Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMirrored Langevin Dynamics
61
0
0.0
(
0
)
Added by
Ya-Ping Hsieh
Publication date
2018
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror descent, to derive novel first-order sampling schemes. We prove that, for a general target distribution with strongly convex potential, our framework implies the existence of a first-order algorithm achieving $tilde{O}(epsilon^{-2}d)$ convergence, suggesting that the state-of-the-art $tilde{O}(epsilon^{-6}d^5)$ can be vastly improved. With the important Latent Dirichlet Allocation (LDA) application in mind, we specialize our algorithm to sample from Dirichlet posteriors, and derive the first non-asymptotic $tilde{O}(epsilon^{-2}d^2)$ rate for first-order sampling. We further extend our framework to the mini-batch setting and prove convergence rates when only stochastic gradients are available. Finally, we report promising experimental results for LDA on real datasets.
rate research
Read More
Stochastic gradient Langevin dynamics (SGLD) has gained the attention of optimization researchers due to its global optimization properties. This paper proves an improved convergence property to local minimizers of nonconvex objective functions using SGLD accelerated by variance reductions. Moreover, we prove an ergodicity property of the SGLD scheme, which gives insights on its potential to find global minimizers of nonconvex objectives.
In this paper, we explore a general Aggregated Gradient Langevin Dynamics framework (AGLD) for the Markov Chain Monte Carlo (MCMC) sampling. We investigate the nonasymptotic convergence of AGLD with a unified analysis for different data accessing (e.g. random access, cyclic access and random reshuffle) and snapshot updating strategies, under convex and nonconvex settings respectively. It is the first time that bounds for I/O friendly strategies such as cyclic access and random reshuffle have been established in the MCMC literature. The theoretic results also indicate that methods in AGLD possess the merits of both the low per-iteration computational complexity and the short mixture time. Empirical studies demonstrate that our framework allows to derive novel schemes to generate high-quality samples for large-scale Bayesian posterior learning tasks.
We present a new class of adaptive stochastic optimization algorithms, which overcomes many of the known shortcomings of popular adaptive optimizers that are currently used for the fine tuning of artificial neural networks (ANNs). Its underpinning theory relies on advances of Eulers polygonal approximations for stochastic differential equations (SDEs) with monotone coefficients. As a result, it inherits the stability properties of tamed algorithms, while it addresses other known issues, e.g. vanishing gradients in ANNs. In particular, we provide an nonasymptotic analysis and full theoretical guarantees for the convergence properties of an algorithm of this novel class, which we named TH$varepsilon$O POULA (or, simply, TheoPouLa). Finally, several experiments are presented with different types of ANNs, which show the superior performance of TheoPouLa over many popular adaptive optimization algorithms.
Artificial neural networks (ANNs) are typically highly nonlinear systems which are finely tuned via the optimization of their associated, non-convex loss functions. Typically, the gradient of any such loss function fails to be dissipative making the use of widely-accepted (stochastic) gradient descent methods problematic. We offer a new learning algorithm based on an appropriately constructed variant of the popular stochastic gradient Langevin dynamics (SGLD), which is called tamed unadjusted stochastic Langevin algorithm (TUSLA). We also provide a nonasymptotic analysis of the new algorithms convergence properties in the context of non-convex learning problems with the use of ANNs. Thus, we provide finite-time guarantees for TUSLA to find approximate minimizers of both empirical and population risks. The roots of the TUSLA algorithm are based on the taming technology for diffusion processes with superlinear coefficients as developed in citet{tamed-euler, SabanisAoAP} and for MCMC algorithms in citet{tula}. Numerical experiments are presented which confirm the theoretical findings and illustrate the need for the use of the new algorithm in comparison to vanilla SGLD within the framework of ANNs.
We introduce a sampling perspective to tackle the challenging task of training robust Reinforcement Learning (RL) agents. Leveraging the powerful Stochastic Gradient Langevin Dynamics, we present a novel, scalable two-player RL algorithm, which is a sampling variant of the two-player policy gradient method. Our algorithm consistently outperforms existing baselines, in terms of generalization across different training and testing conditions, on several MuJoCo environments. Our experiments also show that, even for objective functions that entirely ignore potential environmental shifts, our sampling approach remains highly robust in comparison to standard RL algorithms.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
