The paper analyzes and validates two step size schedules for SGD: exponential and cosine, proving their adaptivity and performance.
problem The variability of SGD performance due to step size choice.
method Analysis and empirical evaluation of exponential and cosine step sizes.
result Exponential and cosine step sizes are adaptive to noise and achieve optimal performance without tuning hyperparameters.
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 variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces `…
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.
Reinforcement learning (RL) has had many successes in both "deep" and "shallow" settings. In both cases, significant hyperparameter tuning is often required to achieve good performance. Furthermore, when nonlinear function approximation is used, non-stationarity in the state representation can lead to learning instabil…
One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization algorithms, the common practice in SGD is either to use a diminishing step size, or to tune a…
New method predicts and optimizes matrix recovery from noisy measurements.
problem Recovering rank-1 matrices from Gaussian measurements with noise.
method Stochastic prox-linear iterative algorithm with trajectory predictions.
result The method converges linearly with accurate predictions of error.
We analyze SGAs for statistical inference via asymptotics, improving tuning methods.
problem Improper tuning of SGAs for optimization and sampling.
method Characterize large-sample asymptotics of SGAs via step-size and sample-size scaling limits.
result Iterate averaging with large step size is robust and asymptotically has covariance proportional to MLE's.
Guarantees for tuning step size using meta-gradient descent.
problem Choosing optimal parameters for optimization algorithms.
method Learning-to-learn approach with meta-gradient descent.
result Meta-gradient can explode/vanish, requiring careful meta-objective design.
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 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 …
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.
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.
Proposes a neural network for learning step-size policies for L-BFGS optimization.
problem Optimizing step sizes for L-BFGS in large-scale problems.
method Neural network architecture using local iterate information, trained via stochastic optimization.
result Outperforms existing step size selection methods in training classifiers.
New algorithms for sampling and optimization without tuning.
problem Efficient sampling and optimization over probability measures.
method Optimization on the space of probability measures, using gradient flows.
result Strong theoretical guarantees and similar performance to optimally tuned algorithms.
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.
New method tunes SMC samplers efficiently without high costs.
problem Tuning SMC samplers with unadjusted kernels is challenging.
method Greedy Incremental Divergence Minimization (GIDM) for step size tuning.
result GIDM reduces KL divergence and tunes SMC samplers efficiently.
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.
Proposes an automatic cyclical scheduling for gradient-based discrete sampling.
problem Gradient-based sampling in high-dimensional models can get stuck in local modes.
method Cyclical step size and balancing schedules with automatic hyperparameter tuning.
result Proves non-asymptotic convergence and inference guarantees for general discrete distributions.
This paper explores the problem of learning transforms for image compression via autoencoders. Usually, the rate-distortion performances of image compression are tuned by varying the quantization step size. In the case of autoen-coders, this in principle would require learning one transform per rate-distortion point at…
Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size polynomially and lead to optimal sublinear rates on (strongly) convex problems. An alternative schedule, popular in nonconvex optimization, is called \emph{geometric step decay…
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.
New adaptive scheduler improves SAM for better model training.
problem Training machine learning models requires selecting a learning rate, which is often difficult and time-consuming.
method Derive Polyak schedulers tailored to SAM-style updates, proving linear convergence for strongly convex objectives and an O(1/T) rate for convex objectives.
result Polyak schedulers achieve comparable or better performance than tuned SAM baselines, reducing the need for learning-rate tuning.
New algorithm tunes SGMCMC hyperparameters for scalable Bayesian inference.
problem Tuning hyperparameters for SGMCMC is challenging due to lack of principled methods.
method Proposes a bandit-based algorithm using Stein discrepancies to tune hyperparameters.
result The method effectively tunes SGMCMC hyperparameters for various applications.
A new method approximates expected empirical loss for stochastic deep learning tasks.
problem Determining optimal step sizes for stochastic gradient descent in deep learning.
method Applying one-dimensional function fitting to noisy losses of vertical cross sections to approximate expected empirical loss.
result The method leads to a robust and straightforward optimization method that performs well across datasets and architectures.
