  The stable combination of optimal feedback policies with online learning is
studied in a new control-theoretic framework for uncertain nonlinear systems.
The framework can be systematically used in transfer learning and sim-to-real
applications, where an optimal policy learned for a nominal system needs to
remain effective in the presence of significant variations in parameters. Given
unknown parameters within a bounded range, the resulting adaptive control laws
guarantee convergence of the closed-loop system to the state of zero cost.
Online adjustment of the learning rate is used as a key stability mechanism,
and preserves certainty equivalence when designing optimal policies without
assuming uncertainty to be within the control range. The approach is
illustrated on the familiar mountain car problem, where it yields near-optimal
performance despite the presence of parametric model uncertainty.
