arXiv research

Paper examines constant stepsize in LSA for Markovian data inference.

Cyclic and randomized stepsizes can lead to heavier tails in SGD, improving generalization.

Study Whittle index learning algorithms for restless bandits with constant stepsizes.

Study Q-learning with constant stepsize, proving convergence and bias, and applying extrapolation.

Study on nonsmooth contractive SA with constant stepsize and Q-learning.

Large stepsize GD for logistic regression converges faster than expected.

Paper proposes a coupling-based diagnostic for SGD stepsize optimization.

Study on bias and extrapolation in LSA with Markovian data, showing bias reduction with Richardson-Romberg extrapolation.

Unified framework for analyzing convergence of RSAs using Wasserstein divergence.

SGD with constant stepsize converges to a non-Gaussian limit near flat minima.

Large stepsizes can accelerate gradient descent for logistic regression.

New PG methods tackle nonconvex optimization with auto-conditioned stepsizes.

Gradient-based temporal difference (GTD) algorithms are widely used in off-policy learning scenarios. Among them, the two time-scale TD with gradient correction (TDC) algorithm has been shown to have superior performance. In contrast to previous studies that characterized the non-asymptotic convergence rate of TDC only…

Last SGD iterate bounds for overparameterized linear regression.

GD at EoS edge minimizes logistic loss without monotonic convergence.

GD with large, adaptive stepsizes achieves optimal risk in logistic regression.

We propose a stepsize adaptation scheme for stochastic gradient descent. It operates directly with the loss function and rescales the gradient in order to make fixed predicted progress on the loss. We demonstrate its capabilities by conclusively improving the performance of Adam and Momentum optimizers. The enhanced op…

The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence rates are also limited to linear convergence. Due to the mathematical techniques, th…

Paper analyzes convergence of Adam-type RL algorithms under Markovian sampling.

Stochastic methods with coordinate-wise adaptive stepsize (such as RMSprop and Adam) have been widely used in training deep neural networks. Despite their fast convergence, they can generalize worse than stochastic gradient descent. In this paper, by revisiting the design of Adagrad, we propose to split the network par…

MARINA-P improves non-smooth federated optimization with adaptive stepsizes.

New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.

Classical stochastic gradient methods for optimization rely on noisy gradient approximations that become progressively less accurate as iterates approach a solution. The large noise and small signal in the resulting gradients makes it difficult to use them for adaptive stepsize selection and automatic stopping. We prop…

Study on GD and SGD over diagonal networks, focusing on stepsizes and regularisation.

We revisit the classical Douglas-Rachford (DR) method for finding a zero of the sum of two maximal monotone operators. Since the practical performance of the DR method crucially depends on the stepsizes, we aim at developing an adaptive stepsize rule. To that end, we take a closer look at a linear case of the problem a…

This paper analyzes the sample complexity of two timescale reinforcement learning algorithms.

Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a large body of research on adaptive stepsizes. However, there is currently a gap in o…

The paper analyzes variance reduction in stochastic gradient Langevin dynamics.

We propose a general yet simple theorem describing the convergence of SGD under the arbitrary sampling paradigm. Our theorem describes the convergence of an infinite array of variants of SGD, each of which is associated with a specific probability law governing the data selection rule used to form mini-batches. This is…

Variable metric proximal gradient (VM-PG) is a widely used class of convex optimization method. Lately, there has been a lot of research on the theoretical guarantees of VM-PG with different metric selections. However, most such metric selections are dependent on (an expensive) Hessian, or limited to scalar stepsizes l…

New algorithms eliminate stepsize tuning for bilevel optimization problems.

New adaptive stepsize method for stochastic approximation converges to target point.

Adaptive-stepsize MCMC sampling inspired by Adam optimizer.

Adaptive gradient methods such as AdaGrad and its variants update the stepsize in stochastic gradient descent on the fly according to the gradients received along the way; such methods have gained widespread use in large-scale optimization for their ability to converge robustly, without the need to fine-tune the stepsi…

A new decentralized Bayesian learning method using Metropolis-adjusted Hamiltonian Monte Carlo.

Adaptive stepsizing improves sampling in Bayesian neural networks.

This work analyzes $Q$-learning with adaptive stepsizes for finite-time convergence.

Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several years, a plethora of adaptive gradient-based algorithms have emerged to ameliorate t…

Large GD stepsizes improve margins and speed up training for non-homogeneous networks.

The paper improves convergence for linear systems using entropic mirror descent with Polyak stepsizes.

OSGM uses online learning to adapt stepsize for faster convergence.

This work accelerates gradient descent with anytime convergence guarantees.

Approximate dynamic programming (ADP) has proven itself in a wide range of applications spanning large-scale transportation problems, health care, revenue management, and energy systems. The design of effective ADP algorithms has many dimensions, but one crucial factor is the stepsize rule used to update a value functi…

Gradient descent converges with arbitrary stepsize for separable data under Fenchel-Young losses.

Proposes a new adaptive gradient method based on gradient differences.

SGD in linear regression overfits but performs well due to bias-variance trade-off.

SARAH and SPIDER are two recently developed stochastic variance-reduced algorithms, and SPIDER has been shown to achieve a near-optimal first-order oracle complexity in smooth nonconvex optimization. However, SPIDER uses an accuracy-dependent stepsize that slows down the convergence in practice, and cannot handle objec…

The paper provides bounds for LSA with fixed stepsizes under random estimates.