REVIEW 2 cited by
Second-order Guarantees of Distributed Gradient Algorithms
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We consider distributed smooth nonconvex unconstrained optimization over networks, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i) the renowned Distributed Gradient Descent (DGD) algorithm likely converges to a neighborhood of a Second-order Stationary (SoS) solution; and (ii) the more recent class of distributed algorithms based on gradient tracking--implementable also over digraphs--likely converges to exact SoS solutions, thus avoiding (strict) saddle-points. Furthermore, new convergence rate results to first-order critical points is established for the latter class of algorithms.
Forward citations
Cited by 2 Pith papers
-
Second-Order Guarantees of Stochastic Gradient Descent in Non-Convex Optimization
Under a relative gradient-noise bound plus a local noise condition at saddles, SGD reaches an approximate second-order stationary point in O(1/(μ²τ)) iterations.
-
Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem
Distributed gradient descent in continuous time almost surely converges to local minima, because saddle points only attract initializations from a lower-dimensional stable manifold.
Discussion (0). Continue with ORCID to comment.