A Lower Bound for the Sample Complexity of Inverse Reinforcement Learning
This provides a theoretical foundation for sample efficiency in IRL, which is incremental as it builds on existing information-theoretic methods.
The paper tackles the problem of determining the minimum number of samples needed for inverse reinforcement learning (IRL) in finite state and action Markov Decision Processes, deriving a lower bound of O(n log n) where n is the number of states.
Inverse reinforcement learning (IRL) is the task of finding a reward function that generates a desired optimal policy for a given Markov Decision Process (MDP). This paper develops an information-theoretic lower bound for the sample complexity of the finite state, finite action IRL problem. A geometric construction of $β$-strict separable IRL problems using spherical codes is considered. Properties of the ensemble size as well as the Kullback-Leibler divergence between the generated trajectories are derived. The resulting ensemble is then used along with Fano's inequality to derive a sample complexity lower bound of $O(n \log n)$, where $n$ is the number of states in the MDP.