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Transient Amplification in Cascaded Gradient Methods: Exact Minimax Laws and Tracking without Resonance
Leader-follower gradient iterations, including bilevel and two-time-scale methods, can exhibit large finite-time excursions despite asymptotic stability. For cascaded iterations with block matrix J = [[A,0],[C,D]], symmetric diagonal blocks of norm at most gamma < 1, and coupling norm at most c, we
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