Planning and Learning with Stochastic Action Sets
This work provides foundational theory for RL applications where action availability is stochastic, such as in dynamic or uncertain environments, though it is incremental in extending existing MDP frameworks.
The paper formalizes MDPs with stochastic action sets (SAS-MDPs) to address the unaddressed foundations of reinforcement learning where available actions vary randomly, showing that optimal policies have a compact structure and that Q-learning with sampled action sets is sound, with poly-time methods developed for model-based cases.
In many practical uses of reinforcement learning (RL) the set of actions available at a given state is a random variable, with realizations governed by an exogenous stochastic process. Somewhat surprisingly, the foundations for such sequential decision processes have been unaddressed. In this work, we formalize and investigate MDPs with stochastic action sets (SAS-MDPs) to provide these foundations. We show that optimal policies and value functions in this model have a structure that admits a compact representation. From an RL perspective, we show that Q-learning with sampled action sets is sound. In model-based settings, we consider two important special cases: when individual actions are available with independent probabilities; and a sampling-based model for unknown distributions. We develop poly-time value and policy iteration methods for both cases; and in the first, we offer a poly-time linear programming solution.