In this paper, we introduce a method for adapting the step-sizes of temporal difference (TD) learning. The performance of TD methods often depends on well chosen step-sizes, yet few algorithms have been developed for setting the step-size automatically for TD learning. An important limitation of current methods is that…
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48 results for “Adaptive Step Size”
Adaptive step-size improves optimization in complex geometries.
problem Optimizing functions with non-Euclidean geometries.
method Adaptive step-size strategy for optimization algorithms.
result Guaranteed convergence for Adaptive Conditional Gradient Descent.
New adaptive step-size method for convex optimization without tuning.
problem Optimizing convex functions efficiently with stochastic gradients.
method Adapted Adaptive Gradient Descent Without Descent to stochastic setting.
result Stochastic gradient descent converges under various assumptions.
The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies …
AutoStep MCMC adapts step size locally for better sampling efficiency.
problem Challenging step size selection for complex, multiscale targets.
method AutoStep MCMC uses a locally adaptive step size for involutive proposals.
result AutoStep MCMC is π-invariant, irreducible, and aperiodic.
Adaptive step-size method improves compressed SGD performance in machine learning.
problem Communication bottleneck in distributed and decentralized optimization.
method Developed an adaptive step-size method for compressed SGD.
result Order-optimal convergence rates for various objective functions.
New algorithm improves stability of optimization algorithms by adapting step-size.
problem Optimization algorithms' effectiveness is sensitive to step-size hyperparameters.
method Adapts NGN step-size method with momentum to enhance stability.
result Achieves convergence rate of O(1/√K) without restrictive assumptions.
Improved variational inequality algorithms using adaptive step sizes.
problem Solving monotone variational inequalities and convex-concave min-max problems efficiently.
method Adaptive step sizes that eliminate hyperparameters and global Lipschitz continuity requirements.
result Eliminated the need for the golden ratio in the algorithm and improved complexity bounds.
New insights into SGD and SGD-M in high dimensions.
problem Understanding and comparing SGD and SGD-M in high-dimensional settings.
method Developed high-dimensional scaling limits for SGD-M and online SGD, examining their dynamics and performance.
result SGD-M amplifies high-dimensional effects, potentially degrading performance compared to online SGD.
Speed learning on the flymath.OC
The practical performance of online stochastic gradient descent algorithms is highly dependent on the chosen step size, which must be tediously hand-tuned in many applications. The same is true for more advanced variants of stochastic gradients, such as SAGA, SVRG, or AdaGrad. Here we propose to adapt the step size by …
The main goal of this work is equipping convex and nonconvex problems with Barzilai-Borwein (BB) step size. With the adaptivity of BB step sizes granted, they can fail when the objective function is not strongly convex. To overcome this challenge, the key idea here is to bridge (non)convex problems and strongly convex …
The correspondence between residual networks and dynamical systems motivates researchers to unravel the physics of ResNets with well-developed tools in numeral methods of ODE systems. The Runge-Kutta-Fehlberg method is an adaptive time stepping that renders a good trade-off between the stability and efficiency. Can we …
Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for tuning the step sizes have been proposed, ranging from coordinate-wise approach…
ATLAS adapts HMC step size and trajectory length for complex geometries.
problem Sampling complex geometries with constant step size HMC/NUTS.
method Adapts step size and trajectory length using local Hessian and no U-turn condition.
result ATLAS accurately samples complex geometries, outperforming NUTS.
Sparse Polyak improves high-dimensional statistical estimation.
problem High-dimensional statistical estimation problems with growing problem dimension.
method Sparse Polyak modifies Polyak's adaptive step size to estimate restricted Lipschitz smoothness.
result Sparse Polyak achieves optimal statistical precision with fewer iterations.
Adaptive gradient methods converge faster with over-parameterization and line-search.
problem Training over-parameterized models using adaptive gradient methods.
method Simplified setting of smooth, convex losses with over-parameterized models, proving convergence rates and demonstrating improvements with line-search techniques.
result Adaptive gradient methods, particularly AMSGrad, converge faster with line-search techniques.
Paper introduces a privacy-preserving line search method for optimization.
problem Optimization performance depends on step size tuning, which is difficult and privacy-sensitive.
method Introduces a stochastic adaptive line search algorithm that satisfies differential privacy.
result The algorithm efficiently uses privacy budget and outperforms existing private optimizers.
