Linear–quadratic control and information relaxations

We apply recently developed duality methods to the classic linear–quadratic (LQ) control problem. Using value-function and gradient methods, we derive two dual optimal penalties for the LQ problem for when the control space is unconstrained. These penalties may be used to, for example, evaluate sub-optimal policies for constrained LQ problems. We also compare these penalties to the dual penalty of Davis and Zervos (1995) [7] and note that some of these duality ideas have been in circulation for some time.