation.
result Promising convergence rates, faster than existing methods.
Paper refutes EM convergence theory and introduces a new EM algorithm.
problem The convergence theory of the EM algorithm is incorrect and affects its performance.
method Proposes a new EM algorithm called the Channel Matching (CM) EM algorithm and provides an initialization map.
result The locally maximal Q can affect the convergent speed but not the global convergence.
Paper proves convergence of SA algorithm via martingale and converse Lyapunov methods.
problem Proves convergence of stochastic approximation algorithm.
method Uses martingale and converse Lyapunov methods to prove convergence.
result Provides alternate proof of convergence for SA algorithm.
Global convergence of SGD proven for two-layer neural nets with regularization.
problem Proving global convergence of SGD for two-layer neural nets.
method Regularized empirical risk, SGD iterates, Villani functions.
result Global convergence of SGD for a special class of initializations.
Gradient descent finds global optima in ResNets with sufficient parameters.
problem Finding optimal parameters in ResNet models.
method Mean-field analysis and gradient-flow PDE to study convergence of first-order optimization methods.
result First-order methods can find global minimizers in overparameterized ResNets.
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear whether the fixed point identified by the variational inference algorithm is a local…
Global convergence for robust regression problems via IRLS with enhancements.
problem Global convergence for robust regression problems.
method Augmentations to IRLS to ensure global recovery and improved robustness.
result Global recovery guarantees for robust regression problems, outperforming state-of-the-art algorithms.
We study the convergence of gradient descent (GD) and stochastic gradient descent (SGD) for training -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…
ProGO optimizes non-convex functions without gradients, outperforming existing methods.
problem Challenges in global optimization, especially with non-convex functions and limited gradient information.
method Probabilistic approach using multidimensional integration and latent slice sampler.
result ProGO converges to global optima efficiently and outperforms existing methods.
New method guarantees global convergence in variational inference.
problem Limited convergence to local optima in variational inference.
method Minimizes inclusive KL divergence using neural networks and neural tangent kernel.
result Gradient descent dynamics converge to a unique solution in function space.
Improved convergence for actor-critic algorithms in MDPs.
problem Global convergence analysis for actor-critic algorithms in MDPs.
method Introduced an analytical framework to handle complex recursions, established convergence to ε-close globally optimal policy with improved sample complexity.
result Converges to ε-close globally optimal policy with sample complexity of O(ε^(-3)) compared to O(ε^(-2)) for ε-close stationary policy.
We study the global convergence of generative adversarial imitation learning for linear quadratic regulators, which is posed as minimax optimization. To address the challenges arising from non-convex-concave geometry, we analyze the alternating gradient algorithm and establish its Q-linear rate of convergence to a uniq…
The paper proves convergence to global optima for a class of distributed algorithms for nonconvex optimization in network-based multi-agent settings. Agents are permitted to communicate over a time-varying undirected graph. Each agent is assumed to possess a local objective function (assumed to be smooth, but possibly …
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.
Proximal policy optimization and trust region policy optimization (PPO and TRPO) with actor and critic parametrized by neural networks achieve significant empirical success in deep reinforcement learning. However, due to nonconvexity, the global convergence of PPO and TRPO remains less understood, which separates theor…
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.
New algorithm ensures global convergence in deep neural networks beyond NTK regime.
problem Existing global convergence guarantees do not apply to practical deep networks.
method Proposes an algorithm with global convergence guarantees under the expressivity condition.
result Algorithm ensures global convergence in practical settings beyond NTK regime.