English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Langevin algorithms are gradient descent methods with additive noise. Theyhave been used for decades in Markov chain Monte Carlo (MCMC) sampling,optimization, and learning. Their convergence properties for unconstrainednon-convex optimization and learning problems have been studied widely in thelast few years. Other work has examined projected Langevin algorithms forsampling from log-concave distributions restricted to convex compact sets. Forlearning and optimization, log-concave distributions correspond to convexlosses. In this paper, we analyze the case of non-convex losses with compactconvex constraint sets and IID external data variables. We term the resultingmethod the projected stochastic gradient Langevin algorithm (PSGLA). We showthe algorithm achieves a deviation of $O(T^{-1/4}(\log T)^{1/2})$ from itstarget distribution in 1-Wasserstein distance. For optimization and learning,we show that the algorithm achieves $\epsilon$-suboptimal solutions, onaverage, provided that it is run for a time that is polynomial in$\epsilon^{-1}$ and slightly super-exponential in the problem dimension.

Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learning