Timezone: »
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different diffusions are suitable for optimizing different classes of convex and non-convex functions. This allows us to design diffusions suitable for globally optimizing convex and non-convex functions not covered by the existing Langevin theory. Our non-asymptotic analysis delivers computable optimization and integration error bounds based on easily accessed properties of the objective and chosen diffusion. Central to our approach are new explicit Stein factor bounds on the solutions of Poisson equations. We complement these results with improved optimization guarantees for targets other than the standard Gibbs measure.
Author Information
Murat Erdogdu (University of Toronto)
Lester Mackey (Microsoft Research)
Ohad Shamir (Weizmann Institute of Science)
More from the Same Authors
-
2020 Poster: On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Method »
Ye He · Krishnakumar Balasubramanian · Murat Erdogdu -
2020 Poster: Neural Networks with Small Weights and Depth-Separation Barriers »
Gal Vardi · Ohad Shamir -
2019 Poster: On the Power and Limitations of Random Features for Understanding Neural Networks »
Gilad Yehudai · Ohad Shamir -
2018 Poster: Are ResNets Provably Better than Linear Predictors? »
Ohad Shamir -
2017 Poster: Robust Estimation of Neural Signals in Calcium Imaging »
Hakan Inan · Murat Erdogdu · Mark Schnitzer -
2017 Poster: Inference in Graphical Models via Semidefinite Programming Hierarchies »
Murat Erdogdu · Yash Deshpande · Andrea Montanari -
2016 Poster: Dimension-Free Iteration Complexity of Finite Sum Optimization Problems »
Yossi Arjevani · Ohad Shamir -
2016 Poster: Without-Replacement Sampling for Stochastic Gradient Methods »
Ohad Shamir -
2016 Oral: Without-Replacement Sampling for Stochastic Gradient Methods »
Ohad Shamir -
2016 Poster: Scaled Least Squares Estimator for GLMs in Large-Scale Problems »
Murat Erdogdu · Lee H Dicker · Mohsen Bayati -
2015 Poster: Convergence rates of sub-sampled Newton methods »
Murat Erdogdu · Andrea Montanari -
2015 Poster: Newton-Stein Method: A Second Order Method for GLMs via Stein's Lemma »
Murat Erdogdu -
2015 Spotlight: Newton-Stein Method: A Second Order Method for GLMs via Stein's Lemma »
Murat Erdogdu -
2015 Poster: Communication Complexity of Distributed Convex Learning and Optimization »
Yossi Arjevani · Ohad Shamir -
2014 Poster: Fundamental Limits of Online and Distributed Algorithms for Statistical Learning and Estimation »
Ohad Shamir -
2014 Poster: On the Computational Efficiency of Training Neural Networks »
Roi Livni · Shai Shalev-Shwartz · Ohad Shamir -
2013 Poster: Online Learning with Switching Costs and Other Adaptive Adversaries »
Nicolò Cesa-Bianchi · Ofer Dekel · Ohad Shamir -
2013 Poster: Estimating LASSO Risk and Noise Level »
Mohsen Bayati · Murat Erdogdu · Andrea Montanari