New algorithm solves federated minimax optimization problems.
problem Federated minimax optimization challenges.
method Federated Stochastic Smoothed Gradient Descent Ascent (FESS-GDA).
result FESS-GDA uniformly solves federated minimax problems.
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48 results for “Stochastic Gradient Descent Ascent”
Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax optimization problem to global optimality, but are in practice successfully trained using stochastic gradient descent-ascent.…
SREDA optimizes complex machine learning problems with fewer evaluations.
problem Finding an optimal point in nonconvex-strongly-concave minimax problems.
method Stochastic Recursive Gradient Descent Ascent (SREDA) with variance reduction.
result Achieves optimal stochastic gradient complexity of O(κ^3ε^-3).
Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradientscs.LG
New framework improves variational inference with Markov chain methods.
problem Challenges of minimizing KL divergence with stochastic gradient descent.
method Markov chain score ascent (MCSA) methods, including parallel MCSA (pMCSA).
result Improved theoretical and empirical performance of MCSA methods.
Gradient descent-ascent converges to strict local minmax equilibria with a finite timescale separation.
problem Analyzing the convergence of gradient descent-ascent in non-convex, non-concave games with a finite timescale separation.
method Investigates the role of a finite timescale separation parameter τ on gradient descent-ascent in two-player zero-sum games, providing convergence rates and non-convergence results.
result Gradient descent-ascent converges to strict local minmax equilibria for a finite timescale separation parameter τ*.
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.
Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA) method has been implemented in various software packages, it has so far lacked go…
New analysis improves understanding of bilevel optimization stability and generalization.
problem Understanding how well bilevel optimization algorithms generalize.
method Algorithmic stability arguments and generalization bounds for three bilevel minimax solvers.
result Precise trade-off between algorithmic stability, generalization gaps, and practical settings.
Paper improves risk bounds for nonconvex-strongly-concave minimax problems.
problem Achieving sharper risk bounds for nonconvex-strongly-concave minimax problems.
method Using uniform localized convergence to derive high probability generalization error bounds.
result Derives n times faster excess primal risk bounds for popular algorithms.
Stochastic dual coordinate ascent (SDCA) is an effective technique for solving regularized loss minimization problems in machine learning. This paper considers an extension of SDCA under the mini-batch setting that is often used in practice. Our main contribution is to introduce an accelerated mini-batch version of SDC…
Optimal multistage method solves noisy minimax problems.
problem Minimizing/maximizing in noisy conditions with smooth and strongly convex-strongly concave settings.
method Multistage Stochastic Gradient Descent Ascent (M-GDA) and Optimistic Gradient Descent Ascent (M-OGDA).
result Achieves optimal linear decay rate with respect to initial error and condition number.
A new decentralized method solves minimax problems with reduced communication and sample complexity.
problem Solving minimax optimization problems in a distributed setting.
method Decentralized stochastic gradient descent ascent with variance reduction.
result Achieved optimal sample and communication complexities for nonconvex-strongly-concave problems.
RSGDA improves convergence rates for nonconvex-strongly concave optimization.
problem Optimization of nonconvex-strongly concave problems.
method Randomized Stochastic Gradient Descent Ascent (RSGDA) with optimal loop sizes.
result First almost sure convergence rates for SGDA algorithms on nonconvex-strongly concave settings.
This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It…
Paper proposes algorithms for solving nonconvex-nonconcave problems with complexity guarantees.
problem Nonconvex-nonconcave minimax problems with PL condition.
method Zeroth-order AGDA and VRAGDA algorithms.
result Iteration complexities for obtaining ε-stationary points.
This paper analyzes neural networks for solving complex optimization problems.
problem Minimax optimization problems in infinite-dimensional function spaces.
method Mean-field analysis of stochastic gradient descent-ascent in neural networks.
result The algorithm converges to a stationary point at a sublinear rate.
Improves posterior approximation speed for Dirichlet process mixture models.
problem Inefficiency of stochastic variational inference in large datasets.
method Uses stochastic gradient ascent with adaptive stepsize optimization.
result Adaptive stepsize improves speed and performance of posterior approximation.
