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Found 25 papers, 8 papers with code
Enhancing Policy Gradient with the Polyak Step-Size Adaption
Policy gradient is a widely utilized and foundational algorithm in the field of reinforcement learning (RL).
Directional Smoothness and Gradient Methods: Convergence and Adaptivity
We develop new sub-optimality bounds for gradient descent (GD) that depend on the conditioning of the objective along the path of optimization, rather than on global, worst-case constants.
Level Set Teleportation: An Optimization Perspective
We study level set teleportation, an optimization sub-routine which seeks to accelerate gradient methods by maximizing the gradient norm on a level-set of the objective function.
Batch and match: black-box variational inference with a score-based divergence
We analyze the convergence of BaM when the target distribution is Gaussian, and we prove that in the limit of infinite batch size the variational parameter updates converge exponentially quickly to the target mean and covariance.
Function Value Learning: Adaptive Learning Rates Based on the Polyak Stepsize and Function Splitting in ERM
We then move onto to develop $\texttt{FUVAL}$, a variant of $\texttt{SPS}_+$ where the loss values at optimality are gradually learned, as opposed to being given.
A Model-Based Method for Minimizing CVaR and Beyond
We develop a variant of the stochastic prox-linear method for minimizing the Conditional Value-at-Risk (CVaR) objective.
Improving Convergence and Generalization Using Parameter Symmetries
Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence.
MoMo: Momentum Models for Adaptive Learning Rates
MoMo uses momentum estimates of the batch losses and gradients sampled at each iteration to build a model of the loss function.
A Stochastic Proximal Polyak Step Size
Developing a proximal variant of SPS is particularly important, since SPS requires a lower bound of the objective function to work well.
Linear Convergence of Natural Policy Gradient Methods with Log-Linear Policies
We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class.
SP2: A Second Order Stochastic Polyak Method
We take a step further and develop a method for solving the interpolation equations that uses the local second-order approximation of the model.
Cutting Some Slack for SGD with Adaptive Polyak Stepsizes
We use this insight to develop new variants of the SPS method that are better suited to nonlinear models.
A general sample complexity analysis of vanilla policy gradient
We then instantiate our theorems in different settings, where we both recover existing results and obtain improved sample complexity, e. g., $\widetilde{\mathcal{O}}(\epsilon^{-3})$ sample complexity for the convergence to the global optimum for Fisher-non-degenerated parametrized policies.
Stochastic Polyak Stepsize with a Moving Target
MOTAPS can be seen as a variant of the Stochastic Polyak (SP) which is also a method that also uses loss values to adjust the stepsize.
Variance-Reduced Methods for Machine Learning
Stochastic optimization lies at the heart of machine learning, and its cornerstone is stochastic gradient descent (SGD), a method introduced over 60 years ago.
Unified Analysis of Stochastic Gradient Methods for Composite Convex and Smooth Optimization
We showcase this by obtaining a simple formula for the optimal minibatch size of two variance reduced methods (\textit{L-SVRG} and \textit{SAGA}).
SGD for Structured Nonconvex Functions: Learning Rates, Minibatching and Interpolation
Stochastic Gradient Descent (SGD) is being used routinely for optimizing non-convex functions.
Almost sure convergence rates for Stochastic Gradient Descent and Stochastic Heavy Ball
We show that these results still hold when using stochastic line search and stochastic Polyak stepsizes, thereby giving the first proof of convergence of these methods in the non-overparametrized regime.
The Power of Factorial Powers: New Parameter settings for (Stochastic) Optimization
The convergence rates for convex and non-convex optimization methods depend on the choice of a host of constants, including step sizes, Lyapunov function constants and momentum constants.
Towards closing the gap between the theory and practice of SVRG
Among the very first variance reduced stochastic methods for solving the empirical risk minimization problem was the SVRG method (Johnson & Zhang 2013).
Optimal mini-batch and step sizes for SAGA
Using these bounds, and since the SAGA algorithm is part of this JacSketch family, we suggest a new standard practice for setting the step sizes and mini-batch size for SAGA that are competitive with a numerical grid search.
Greedy stochastic algorithms for entropy-regularized optimal transport problems
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost.
Characterising particulate random media from near-surface backscattering: a machine learning approach to predict particle size and concentration
Across the concentration range from 1% to 20% we find that the mean backscattered wave field is sufficient to accurately determine the concentration of particles.
Computational Physics Classical Physics 78-02, 82D02 J.2
Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods
Our goal is to improve variance reducing stochastic methods through better control variates.
Sketch and Project: Randomized Iterative Methods for Linear Systems and Inverting Matrices
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization.
Numerical Analysis 15A06, 15B52, 65F10, 68W20, 65N75, 65Y20, 68Q25, 68W40, 90C20 G.1.3
