  For a given problem, the optimal Markov policy can be considerred as a
conditional or contingent plan containing a (potentially large) number of
branches. Unfortunately, there are applications where it is desirable to
strictly limit the number of decision points and branches in a plan. For
example, it may be that plans must later undergo more detailed simulation to
verify correctness and safety, or that they must be simple enough to be
understood and analyzed by humans. As a result, it may be necessary to limit
consideration to plans with only a small number of branches. This raises the
question of how one goes about finding optimal plans containing only a limited
number of branches. In this paper, we present an any-time algorithm for optimal
k-contingency planning (OKP). It is the first optimal algorithm for limited
contingency planning that is not an explicit enumeration of possible contingent
plans. By modelling the problem as a Partially Observable Markov Decision
Process, it implements the Bellman optimality principle and prunes the solution
space. We present experimental results of applying this algorithm to some
simple test cases.
