Temporal plannability by variance of the episode length
  Optimization of decision problems in stochastic environments is usually
concerned with maximizing the probability of achieving the goal and minimizing
the expected episode length. For interacting agents in time-critical
applications, learning of the possibility of scheduling of subtasks (events) or
the full task is an additional relevant issue. Besides, there exist highly
stochastic problems where the actual trajectories show great variety from
episode to episode, but completing the task takes almost the same amount of
time. The identification of sub-problems of this nature may promote e.g.,
planning, scheduling and segmenting Markov decision processes. In this work,
formulae for the average duration as well as the standard deviation of the
duration of events are derived. The emerging Bellman-type equation is a simple
extension of Sobel's work (1982). Methods of dynamic programming as well as
methods of reinforcement learning can be applied for our extension. Computer
demonstration on a toy problem serve to highlight the principle.
