  In this paper we address the class of Sequential Decision Making (SDM)
problems that are characterized by time-varying parameters. These parameter
dynamics are either pre-specified or manipulable. At any given time instant the
decision policy -- that governs the sequential decisions -- along with all the
parameter values determines the cumulative cost incurred by the underlying SDM.
Thus, the objective is to determine the manipulable parameter dynamics as well
as the time-varying decision policy such that the associated cost gets
minimized at each time instant. To this end we develop a control-theoretic
framework to design the unknown parameter dynamics such that it locates and
tracks the optimal values of the parameters, and simultaneously determines the
time-varying optimal sequential decision policy. Our methodology builds upon a
Maximum Entropy Principle (MEP) based framework that addresses the static
parameterized SDMs. More precisely, we utilize the resulting smooth
approximation (from the above framework) of the cumulative cost as a control
Lyapunov function. We show that under the resulting control law the parameters
asymptotically track the local optimal, the proposed control law is Lipschitz
continuous and bounded, as well as ensure that the decision policy of the SDM
is optimal for a given set of parameter values. The simulations demonstrate the
efficacy of our proposed methodology.
