We assume the environment modeled as discrete-time factored-action MDP (FA-MDP)M = hS,A,P,R,γi where S is the set of states s, A is the set of vector-represented actionsa = (a1,...,am),P(s0|s,a) = Pr(st+1 = s0|st = s,at = a)isthe transition probability,R(s,a) R is the immediate reward for taking actiona in state s, and γ [0,1) is the discount factor.

We address the scalability of symbolic planning under uncertainty with factored states and actions. Prior work has focused almost exclusively on factored states but not factored actions, and on value iteration (VI) compared to policy iteration (PI). Our first contribution is a novel method for symbolic policy backups via the application of constraints, which is used to yield a new efficient symbolic implementation of modified PI (MPI) for factored action spaces. While this approach improves scalability in some cases, naive handling of policy constraints comes with its own scalability issues. This leads to our second and main contribution, symbolic Opportunistic Policy Iteration (OPI), which is a novel convergent algorithm lying between VI and MPI. The core idea is a symbolic procedure that applies policy constraints only when they reduce the space and time complexity of the update, and otherwise performs full Bellman backups, thus automatically adjusting the backup per state. We also give a memory bounded version of this algorithm allowing a space-time tradeoff. Empirical results show significantly improved scalability over the state-of-the-art.

We address the scalability of symbolic planning under uncertainty with factored states and actions. Prior work has focused almost exclusively on factored states but not factored actions, and on value iteration (VI) compared to policy iteration (PI). Our first contribution is a novel method for symbolic policy backups via the application of constraints, which is used to yield a new efficient symbolic imple- mentation of modified PI (MPI) for factored action spaces. While this approach improves scalability in some cases, naive handling of policy constraints comes with its own scalability issues. This leads to our second and main contribution, symbolic Opportunistic Policy Iteration (OPI), which is a novel convergent al- gorithm lying between VI and MPI.