Consistent Model Chasing Is Minimax Optimal: The Exact Value of Scalar Adversarial Adaptive Control under Large Parametric Uncertainty

What the math gives to ML

The paper gives an exact minimax result for passive adaptive control with an unknown scalar gain and bounded adversarial disturbances. Its transferable mechanism is consistent-set model chasing: maintain the set of parameters compatible with observations, select its midpoint, and apply certainty-equivalent cancellation rather than probing or optimism. The quantitative certificate is sharp: the worst-case peak is exactly 1 plus Delta, consisting of an unavoidable disturbance response of 1 and an unavoidable identification spike of Delta. A neural transfer is a robust recurrent or state-space block whose uncertain transition gains are tracked by intervals and canceled using midpoint estimates.