Step-Size Decay and Structural Stagnation in Greedy Sparse Learning
Greedy algorithms are central to sparse approximation and stage-wise learning methods such as matching pursuit and boosting. It is known that the Power-Relaxed Greedy Algorithm with step sizes $m^{-α}$ may fail to converge when $α>1$ in general Hilbert spaces. In this work, we revisit this phenomenon from a sparse learning perspective. We study realizable regression problems with controlled feature coherence and derive explicit lower bounds on the residual norm, showing that over-decaying step-size schedules induce structural stagnation even in low-dimensional sparse settings. Numerical experiments confirm the theoretical predictions and illustrate the role of feature coherence. Our resul...
| Authors | Pablo M. Berná |
|---|---|
| Primary category | cs.LG |
| Published | 8 March 2026 |
| Last updated at source | 8 March 2026 |
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