  We combine adaptive control directly with optimal or near-optimal value
functions to enhance stability and closed-loop performance in systems with
parametric uncertainties. Leveraging the fundamental result that a value
function is also a control Lyapunov function (CLF), combined with the fact that
direct adaptive control can be immediately used once a CLF is known, we prove
asymptotic closed-loop convergence of adaptive feedback controllers derived
from optimization-based policies. Both matched and unmatched parametric
variations are addressed, where the latter exploits a new technique based on
adaptation rate scaling. The results may have particular resonance in machine
learning for dynamical systems, where nominal feedback controllers are
typically optimization-based but need to remain effective (beyond mere
robustness) in the presence of significant but structured variations in
parameters.
