NeurIPS 2019
Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center
Paper ID:3080
Title:Acceleration via Symplectic Discretization of High-Resolution Differential Equations

This paper presents new technical results connecting discretization of ODEs to accelerated optimization. However the results are a bit niche. Pros: The main finding is that high-resolution ODEs with symplectic discretization schemes yield accelerated discrete-time algorithms. For the low-resolution ODEs that this paper considers, only implicit discretization yields accelerated iteration complexity. However, symplectic methods are generally superior to implicit methods as implicit methods require solving a nontrivial subproblem in each iteration. Cons: Like previous papers in this line of work, this paper is somewhat unclear on how these techniques might be applied elsewhere or what intuition even suggests that the symplectic method should work.