AI RESEARCH
Spurious Stationarity and Hardness Results for Bregman Proximal-Type Algorithms
arXiv CS.LG
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ArXi:2404.08073v3 Announce Type: replace-cross Bregman proximal-type algorithms (BPs), such as mirror descent, have become popular tools in machine learning and data science for exploiting problem structures through non-Euclidean geometries. In this paper, we show that BPs can get trapped near a class of non-stationary points, which we term \emph{spurious stationary points}. Such stagnation can persist for any finite number of iterations if the gradient of the Bregman kernel is not Lipschitz continuous, even in convex problems.