This paper investigates the ability of closed loop quantum learning control techniques to meet a posed physical objective while simultaneously steering the dynamics to lie in a specified subspace. Achievement of successful control with reduced space dynamics can have a number of benefits including a more easily understood control mechanism. Judicious choices for the cost functional may be introduced such that the closed loop optimal control experiments can steer the dynamics to lie within a subspace of the system eigenstates without requiring any prior detailed knowledge about the system Hamiltonian. Learning control with reduced space dynamics takes advantage of the expected existence of a multiplicity of fields that can all give acceptable quality control outcomes. The procedure eliminates the hard demands of following a specific dynamical path by only asking that the dynamics reside in a subspace. Additional measurements characterizing the subspace are necessary to monitor the system evolution during the control field learning process. This procedure is simulated for optimally controlled population transfer experiments in systems of one and two degrees of freedom. The results demonstrate that optimal control fields can be found that successfully derive the system to the target state while staying within the desired subspace.