Paper proposes an algorithm to solve complex minimax problems efficiently.
problem Stochastic nonconvex-concave minimax problems in various fields.
method Accelerated first-order regularized momentum descent ascent algorithm (FORMDA).
result Achieves best-known complexity bound of for single-loop algorithms.
Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estim…
SoftAD improves classification accuracy with less fine-tuning and fewer computational costs.
problem Improving classification accuracy with less fine-tuning and fewer computational costs.
method SoftAD is a softened, pointwise mechanism that downweights borderline points and limits the effects of outliers.
result SoftAD achieves classification accuracy competitive with flooding and SAM, with a smaller loss generalization gap and model norm.
The stochastic dual coordinate-ascent (S-DCA) technique is a useful alternative to the traditional stochastic gradient-descent algorithm for solving large-scale optimization problems due to its scalability to large data sets and strong theoretical guarantees. However, the available S-DCA formulation is limited to finit…
AGDA and variance-reduced methods solve nonconvex-nonconcave minimax problems globally and faster.
problem Solving nonconvex-nonconcave minimax problems in machine learning.
method Global convergence of AGDA and variance-reduced algorithms.
result AGDA and variance-reduced methods achieve global convergence and faster rates.
Improved zeroth-order algorithms tackle nonconvex minimax problems with reduced complexity.
problem Nonconvex minimax optimization problems in machine learning.
method Design and analysis of Zeroth-Order Gradient Descent Ascent ( exttt{ZO-GDA}) and Zeroth-Order Gradient Descent Multi-Step Ascent ( exttt{ZO-GDMSA}) algorithms.
result Oracle complexity improvements for minimax optimization problems.
In this paper, we study the problem of constrained robust (min-max) optimization ina black-box setting, where the desired optimizer cannot access the gradients of the objective function but may query its values. We present a principled optimization framework, integrating a zeroth-order (ZO) gradient estimator with an a…
Epoch-GDA achieves optimal convergence rate for SCSC min-max problems.
problem Solving stochastic min-max problems with strong convexity and strong concavity.
method Epoch-wise stochastic gradient descent ascent method (Epoch-GDA) without additional assumptions.
result Achieves the optimal rate of for the duality gap of general SCSC min-max problems.
Sampling without replacement speeds up optimization in minimax problems.
problem Optimizing minimax problems with faster convergence rates.
method Analysis of gradient descent ascent and proximal point method with two sampling strategies.
result Sampling without replacement leads to faster convergence rates in minimax optimization.
Optimizes binary regression models with gradient ascent-descent methods.
problem Regression problems with binary weights in quantized learning and digital communication.
method Maximin optimization using gradient ascent-descent methods.
result The approach is optimal in linear regression with low noise and robust regression with few outliers.
Last-Iterate Convergence of Saddle-Point Optimizers via High-Resolution Differential Equationsmath.OC
New ODE models show saddle-point optimization methods converge differently, with last-iterate convergence for OGDA.
problem Analyzing convergence properties of saddle-point optimization methods.
method High-Resolution Differential Equations (HRDEs) to design differential equation models for saddle-point optimization methods.
result HRDEs reveal last-iterate convergence for Optimistic Gradient Descent Ascent (OGDA) in bilinear games.
Paper analyzes convergence of GDA for nonconvex-nonconcave minimax problems.
problem Understanding convergence of GDA for nonconvex-nonconcave minimax problems.
method Local convergence analysis of GDA with stepsize ratio Θ(κ).
result Stepsize ratio of Θ(κ) is necessary and sufficient for local convergence of GDA to a Stackelberg Equilibrium.
The paper tackles robust control with uncertain dependence using data-driven methods.
problem Nonparametric robust control under dependence uncertainty in multi-period stochastic systems.
method Nonparametric adaptive robust control framework using stochastic gradient descent ascent algorithm.
result The controller benefits from knowing more about the uncertain model.
In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a unified analysis as approximations of the classical proximal point method for solving…
Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Łojasiewicz Conditioncs.LG
In 1963, Polyak proposed a simple condition that is sufficient to show a global linear convergence rate for gradient descent. This condition is a special case of the Łojasiewicz inequality proposed in the same year, and it does not require strong convexity (or even convexity). In this work, we show that this much-older…
Method identifies mixed Nash equilibria in high dimensions for training mixtures of GANs.
problem Finding Nash equilibria in two-player zero-sum continuous games, especially in high dimensions.
method Parametrizing mixed strategies as mixtures of particles, updating their positions and weights using gradient descent-ascent.
result Global convergence to an approximate equilibrium for the related Langevin gradient-ascent dynamic.
