Studied SGD convergence under weak conditions.
problem Convergence of SGD in nonconvex optimization.
method Analyzed biased nonconvex SGD under mild conditions.
result Provided convergence rates and complexities.
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48 results for “stochastic convergence”
Unified Convergence Analysis of Stochastic Momentum Methods for Convex and Non-convex Optimizationmath.OC
Recently, {\it stochastic momentum} methods have been widely adopted in training deep neural networks. However, their convergence analysis is still underexplored at the moment, in particular for non-convex optimization. This paper fills the gap between practice and theory by developing a basic convergence analysis of t…
Proof given for SGD convergence in a concise manner.
problem Convergence of Stochastic Gradient Descent (SGD)
method Self-contained proof
result SGD convergence proven
Improves understanding of stochastic NGVI convergence rates.
problem Lack of knowledge about non-asymptotic convergence rates in stochastic NGVI.
method Proved non-asymptotic convergence rates for conjugate likelihoods and showed implicit optimization for non-conjugate likelihoods.
result First non-asymptotic convergence rate for stochastic NGVI in conjugate likelihoods.
Stochastic gradient methods can converge in expectation under heavy-tailed noise.
problem Convergence of stochastic gradient methods under heavy-tailed noise.
method Comprehensive study of stochastic optimization under heavy-tailed noise for , , , in convex and nonconvex optimization.
result Established in-expectation convergence results for various stochastic gradient methods.
The paper analyzes convergence rates for SGD and SHB methods.
problem Analyzing convergence rates for stochastic gradient descent and heavy ball methods.
method Stochastic gradient descent and stochastic heavy ball method for general stochastic approximation problems.
result The last iterate of SHB converges almost surely to a minimizer and has faster convergence rates than SGD.
In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal stationary points. However, existing results on stochastic non-convex optimizatio…
Stochastic proximal point algorithm with momentum converges faster and is more stable than standard methods.
problem Improving convergence and stability of stochastic optimization methods.
method Developed and analyzed the convergence and stability of the stochastic proximal point algorithm with momentum (SPPAM).
result SPPAM converges faster and is more stable than standard stochastic proximal point algorithm (SPPA) and stochastic gradient descent with momentum (SGDM).
New method improves convergence for smooth games.
problem Improving convergence for smooth games.
method Stochastic Hamiltonian Gradient Methods (SHGD).
result SHGD converges linearly to the neighbourhood of a stationary point.
This work establishes uniform convergence of subdifferentials in stochastic optimization.
problem Understanding how empirical stationary points approximate population ones in nonsmooth, nonconvex stochastic optimization.
method Reduction principle for weakly convex stochastic objectives, focusing on subgradient convergence.
result Sharp uniform convergence rates for subdifferential mappings in stochastic convex-composite optimization.
Paper establishes convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
problem Analyzing convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
method Novel discretization of the mean ODE of stochastic approximation algorithms using intervals with diminishing length.
result First almost sure convergence rate and maximal concentration bound with exponential tails for contractive stochastic approximation algorithms with Markovian noise.
Conservative SPDEs emerge from fluctuating SGD dynamics in neural networks.
problem Understanding the convergence of stochastic gradient descent to SPDEs.
method Mean-field analysis and central limit theorem for SPDEs.
result Optimal convergence rates for SPDEs derived from SGD.
Paper studies stochastic optimization methods with momentum, proving convergence and avoiding traps.
problem Optimizing non-convex functions with momentum.
method Unified analysis of stochastic gradient descent variants, including S-NAG and Adam.
result Convergence to critical points and avoidance of undesired critical points like local maxima or saddle points.
Stochastic gradient methods converge for training wide PINNs.
problem Convergence of stochastic gradient descent in training over-parameterized PINNs.
method Established linear convergence of stochastic gradient descent/flow in training over-parameterized two-layer PINNs.
result Linear convergence with high probability for general activation functions.
The paper proves a convergence theorem for Wiener measures on holonomy groups.
problem Understanding convergence of Wiener measures on holonomy groups.
method Using stochastic parallel transports along convergent metric connections.
result Proves a convergence theorem for push-forward Wiener measures on holonomy groups.
New step-size methods improve SHB convergence for stochastic optimization.
problem Tuning step-size and momentum parameters in SHB is challenging.
method Proposed MomSPS, MomDecSPS, and MomAdaSPS for SHB.
result Convergence guarantees for SHB to solution neighborhoods and exact minimizers.
A new hybrid Newton algorithm improves convergence in logistic regression.
problem Solving large-scale binary classification problems efficiently.
method Proposes a hybrid stochastic Newton algorithm with two weighted components in the Hessian matrix estimation.
result Proves almost sure convergence to the true parameter of logistic regression.
Study proves convergence of interest rate model approximations.
problem Investigating convergence of stochastic interest rate models.
method Developed analytical tools for true and truncated EM solutions, proving convergence in probability.
result True solution converges in probability to truncated EM solution as step size approaches zero.
New convergence guarantees for learning with unknown nuisance parameters.
problem Learning problems with unknown nuisance parameters.
method Stochastic gradient optimization with Neyman orthogonality and approximately orthogonalized updates.
result Stochastic gradient algorithms can converge under conditions of nuisance parameters.
New averaging technique speeds up Newton method convergence.
problem Superlinear convergence of stochastic Newton methods with noisy Hessians.
method Hessian averaging to reduce noise and maintain superlinear convergence.
result Hessian averaging achieves superlinear convergence with a non-asymptotic rate.
