Jia Chen

Sharp Critical Minimax Laws and No-Learning Thresholds in Continuous-Time Adaptive Control

We study episodic continuous-time control with an unknown vector control gain, scalar state, quadratic action cost, and smooth convex terminal cost. In the scalar Gaussian experiment, let $\Delta(H)$ denote the minimax improvement over zero control and set $\delta=\sqrt2H^2-1$. We prove the critical law $$ \Delta(H)\as...