Extreme State Aggregation Beyond MDPs
This work addresses the challenge of applying RL algorithms beyond MDPs, which is incremental as it generalizes existing aggregation results.
The paper tackles the problem of reinforcement learning in environments without Markov Decision Process assumptions by showing that even if state aggregation does not yield an MDP, solutions from an associated MDP can still solve the original problem if representable as functions of reduced states, leading to a uniform upper bound on state space size.
We consider a Reinforcement Learning setup where an agent interacts with an environment in observation-reward-action cycles without any (esp.\ MDP) assumptions on the environment. State aggregation and more generally feature reinforcement learning is concerned with mapping histories/raw-states to reduced/aggregated states. The idea behind both is that the resulting reduced process (approximately) forms a small stationary finite-state MDP, which can then be efficiently solved or learnt. We considerably generalize existing aggregation results by showing that even if the reduced process is not an MDP, the (q-)value functions and (optimal) policies of an associated MDP with same state-space size solve the original problem, as long as the solution can approximately be represented as a function of the reduced states. This implies an upper bound on the required state space size that holds uniformly for all RL problems. It may also explain why RL algorithms designed for MDPs sometimes perform well beyond MDPs.