no code implementations • 11 Apr 2024 • Yunxiang Li, Rui Yuan, Chen Fan, Mark Schmidt, Samuel Horváth, Robert M. Gower, Martin Takáč
Policy gradient is a widely utilized and foundational algorithm in the field of reinforcement learning (RL).
no code implementations • 6 Mar 2024 • Aaron Mishkin, Ahmed Khaled, Yuanhao Wang, Aaron Defazio, Robert M. Gower
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.
no code implementations • 5 Mar 2024 • Aaron Mishkin, Alberto Bietti, Robert M. Gower
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.
1 code implementation • 22 Feb 2024 • Diana Cai, Chirag Modi, Loucas Pillaud-Vivien, Charles C. Margossian, Robert M. Gower, David M. Blei, Lawrence K. Saul
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.
no code implementations • 26 Jul 2023 • Guillaume Garrigos, Robert M. Gower, Fabian Schaipp
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.
no code implementations • 27 May 2023 • Si Yi Meng, Robert M. Gower
We develop a variant of the stochastic prox-linear method for minimizing the Conditional Value-at-Risk (CVaR) objective.
1 code implementation • 22 May 2023 • Bo Zhao, Robert M. Gower, Robin Walters, Rose Yu
Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence.
1 code implementation • 12 May 2023 • Fabian Schaipp, Ruben Ohana, Michael Eickenberg, Aaron Defazio, Robert M. Gower
MoMo uses momentum estimates of the batch losses and gradients sampled at each iteration to build a model of the loss function.
1 code implementation • 12 Jan 2023 • Fabian Schaipp, Robert M. Gower, Michael Ulbrich
Developing a proximal variant of SPS is particularly important, since SPS requires a lower bound of the objective function to work well.
no code implementations • 4 Oct 2022 • Rui Yuan, Simon S. Du, Robert M. Gower, Alessandro Lazaric, Lin Xiao
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.
no code implementations • 17 Jul 2022 • Shuang Li, William J. Swartworth, Martin Takáč, Deanna Needell, Robert M. Gower
We take a step further and develop a method for solving the interpolation equations that uses the local second-order approximation of the model.
no code implementations • 24 Feb 2022 • Robert M. Gower, Mathieu Blondel, Nidham Gazagnadou, Fabian Pedregosa
We use this insight to develop new variants of the SPS method that are better suited to nonlinear models.
no code implementations • 23 Jul 2021 • Rui Yuan, Robert M. Gower, Alessandro Lazaric
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.
no code implementations • 22 Jun 2021 • Robert M. Gower, Aaron Defazio, Michael Rabbat
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.
no code implementations • 2 Oct 2020 • Robert M. Gower, Mark Schmidt, Francis Bach, Peter Richtarik
Stochastic optimization lies at the heart of machine learning, and its cornerstone is stochastic gradient descent (SGD), a method introduced over 60 years ago.
no code implementations • 20 Jun 2020 • Ahmed Khaled, Othmane Sebbouh, Nicolas Loizou, Robert M. Gower, Peter Richtárik
We showcase this by obtaining a simple formula for the optimal minibatch size of two variance reduced methods (\textit{L-SVRG} and \textit{SAGA}).
no code implementations • 18 Jun 2020 • Robert M. Gower, Othmane Sebbouh, Nicolas Loizou
Stochastic Gradient Descent (SGD) is being used routinely for optimizing non-convex functions.
no code implementations • 14 Jun 2020 • Othmane Sebbouh, Robert M. Gower, Aaron Defazio
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.
no code implementations • 1 Jun 2020 • Aaron Defazio, Robert M. Gower
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.
1 code implementation • NeurIPS 2019 • Othmane Sebbouh, Nidham Gazagnadou, Samy Jelassi, Francis Bach, Robert M. Gower
Among the very first variance reduced stochastic methods for solving the empirical risk minimization problem was the SVRG method (Johnson & Zhang 2013).
2 code implementations • 31 Jan 2019 • Nidham Gazagnadou, Robert M. Gower, Joseph Salmon
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.
no code implementations • 4 Mar 2018 • Brahim Khalil Abid, Robert M. Gower
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.
2 code implementations • 13 Jan 2018 • Artur L. Gower, Robert M. Gower, Jonathan Deakin, William J. Parnell, I. David Abrahams
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
1 code implementation • 20 Oct 2017 • Robert M. Gower, Nicolas Le Roux, Francis Bach
Our goal is to improve variance reducing stochastic methods through better control variates.
1 code implementation • 19 Dec 2016 • Robert M. Gower
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