SGD converges almost surely in non-convex problems, avoiding saddle points and accelerating convergence.
problem Understanding convergence of SGD in non-convex optimization problems.
method Analysis of SGD trajectories, focusing on boundedness, convergence to strict saddle points, and rate of convergence.
result SGD converges almost surely to a minimizer in non-convex problems, avoiding strict saddle points.
ICE-Pruning accelerates deep neural network pruning by 9.61x.
problem Efficiently pruning deep neural networks while maintaining accuracy.
method Iterative pruning with automatic fine-tuning steps, freezing strategy, and custom learning rate scheduler.
result Significantly reduces pruning time by up to 9.61x.
We consider d-dimensional linear stochastic approximation algorithms (LSAs) with a constant step-size and the so called Polyak-Ruppert (PR) averaging of iterates. LSAs are widely applied in machine learning and reinforcement learning (RL), where the aim is to compute an appropriate θ∗∈Rd (that is a…
New TD method stabilizes average-reward learning.
problem Stability issues in average-reward TD learning.
method Implicit fixed point update for average-reward TD(λ). result Improved numerical stability and broader step-size range.
New step-size methods improve SHB convergence for stochastic optimization.
problem Tuning step-size and momentum parameters in SHB is challenging.
method Proposed MomSPSmax, MomDecSPS, and MomAdaSPS for SHB. result Convergence guarantees for SHB to solution neighborhoods and exact minimizers.
StochAstic Recursive grAdient algoritHm (SARAH), originally proposed for convex optimization and also proven to be effective for general nonconvex optimization, has received great attention due to its simple recursive framework for updating stochastic gradient estimates. The performance of SARAH significantly depends o…
Learning Rate (LR) is an important hyper-parameter to tune for effective training of deep neural networks (DNNs). Even for the baseline of a constant learning rate, it is non-trivial to choose a good constant value for training a DNN. Dynamic learning rates involve multi-step tuning of LR values at various stages of th…
In reinforcement learning, the TD(λ) algorithm is a fundamental policy evaluation method with an efficient online implementation that is suitable for large-scale problems. One practical drawback of TD(λ) is its sensitivity to the choice of the step-size. It is an empirically well-known fact that a large step-size l…
High sensitivity of neural architecture search (NAS) methods against their input such as step-size (i.e., learning rate) and search space prevents practitioners from applying them out-of-the-box to their own problems, albeit its purpose is to automate a part of tuning process. Aiming at a fast, robust, and widely-appli…
Gradient descent outperforms ridge regression under certain covariance matrix decay conditions.
problem Comparing the performance of gradient descent and ridge regression in linear models.
method Investigated gradient descent and ridge regression for linear regression with random isotropic ground truth.
result Gradient descent outperforms ridge regression under specific covariance matrix decay conditions.
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.
Meta-strategy learns tuning parameters for online learning methods.
problem Difficulty in setting tuning parameters for online learning methods.
method Meta-learning approach to learn parameters from past tasks.
result Meta-strategy improves on learning each task in isolation.
Delayed rejection HMC improves sampling efficiency for multiscale distributions.
problem Hamiltonian Monte Carlo struggles with wide-ranging distributions, especially in high-curvature areas.
method Introduces a delayed rejection variant of HMC, using geometrically smaller step sizes for retries.
result Up to five-fold performance gains in effective sample size per gradient evaluation.
Annealed Langevin dynamics improves sampling from composite scores in SBI.
problem Irreducible bias in sampling from composite scores of SBI methods.
method Derive Wasserstein bounds and decision rules for hyperparameters.
result Explicit decision rules for hyperparameters guarantee prescribed sampling accuracy.
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…
Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the whole data set. The recently proposed stochastic gradient Langevin dynamics (SG…
We present a novel Metropolis-Hastings method for large datasets that uses small expected-size minibatches of data. Previous work on reducing the cost of Metropolis-Hastings tests yield variable data consumed per sample, with only constant factor reductions versus using the full dataset for each sample. Here we present…
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.
LoRA enhances model adaptability without increasing parameters.
problem Theoretical understanding of LoRA's adaptability.
method Theoretical analysis of LoRA's expressive power.
result LoRA can adapt any model to a smaller target model with a specific rank.
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…
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).
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.