Stable Fitted Reinforcement Learning

Imagine an agent acting in some environment. At time t, the environment is in some state Xt chosen from a finite set of states. The agent perceives Xt, and is allowed to choose an action at from some finite set of actions. The environment then changes state, so that at time (t 1) it is in a new state Xt 1 chosen from a probability distribution which depends only on Xt and at. Meanwhile, the agent experiences a real-valued cost Ct, chosen from a distribution which also depends only on Xt and at and which has finite mean and variance.