New algorithm for active exploration in bandit problems.
problem Active exploration in bandit problems.
method Gradient ascent with online lazy mirror ascent sampling rule.
result Asymptotically optimal and computationally efficient.
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48 results for “optimal gradient ascent”
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.
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.
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.
On Policy Gradientscs.LG
Policy gradient aims to maximize expected return using gradient ascent.
problem Finding a policy that maximizes expected return in a given class of policies.
method Gradient ascent applied to a differentiable model of the policy, estimating the gradient of expected return.
result Policy gradient methods require on-policy data for gradient estimation, limiting sample efficiency.
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.
Optimal Coordinate Ascent (OCA) improves feature selection in machine learning.
problem Efficiently selecting features in machine learning models.
method Optimal Coordinate Ascent (OCA) for feature selection.
result OCA outperforms previous methods in feature selection and model performance.
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).
SGD finds global optima in WGANs for 1-layer generators.
problem Training GANs with WGANs requires global optimality, which is hard.
method Used SGD to train 1-layer generator networks in WGANs.
result SGD converges to global solution in polynomial time and sample complexity.
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.
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.
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.
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.
SAVO actor improves reinforcement learning by avoiding local optima in complex Q-functions.
problem Gradient ascent in complex Q-functions leads to suboptimal solutions.
method SAVO actor generates multiple action proposals and truncates poor local optima.
result SAVO actor finds optimal actions more frequently and outperforms other architectures.
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 tackles constrained robust optimization without gradients.
problem Constrained robust (min-max) optimization in a black-box setting.
method Integrates ZO gradient estimator with alternating projected SGD-ascent method.
result Proposed ZO-Min-Max framework converges sub-linearly under mild conditions.
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…
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.
Gradient-descent-ascent dynamics can exhibit various behaviors in non-convex non-concave games.
problem Gradient-descent-ascent dynamics in non-convex non-concave games can lead to recurrent behavior and spurious equilibria.
method Combines optimization theory, game theory, and dynamical systems.
result Gradient-descent-ascent dynamics can exhibit Poincaré recurrence and converge to spurious equilibria.
Gradient-based optimization improves variational empirical Bayes regression.
problem Sparse, large-scale multiple regression models.
method Gradient-based optimization (GradVI) for variational empirical Bayes (VEB) regression.
result GradVI produces similar predictive performance to CAVI but converges faster and is faster in certain settings.
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.
New methods optimize training VQAs without barren plateaus, improving efficiency and applicability.
problem Barren plateaus in training variational quantum algorithms.
method Derive adaptive learning rates and use Gaussian kernels to optimize movement in parameter space.
result Optimized training methods outperform other routines and can train VQAs free of barren plateaus.
New algorithm for optimizing statistical utilities in bandits.
problem Optimizing statistical functionals of long-run reward distributions.
method Influence-function calculus for stochastic gradient estimation, entropic mirror-ascent algorithm.
result Regret bounds that separate optimization and estimation errors.
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.
Generalizes PCA to maximize any convex function of components.
problem Finding a principal vector that maximizes a convex function of components.
method Gradient ascent algorithm for solving the generalized PCA problem; fixed points of neural networks for kernel version.
result Solutions can be obtained as fixed points of simple neural networks.
New method for probabilistic clustering using matrix norm couplings.
problem Probabilistic clustering of discrete random variables.
method Local information theoretic approach with convex maximization problem solved via gradient ascent and alternating maximization.
result Our approach is competitive with existing techniques and worthy of further investigation.
New method optimizes portfolio weights as functions, outperforming traditional approaches.
problem Optimizing portfolio weights in mean-variance models.
method Functional optimization approach, treating weights as functions of past values.
result Gradient-ascent algorithms can solve functional optimization problems for mean-variance portfolio management.
Improves BED scalability for implicit models.
problem Designing experiments for implicit models with intractable data distributions.
method Hybrid gradient approach combining variational MI estimator, ES, and SGA.
result Significantly improves scalability of BED for implicit models.
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.
Unified analysis of EG and OGDA for saddle point problems using proximal point method.
problem Solving saddle point problems in bilinear and strongly convex-strongly concave settings.
method Unified analysis as approximations of the proximal point method.
result Unified analysis of EG and OGDA for saddle point problems.
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*.
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.
New method boosts BOED using SBI and neural likelihood.
problem Maximizing EIG in BOED with intractable likelihood.
method Neural likelihood estimation, multi-start gradient ascent.
result Significantly improved BOED performance over state-of-the-art.
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.
Paper solves non-convex min-max games using gradient descent-ascent.
problem Solving saddle point games in non-convex settings.
method Iterative gradient descent-ascent algorithms for both players.
result First order stationary points found efficiently.
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.
Lazy neural networks are vulnerable to adversarial attacks.
problem Adversarial robustness issues in lazy training models.
method Extending recent work on adversarial examples to lazy training models.
result Over-parametrized neural networks that generalize well remain vulnerable to single-step gradient ascent attacks.
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…
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.
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…
The paper connects two clustering methods by showing gradient ascent flow can move up the cluster tree.
problem Establishing a strong correspondence between clustering methods.
method Moving up the cluster tree by following the gradient ascent flow.
result Gradient ascent flow can be used to move up the cluster tree.
A new acquisition function RMES improves Bayesian optimization performance.
problem Improper evaluation of mutual information in MES leads to suboptimal performance.
method Developed rectified MES (RMES) and used stochastic gradient ascent with reparameterization.
result RMES shows consistent improvement over MES in benchmarks and real-world problems.
Off-policy stochastic actor-critic methods rely on approximating the stochastic policy gradient in order to derive an optimal policy. One may also derive the optimal policy by approximating the action-value gradient. The use of action-value gradients is desirable as policy improvement occurs along the direction of stee…
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.
We consider parallel global optimization of derivative-free expensive-to-evaluate functions, and propose an efficient method based on stochastic approximation for implementing a conceptual Bayesian optimization algorithm proposed by Ginsbourger et al. (2007). At the heart of this algorithm is maximizing the information…
Optimizes experimental designs for intractable models using mutual information bounds.
problem Finding optimal experimental designs for models with intractable data-generating distributions.
method Maximizes mutual information lower bounds parametrized by neural networks, updating network parameters and designs simultaneously.
result Framework enables experimental design for various tasks including parameter estimation and model discrimination.
SMAVE optimizes SDR by projecting onto a low-dimensional subspace on a Riemannian manifold.
problem High-dimensional regression challenges due to the curse of dimensionality.
method SMAVE combines nearest-neighbor localization and Riemannian stochastic gradient ascent.
result SMAVE achieves almost-sure convergence and matches RMAVE's synthetic subspace recovery rate.