Stochastic tasks: Difficulty and levin search

Abstract

We establish a setting for asynchronous stochastic tasks that account for episodes, rewards and responses, and, most especially, the computational complexity of the algorithm behind an agent solving a task. This is used to determine the difficulty of a task as the (logarithm of the) number of computational steps required to acquire an acceptable policy for the task, which includes the exploration of policies and their verification. We also analyse instance difficulty, task compositions and decompositions.