  Many control policies used in various applications determine the input or
action by solving a convex optimization problem that depends on the current
state and some parameters. Common examples of such convex optimization control
policies (COCPs) include the linear quadratic regulator (LQR), convex model
predictive control (MPC), and convex control-Lyapunov or approximate dynamic
programming (ADP) policies. These types of control policies are tuned by
varying the parameters in the optimization problem, such as the LQR weights, to
obtain good performance, judged by application-specific metrics. Tuning is
often done by hand, or by simple methods such as a crude grid search. In this
paper we propose a method to automate this process, by adjusting the parameters
using an approximate gradient of the performance metric with respect to the
parameters. Our method relies on recently developed methods that can
efficiently evaluate the derivative of the solution of a convex optimization
problem with respect to its parameters. We illustrate our method on several
examples.
