In “Clustering via Dirichlet Process Mixture Models for Portable Skill Discovery“, Niekum and Barto (2011) apply Sub-goal Discovery and Skill Discovery to improve Reinforcement Learning on Markov Decision Processes. They write,
“Skill discovery algorithms in reinforcement learning typically identify single states or regions in state space that correspond to task-speciﬁc subgoals. However, such methods do not directly address the question of how many distinct skills are appropriate for solving the tasks that the agent faces. This can be highly inefficient when many identified subgoals correspond to the same underlying skill, but are all used individually as skill goals. For example, opening a door ought to be the same skill whether an agent is one inch or two inches away from the door, or whether the door is red or blue; making each possible configuration a separate skill would be unwise. Furthermore, skills created in this manner are often only transferable to tasks that share identical state spaces, since corresponding subgoals across tasks are not merged into a single skill goal.
We show that these problems can be overcome by collecting subgoal data from a series of tasks and clustering it in an agent-space , a shared feature space across multiple tasks. The resulting clusters generalize subgoals within and across tasks and can be used as templates for portable skill termination conditions. Clustering also allows the creation of skill termination conditions in a datadriven way that makes minimal assumptions and can be tailored to the domain through a careful choice of clustering algorithm. Additionally, this framework extends the utility of single-state subgoal discovery algorithms to continuous domains, in which the agent may never see the same state twice. We argue that clustering based on a Dirichlet process mixture model is appropriate in the general case when little is known about the nature or number of skills needed in a domain. Experiments in a continuous domain demonstrate the utility of this approach and illustrate how it may be useful even when traditional subgoal discovery methods are infeasible.”
They apply Dirichlet process mixture models (more specifically an inﬁnite Gaussian mixture model with a Dirichlet prior on the number of Gaussians and the parameters of the Gaussians) using expectation-maximization to do clustering of the states—each cluster corresponding to a stratagem referred to as a “latent option”. Experimental results in an environment similar to the Lightworld domain (see “Building Portable Options: Skill Transfer in Reinforcement Learning” by Konidaris and Barto (2007)) are reported.