  Markov decision processes (MDPs) are widely used for modeling decision-making
problems in robotics, automated control, and economics. Traditional MDPs assume
that the decision maker (DM) knows all states and actions. However, this may
not be true in many situations of interest. We define a new framework, MDPs
with unawareness (MDPUs) to deal with the possibilities that a DM may not be
aware of all possible actions. We provide a complete characterization of when a
DM can learn to play near-optimally in an MDPU, and give an algorithm that
learns to play near-optimally when it is possible to do so, as efficiently as
possible. In particular, we characterize when a near-optimal solution can be
found in polynomial time.
