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.
Improved SGD methods converge faster for nonconvex optimization.
problem Nonconvex optimization challenges in machine learning.
method Adaptive SGD with line-search and Polyak stepsizes.
result Unified convergence rates for various nonconvex functions.
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.
A new line search rule improves support recovery in high-dimensional data.
problem Support recovery in high-dimensional data analysis with ℓ0 penalty. method Data-driven line search rule for adaptive step size determination.
result Proves ℓ2 error bound without restrictions on cost functional. Exact risk and learning rate curves derived for adaptive SGD on high-dimensional problems.
problem Analyzing risk and learning rate dynamics in high-dimensional optimization problems.
method Developed a framework to give exact expressions for risk and learning rate curves using ODEs.
result Exact expressions for risk and learning rate curves, with detailed analysis of two adaptive learning rates.
Step sizes in neural network training are largely determined using predetermined rules such as fixed learning rates and learning rate schedules. These require user input or expensive global optimization strategies to determine their functional form and associated hyperparameters. Line searches are capable of adaptively…
New methods solve saddle point problems without line search.
problem Solving saddle point problems efficiently and adaptively.
method Auto-conditioned primal-dual hybrid gradient (AC-PDHG) and auto-conditioned ADMM (AC-ADMM) methods.
result Methods achieve optimal complexity and convergence guarantees.
SALSA automatically adjusts learning rates in stochastic gradient methods.
problem Automatic adjustment of learning rates in stochastic gradient methods.
method SALSA uses a line-search procedure to gradually increase the learning rate, then a statistical test to decrease it.
result SALSA matches the performance of best hand-tuned learning rate schedules in deep learning tasks.
In this paper, we consider a class of possibly nonconvex, nonsmooth and non-Lipschitz optimization problems arising in many contemporary applications such as machine learning, variable selection and image processing. To solve this class of problems, we propose a proximal gradient method with extrapolation and line sear…
GOLS-I automatically determines learning rates for various neural network training algorithms.
problem Adapting learning rates in stochastic training algorithms for neural networks.
method Gradient-Only Line Search (GOLS-I) for automatically setting learning rates.
result GOLS-I learning rate schedules are competitive with manually tuned rates across multiple algorithms, architectures, datasets, and loss functions.
PGS uses neural networks to improve policies online without search trees.
problem Limited scalability of Monte Carlo Tree Search (MCTS) for high branching factor games.
method Adapts a neural network simulation policy via policy gradient updates, avoiding search trees.
result PGS achieves comparable performance to MCTS and defeats strong Hex agents.
Armijo line-search speeds up gradient descent for various functions.
problem Improving convergence rate of gradient descent.
method Applying Armijo line-search to adjust step-size in gradient descent.
result GD with Armijo line-search converges faster than GD with a fixed step-size.
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.
New method finds optimal learning rates for neural nets.
problem Finding optimal learning rates in stochastic neural networks.
method Gradient-only line searches using Non-negative Associative Gradient Projection Points (NN-GPPs).
result Learning rates can be reliably resolved as step sizes along search directions.
New algorithm solves stochastic optimization problems with unknown gradients.
problem Solving nonlinear optimization problems with stochastic objectives and deterministic constraints.
method Adaptive SQP with differentiable exact augmented Lagrangian and stochastic line search.
result Global convergence established for both non-adaptive and adaptive SQP methods.
Enhanced DFO using adaptive batch-based FD estimates.
problem Derivative-free optimization with imprecise gradient estimates.
method Adaptive batch-based finite difference estimation and dynamic sampling strategy.
result Algorithm achieves convergence rate similar to KW and SPSA methods.
Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.
problem Optimizing smooth unconstrained problems with geometrically adapted directions.
method Yau's Affine Normal Descent (YAND) uses the equi-affine normal of level-set hypersurfaces as search directions.
result YAND converges globally under standard smoothness assumptions and locally quadratically near nondegenerate minimizers.
Improved SGD with line-search achieves fast convergence rates for various models.
problem Achieving fast convergence rates for stochastic gradient descent (SGD) in over-parameterized models.
method Proposes using line-search techniques to automatically set the step-size in SGD, proving convergence rates for convex, strongly-convex, and non-convex functions.
result SGD with Armijo line-search attains deterministic convergence rates for convex and strongly-convex functions, and linear convergence for non-convex functions.
GOLS finds activation functions affect training robustness, especially ReLU.
problem Investigate how different activation functions impact GOLS in neural network training.
method Identify SNN-GPPs for GOLS, analyze activation function effects on gradient continuity.
result GOLS robust for most activation functions but sensitive to ReLU.
A major challenge in current optimization research for deep learning is to automatically find optimal step sizes for each update step. The optimal step size is closely related to the shape of the loss in the update step direction. However, this shape has not yet been examined in detail. This work shows empirically that…
New algorithms improve SGD convergence and reduce variance for over-parameterized models.
problem Slower convergence in non-interpolation settings for SGD variants.
method Proposed AdaSPS and AdaSLS with variance reduction for robust convergence.
result Achieves faster convergence rates and robustness in non-interpolation settings.
Study examines line search approximations for neural networks using MBSS.
problem Reducing computational cost in training large-scale neural networks.
method Empirical study of quadratic line search approximations for dynamic MBSS loss functions, enforcing different types of function and derivative information.
result Selectively enforcing information in approximations reduces the variance of predicted step sizes.
