Pseudospectral Bounds for Transient Amplification in Coupled Gradient Descent

In three linesPseudospectral theory for coupled gradient descent (bilevel optimization, two-time-scale stochastic approximation, adversarial training). Kreiss constant bound K(J) ≤ 2/(1-γ) + ‖C‖/(4(1-γ)) for block-triangular Jacobians. Finite-horizon iteration complexity O(K(J)² log(1/δ)). Experiments on linear-quadratic problems and neural network training.

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