Paper studies convergence of Mean-Field GDA dynamics for MNE of continuous games.
problem Finding mixed Nash equilibria in continuous games.
method Two-scale Mean-Field Gradient Descent Ascent dynamics.
result Two-scale Mean-Field GDA converges exponentially to MNE without convexity assumptions.
Omega method mitigates noise in stochastic game optimization.
problem Noise sensitivity and convergence issues in stochastic game optimization.
method Omega method incorporates EMA of historic gradients in its update rule.
result Omega method outperforms optimistic gradient method in stochastic games.
GANs can learn hierarchical distributions in real-world images efficiently.
problem Understanding and efficiently learning complex, real-world distributions with GANs.
method Formally studying how GANs can learn hierarchically generated distributions close to real-life image distributions using SGDA.
result Training GANs via SGDA can efficiently learn distributions with a 'forward super-resolution' structure, both in sample and time complexities.
Algorithm converges to Nash equilibria in competitive games.
problem Finding Nash equilibria in decentralized, competitive Markov games.
method Decentralized Optimistic Gradient Descent/Ascent with a critic.
result Converges to the set of Nash equilibria under self-play.
Gradient Descent Ascent converges to von-Neumann solution in hidden zero-sum games.
problem Understanding dynamics of zero-sum games with hidden structure.
method Gradient Descent Ascent applied to hidden zero-sum games with specific convex-concave structure.
result Gradient Descent Ascent converges to von-Neumann solution in strictly convex-concave hidden games.
Gradient ascent method successfully removes specific data points from neural networks without retraining.
problem Addressing privacy and ethical concerns by removing specific data points from trained models.
method Gradient ascent approach to unlearning, leveraging the implicit bias of gradient descent towards margin maximization conditions.
result Gradient ascent method can successfully unlearn specific data points from two-layer ReLU neural networks without retraining.
Given data with noisy labels, over-parameterized deep networks can gradually memorize the data, and fit everything in the end. Although equipped with corrections for noisy labels, many learning methods in this area still suffer overfitting due to undesired memorization. In this paper, to relieve this issue, we propose …
Study local convergence of GDA for training GANs with kernel-based discriminators.
problem Analyzing the local dynamics of GDA for GANs with kernel-based discriminators.
method Linearization of a non-linear dynamical system, under an isolated points model assumption.
result Showed phase transitions indicating convergence, oscillation, or divergence of GDA.
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these metho…
New SGDA method speeds up nonconvex minimax optimization.
problem Improving convergence of nonconvex minimax optimization.
method SGDA with random reshuffling for nonconvex-PŁ objectives.
result Convergence rates faster than with-replacement SGDA.
Alt-GDA outperforms Sim-GDA in minimax games with near-optimal local convergence.
problem Minimax optimization convergence rate comparison
method Alternating Gradient Descent-Ascent (Alt-GDA) vs. Simultaneous Gradient Descent-Ascent (Sim-GDA)
result Alt-GDA achieves near-optimal local convergence rate for strongly convex-strongly concave problems, while Sim-GDA converges slower.
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic subspace ascent. A common feature of these methods is that in their update rule a cert…
Sobolev Gradient Ascent for Optimal Transport: Barycenter Optimization and Convergence Analysismath.OC
Paper introduces SGA for barycenter optimization in optimal transport.
problem Optimizing Wasserstein barycenter for discrete distributions.
method Sobolev gradient ascent algorithm tailored to Wasserstein geometry.
result SGA achieves convergence rate similar to subgradient descent.
Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study. It has been recognized that they may cycle, and there is no good understanding of their limit points when they…
Flooding prevents deep networks from achieving zero training loss, improving test performance.
problem Deep networks can achieve zero training error but often have zero training loss, leading to overconfidence and poor test performance.
method Flooding prevents training loss from reaching zero by applying gradient ascent when loss is below a preset flood level.
result Flooding improves test performance and induces a double descent curve of the test loss.