Optimistic method adapted for faster convex-concave min-max problems.
problem Solving convex-concave min-max optimization problems efficiently.
method Adaptive, line search-free second-order methods combining optimistic updates and second-order information.
result Achieves optimal convergence rate without line search or backtracking.
Convergence Analysis of a Momentum Algorithm with Adaptive Step Size for Non Convex Optimizationmath.OC
Although ADAM is a very popular algorithm for optimizing the weights of neural networks, it has been recently shown that it can diverge even in simple convex optimization examples. Several variants of ADAM have been proposed to circumvent this convergence issue. In this work, we study the ADAM algorithm for smooth nonc…
Calibrated probabilistic solvers improve accuracy of ODE estimates.
problem Uncertainty in probabilistic ODE solutions is not well-calibrated for adaptive step sizes.
method Introduce and assess several calibration methods for probabilistic ODE solvers.
result Calibration methods interact efficiently with adaptive step-size selection, improving posteriors.
Implicit Q-learning and SARSA adjust step-sizes automatically, improving stability and performance.
problem Numerical instability and slow progress in Q-learning and SARSA due to step-size calibration.
method Reformulate iterative updates as fixed-point equations, scaling step-sizes inversely with feature norms.
result Implicit methods maintain stability over broader step-size ranges and achieve comparable convergence rates.
The Power of Adaptivity in SGD: Self-Tuning Step Sizes with Unbounded Gradients and Affine Variancestat.ML
AdaGrad-Norm achieves optimal convergence rates for non-convex objectives without tuning.
problem Optimal convergence rates for non-convex, smooth objectives with adaptive step sizes.
method Adaptive SGD (AdaGrad-Norm) with self-tuning step sizes, analyzing under unbounded gradients and affine variance scaling.
result AdaGrad-Norm achieves order optimal convergence rate of $\mathcal{O}\left(\frac{\mathrm{poly}\log(T)}{\sqrt{T}}
ight)$ under optimal assumptions.
MaxVA improves Adam's step sizes by maximizing gradient variance.
problem Unstable or extreme adaptive learning rates in Adam.
method Maximizing the variance of gradient coordinates in Adam's running mean of squared gradients.
result Faster adaptation and more desirable convergence behaviors than Adam.
ProxSARAH: An Efficient Algorithmic Framework for Stochastic Composite Nonconvex Optimizationmath.OC
We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in (Nguyen et al, 2017) and consist of two steps: a proximal gradient and an averaging s…
A recent algorithmic family for distributed optimization, DIGing's, have been shown to have geometric convergence over time-varying undirected/directed graphs. Nevertheless, an identical step-size for all agents is needed. In this paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation of the DI…
The article examines in some detail the convergence rate and mean-square-error performance of momentum stochastic gradient methods in the constant step-size and slow adaptation regime. The results establish that momentum methods are equivalent to the standard stochastic gradient method with a re-scaled (larger) step-si…
We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a conv…
Adaptive Importance Sampling for Finite-Sum Optimization and Sampling with Decreasing Step-Sizescs.LG
Avare improves optimization and sampling with adaptive importance sampling.
problem Improving convergence rate of stochastic gradient-based algorithms.
method Adaptive importance sampling with decreasing step-sizes.
result Achieves dynamic regret bounds of and .
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to adapt their strategies together. This change in the environment results in dynamical…
This paper examines the convergence of adaptive sampling methods for Bayesian neural networks.
problem Uncertainty quantification in deep neural networks, especially for medical applications.
method Locally adaptive and scalable diffusion-based sampling methods.
result These methods can have a substantial bias in the distribution they sample, even in the limit of vanishing step sizes.
Predictions and predictive knowledge have seen recent success in improving not only robot control but also other applications ranging from industrial process control to rehabilitation. A property that makes these predictive approaches well suited for robotics is that they can be learned online and incrementally through…
This work provides formal guarantees for heuristic optimization methods in machine learning.
problem Lack of theoretical understanding of heuristic optimization methods in machine learning.
method Analysis and formal guarantees for AdaGrad, SGD with exponential and cosine step sizes, and momentum methods.
result First formal guarantees for AdaGrad and SGD variants, including convergence and adaptivity to noise.
