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Decentralized Riemannian Gradient Descent on the Stiefel Manifold
Shixiang Chen · Alfredo Garcia · Mingyi Hong · Shahin Shahrampour

Thu Jul 22 08:30 PM -- 08:35 PM (PDT) @
in Optimization 6 »
We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a finite sum of smooth local functions, where each local function is associated with one agent and agents communicate with each other over an undirected connected graph. The problem is non-convex as local functions are possibly non-convex (but smooth) and the Steifel manifold is a non-convex set. We present a decentralized Riemannian stochastic gradient method (DRSGD) with the convergence rate of $\mathcal{O}(1/\sqrt{K})$ to a stationary point. To have exact convergence with constant stepsize, we also propose a decentralized Riemannian gradient tracking algorithm (DRGTA) with the convergence rate of $\mathcal{O}(1/K)$ to a stationary point. We use multi-step consensus to preserve the iteration in the local (consensus) region. DRGTA is the first decentralized algorithm with exact convergence for distributed optimization on Stiefel manifold.
Keywords: Computer Vision · Distributed and Parallel Optimization

Author Information

Shixiang Chen (Texas A&M University)
Alfredo Garcia (Texas A&M University)
Mingyi Hong (University of Minnesota)
Shahin Shahrampour (Texas A&M University)

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