how to express the performance of a policy in policy parameters
I suggest you study reinforcement learning, and possibly Q-learning.  They are aimed at dealing with this kind of situation. 

The short answer is that we almost never have a way to give a closed-form formula that measures how good a policy is, as a function of the policy parameters.  Rather, we use simulations: we conduct a bunch of simulations using that policy, measure how well it performs in simulation, and use that our estimate of the quality of the policy.  Then we apply stochastic gradient descent or other optimization methods to find parameter values that maximize the quality of the policy.