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Mathematics > Optimization and Control

arXiv:2108.01219 (math)
[Submitted on 2 Aug 2021]

Title:Computing the Newton-step faster than Hessian accumulation

Authors:Akshay Srinivasan, Emanuel Todorov
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Abstract:Computing the Newton-step of a generic function with $N$ decision variables takes $O(N^3)$ flops. In this paper, we show that given the computational graph of the function, this bound can be reduced to $O(m\tau^3)$, where $\tau, m$ are the width and size of a tree-decomposition of the graph. The proposed algorithm generalizes nonlinear optimal-control methods based on LQR to general optimization problems and provides non-trivial gains in iteration-complexity even in cases where the Hessian is dense.
Comments: Presented at the Beyond First-order Methods workshop, ICML '21
Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG); Symbolic Computation (cs.SC); Systems and Control (eess.SY)
Cite as: arXiv:2108.01219 [math.OC]
  (or arXiv:2108.01219v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2108.01219

Submission history

From: Akshay Srinivasan [view email]
[v1] Mon, 2 Aug 2021 11:22:08 UTC (37 KB)
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