Control policy

A control policy selects admissible actions using only the information available at each time, possibly with randomization. General policies may depend on the whole observed history. Nonanticipation and measurability are part of admissibility in a controlled Markov process.

A Markov policy uses only the current state and, in the nonstationary case, the current time. A stationary Markov policy has the form $u_t=u_{\ast }(X_t)$ for one measurable selector $u_{\ast }$. It is a restricted class of control policies, whose sufficiency for an optimization problem requires the appropriate dynamic-programming hypotheses.