Neural ODEs' performance varies with numerical method, requiring adaptive step size control.
problem Neural ODEs' performance depends on the numerical method used during training.
method Proposes an adaptive step size control algorithm to ensure a valid ODE without increasing computational cost.
result Valid Neural ODEs require careful numerical method selection and step size adaptation.
Sparse coding is typically solved by iterative optimization techniques, such as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and learning weights of ISTA using neural networks is a practical way to accelerate estimation. In this paper, we study the selection of adapted step sizes for ISTA. We show t…
GradaGrad adapts learning rate non-monotonically, overcoming AdaGrad's step size decrease.
problem Fixed learning rate in AdaGrad leads to step size decrease over time.
method Introduces GradaGrad, which grows or shrinks the learning rate based on a different accumulation in the denominator.
result GradaGrad achieves similar convergence rates as AdaGrad and demonstrates non-monotone adaptation.
A new line search rule improves support recovery in high-dimensional data.
problem Support recovery in high-dimensional data analysis with penalty.
method Data-driven line search rule for adaptive step size determination.
result Proves error bound without restrictions on cost functional.
Adam is shown not being able to converge to the optimal solution in certain cases. Researchers recently propose several algorithms to avoid the issue of non-convergence of Adam, but their efficiency turns out to be unsatisfactory in practice. In this paper, we provide new insight into the non-convergence issue of Adam …
ProxSPS improves on SPS for regularization tasks, offering better stability and performance.
problem Handling regularization terms in adaptive step size schemes for stochastic gradient descent.
method Developed a proximal variant of the stochastic Polyak step size (SPS) scheme.
result ProxSPS is easier to tune and more stable with regularization, and performs well in image classification tasks.
Communication-Efficient Adaptive Batch Size Strategies for Distributed Local Gradient Methodsstat.ML
Adaptive batch sizes improve local gradient methods in distributed training.
problem Communication bottlenecks in distributed deep learning.
method Adaptive batch size strategies for local gradient methods.
result Adaptive batch sizes reduce minibatch gradient variance and improve training efficiency.
WALNUTS improves sampling efficiency and robustness for multi-scale distributions.
problem Adapting leapfrog step size for multi-scale posterior distributions.
method Adapts leapfrog step size at fixed intervals of simulated time, selecting the largest step size to keep energy error below a threshold.
result Substantial improvements in sampling efficiency and robustness compared to standard NUTS.
New solver avoids memory issues for long differential equations.
problem Memory constraints in adaptive probabilistic ODE solvers.
method Fixed memory demands adaptive probabilistic solver using robust state estimation.
result Eliminates memory issues for long time series simulations.
There is a long history of using meta learning as representation learning, specifically for determining the relevance of inputs. In this paper, we examine an instance of meta-learning in which feature relevance is learned by adapting step size parameters of stochastic gradient descent---building on a variety of prior w…
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.
Variance-reduced algorithms, although achieve great theoretical performance, can run slowly in practice due to the periodic gradient estimation with a large batch of data. Batch-size adaptation thus arises as a promising approach to accelerate such algorithms. However, existing schemes either apply prescribed batch-siz…
A new method for faster optimization of noisy functions.
problem Optimizing noisy functions efficiently.
method A universal and adaptive second-order method for convex functions.
result Achieves convergence for stochastic oracles and for deterministic oracles.
Improved variance reduction for Riemannian non-convex optimization with adaptive batch size.
problem Optimizing non-convex functions on Riemannian manifolds.
method Batch size adaptation in R-SVRG, R-SRG, and R-SPIDER.
result Achieves lower total complexities for various non-convex functions.
A common way to train neural networks is the Backpropagation. This algorithm includes a gradient descent method, which needs an adaptive step size. In the area of neural networks, the ADAM-Optimizer is one of the most popular adaptive step size methods. It was invented in \cite{Kingma.2015} by Kingma and Ba. The …
Adapts SGD to noise and problem specifics for faster convergence.
problem Minimizing smooth, strongly-convex functions with varying noise and problem constants.
method Adaptive SGD with exponentially decreasing step-sizes, Nesterov acceleration, and stochastic line-search.
result Achieves near-optimal convergence rates without knowing noise or problem specifics.