MDPs with Unawareness in Robotics

We formalize decision-making problems in robotics and automated control using continuous MDPs and actions that take place over continuous time intervals. We then approximate the continuous MDP using finer and finer discretizations. Doing this results in a family of systems, each of which has an extremely large action space, although only a few actions are "interesting". We can view the decision maker as being unaware of which actions are "interesting". We can model this using MDPUs, MDPs with unawareness, where the action space is much smaller. As we show, MDPUs can be used as a general framework for learning tasks in robotic problems. We prove results on the difficulty of learning a near-optimal policy in an an MDPU for a continuous task. We apply these ideas to the problem of having a humanoid robot learn on its own how to walk.

MDPs with Unawareness

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.