New convergence guarantees for SGDA and SCO under expected co-coercivity.
problem Solving smooth games with stochastic gradient descent-ascent and consensus optimization.
method Introducing expected co-coercivity and proving convergence guarantees for SGDA and SCO.
result Linear convergence of SGDA and SCO to a neighborhood of the solution with constant step-size, and convergence to the exact solution with stepsize-switching rules.
Paper proves deep learning method for stochastic control converges and outperforms existing algorithms.
problem Formulating and solving stochastic control problems using FBSDE and SMP.
method Deep learning algorithm based on SMP, with convergence proof and error bounds.
result Deep SMP-BSDE algorithm converges and outperforms existing methods in high-dimensional stochastic control problems.
This paper improves convergence guarantees for gradient clipping in deep learning.
problem Improving convergence guarantees for gradient clipping in deep learning models.
method Analyzes and provides precise convergence guarantees for arbitrary clipping thresholds.
result Shows tight convergence guarantees for clipped stochastic gradient descent.
Improved convergence for non-log-concave sampling.
problem Sampling from non-log-concave distributions.
method Novel conductance analysis of SGLD with auxiliary Markov Chain.
result SGLD achieves ε-sampling error with fewer evaluations.
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.
Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms are usually slow to converge and achieve sub-linear convergence rates, due to t…
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.
New method uses momentum to converge in DC optimization with small batches.
problem Lack of convergence properties for stochastic difference-of-convex optimization with small batch sizes.
method Introduces momentum to enable convergence under standard assumptions for any batch size.
result Proves convergence of the algorithm under smoothness and bounded variance assumptions.
Convergence of First-Order Methods for Constrained Nonconvex Optimization with Dependent Datamath.OC
Improved convergence for nonconvex optimization with dependent data.
problem Constrained smooth nonconvex optimization with dependent data.
method Stochastic projected gradient methods under a general dependent data sampling scheme.
result Achieved worst-case rate of convergence and complexity .
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…
Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving stochastic gradient methods named predictive local smoothness (PLS). First, we …
We study the convergence rate of stochastic optimization of exact (NP-hard) objectives, for which only biased estimates of the gradient are available. We motivate this problem in the context of learning the structure and parameters of Ising models. We first provide a convergence-rate analysis of deterministic errors fo…
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.
Study shows convergence of stochastic gradient method for unregularized Wasserstein optimization.
problem Wasserstein distributionally robust optimization under potential distribution shifts.
method Regularized approximation with stochastic gradient methods, convergence analysis.
result Stochastic gradient method converges to subgradients of unregularized objective as regularization vanishes.
MSGD outperforms SGD in overparametrized settings with faster convergence rates.
problem Optimization of non-convex functions with momentum.
method Momentum Stochastic Gradient Descent (MSGD) with rigorous analysis.
result MSGD converges exponentially faster than SGD in overparametrized settings.
In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan an…
New convergence results for NGVI with various step sizes and sample sizes.
problem Understanding convergence of stochastic NGVI for various schedules.
method Projected stochastic NGVI for exponential family variational distributions.
result Geometric convergence and $\mathcal{O}\left(\frac{1}{T^ρ}
ight)$ rates for different schedules.
Convergence of continuous-time stochastic gradient descent with applications to deep neural networkscs.LG
Continuous-time SGD converges under certain conditions, useful for deep learning.
problem Minimizing population expected loss in learning problems.
method Continuous-time approximation of stochastic gradient descent.
result Establishes sufficient conditions for convergence, applicable to overparametrized neural networks.
Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive gradient) methods are the two main techniques to improve the slow convergence of \text…
SGD fails to converge for deep ReLU networks with limited random initializations.
problem SGD convergence in deep neural networks with limited random initializations.
method Analysis of four discretization parameters: network architecture, training data, gradient steps, and random initializations.
result SGD fails to converge for ReLU networks with depth much larger than width.
The multinomial logistic regression (MLR) model is widely used in statistics and machine learning. Stochastic gradient descent (SGD) is the most common approach for determining the parameters of a MLR model in big data scenarios. However, SGD has slow sub-linear rates of convergence. A way to improve these rates of con…
Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate convergence of simultaneous gradient descent (simGD) and its variants under the assump…
In this paper, we quantitative convergence in for a family of Langevin-like stochastic processes that includes stochastic gradient descent and related gradient-based algorithms. Under certain regularity assumptions, we show that the iterates of these stochastic processes converge to an invariant distribution at a…
Unified framework for analyzing convergence of RSAs using Wasserstein divergence.
problem Analyzing convergence of constant stepsize recursive stochastic algorithms (RSAs).
method Lifting RSA into a higher-dimensional space as a Markov chain and studying the distribution's contraction property with respect to Wasserstein divergence.
result RSAs' iterates' distribution converges to an invariant distribution under certain contraction properties.
Riemannian stochastic gradient descent converges faster with increasing batch size.
problem Improving convergence rate of Riemannian stochastic gradient descent.
method Theoretical analysis and numerical investigation of increasing batch size effects.
result Riemannian stochastic gradient descent converges faster with increasing batch size.
New method improves convergence and reduces variance in noisy optimization problems.
problem Computing exact minimizers with noisy gradient information.
method Stochastic mirror descent with interacting particles.
result Interaction helps improve convergence and reduce variance.
The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and gradually nonconvex composite functions have been adopted to obtain more desirable prop…
Convergence of the Stochastic Heavy Ball Method With Approximate Gradients and/or Block Updatingmath.OC
Paper proves SHB convergence with biased gradients and approximate step sizes.
problem Establishing convergence of SHB with biased gradients and approximate step sizes.
method Generalizes SHB convergence conditions for biased gradients, approximate step sizes, and block updating.
result Proves convergence of SHB with new conditions for biased gradients and approximate step sizes.