skip to main content


Title: Non-equilibrium statistical mechanical approach to the formation of non-Maxwellian electron distribution in space
Award ID(s):
1842643
NSF-PAR ID:
10212479
Author(s) / Creator(s):
Date Published:
Journal Name:
The European Physical Journal Special Topics
Volume:
229
Issue:
5
ISSN:
1951-6355
Page Range / eLocation ID:
819 to 840
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (δ,ϵ)-stationary point from O(ϵ^(-4),δ^(-1)) stochastic gradient queries to O(ϵ^(-3),δ^(-1)), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(ϵ^(-1.5),δ^(-0.5)). Our techniques also recover all optimal or best-known results for finding ϵ stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings. 
    more » « less