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a prob…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a prob…
During recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second order information. In this work we propose a direct least-squares approach conceptually similar to…
New method solves constrained optimization problems efficiently.
problem Equality-constrained nonlinear, nonconvex optimization problems.
method Adaptive inexact Newton method with randomized iterative sketching.
result Global almost sure convergence and local linear/superlinear convergence.
Optimizes ad pruning in sponsored search systems using reinforcement learning.
problem How to efficiently select top K ads from N candidates to maximize revenue.
method Model-free reinforcement learning approach considering downstream as a black-box environment.
result Remarkable improvements in revenue achieved through reinforcement learning.
Co-adaptation is a special form of on-line learning where an algorithm A must assist an unknown algorithm B to perform some task. This is a general framework and has applications in recommendation systems, search, education, and much more. Today, the most common use of co-adaptive algorithms is …
D-Adaptation automatically sets optimal learning rates without manual tuning.
problem Optimizing learning rates for efficient convergence in machine learning.
method D-Adaptation, which asymptotically achieves optimal learning rates without back-tracking or additional evaluations.
result D-Adaptation automatically matches hand-tuned learning rates across diverse problems.
We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian approximation computed using a receding history of iterates and gradients. It is th…
In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms and block coordinate descent algorithms. On the other hand,…
New algorithm optimizes AUC in binary classification and changepoint detection.
problem Difficult to optimize AUC in binary classification and changepoint detection.
method Proposes efficient path-following algorithms for choosing optimal learning rate.
result Proposed line search algorithm computes complete AUM/AUC representation.
The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…
This work investigates the training of conditional random fields (CRFs) via the stochastic dual coordinate ascent (SDCA) algorithm of Shalev-Shwartz and Zhang (2016). SDCA enjoys a linear convergence rate and a strong empirical performance for binary classification problems. However, it has never been used to train CRF…
GOALS improves learning rate selection for dynamic MBSS in deep learning.
problem Challenges in selecting learning rates for dynamic MBSS in deep learning.
method Gradient-only approximation line search (GOALS) for dynamic MBSS loss functions.
result GOALS reduces model errors in multimodal cases.
VecHGrad solves complex tensor decomposition problems more accurately and efficiently.
problem Complex tensor decomposition with multiple matrices and diagonal tensors.
method VecHGrad algorithm using gradient, Hessian-vector product, and adaptive line search.
result VecHGrad converges faster and more accurately than existing methods.
Stochastic quasi-Newton tackles noisy gradients in optimization.
problem Optimizing with noisy data in stochastic settings.
method Extends quasi-Newton methods to handle stochastic gradients through flexible Hessian modeling and line-search regularization.
result Demonstrates superior performance in maximum likelihood estimation for complex models.
Online boosting method improves weak to strong learner.
problem Online learning of weak to strong learner.
method Extends batch GentleAdaBoost to online approach with line search.
result Online boosting performs better than other methods.
Simple DP algorithms find approximate solutions for nonconvex ERM.
problem Finding approximate solutions to nonconvex ERM problems with privacy.
method Differential privacy, descent directions, line search, mini-batching, two-phase strategy.
result Effective algorithms for nonconvex ERM with privacy guarantees.
New scheme adapts batch size for faster variance-reduced algorithms.
problem Slowness of variance-reduced algorithms due to large batch size.
method Eliminates backtracking line search, adapts batch size via history stochastic gradients.
result Significantly reduces overall complexity for SVRG and SARAH/SPIDER.
Paper introduces FoMoH for optimization without backpropagation.
problem Optimizing machine learning models without backpropagation.
method Second-order hyperplane search, forward-mode stochastic gradient method, hyper-dual numbers, FoMoH.
result Developed a novel optimization algorithm that avoids backpropagation.
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.
Simple rules ensure gradient descent adapts to local geometry, converging for convex and nonconvex problems.
problem Minimizing convex and nonconvex functions efficiently.
method Two rules: don't increase stepsize too fast and don't overstep local curvature.
result Method converges for convex and nonconvex problems, even with infinite global smoothness.
Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (2016; JMLR) based on randomized sketching matrices. However, it is computationally intensive due to the iterative sketch process. In this paper, we analyze the IHS algorit…
A new L-BFGS method tackles large-scale optimization with fewer evaluations.
problem Efficiently solving large-scale unconstrained optimization problems.
method Proposes a regularized L-BFGS method with line search techniques.
result Shows global convergence and robust performance in numerical tests.
Adaptive contrastive search improves text generation quality and diversity.
problem Decoding high-quality text from language model outputs.
method Adaptive contrastive search incorporating uncertainty-guided degeneration penalty.
result Enhanced text generation quality and diversity across different models and datasets.
NSGD-M optimizes machine learning models without hyperparameter tuning, even under relaxed smoothness.
problem Training machine learning models with optimal complexity under relaxed smoothness assumptions.
method Normalized Stochastic Gradient Descent with Momentum (NSGD-M) without stepsize tuning.
result NSGD-M achieves nearly optimal complexity without prior knowledge of problem parameters.
Study on adversarial training dynamics in high dimensions using SGD.
problem Analyzing adversarial training of models in high-dimensional settings.
method Deriving deterministic equivalents for SGD iterates under Gaussian mixtures.
result No constant learning rate guarantees monotone descent in adversarial training.