Model-Free Reinforcement Learning: from Clipped Pseudo-Regret to Sample Complexity
This addresses the sample efficiency challenge in reinforcement learning for researchers and practitioners, offering near-optimal theoretical guarantees, though it is incremental in improving existing bounds.
The paper tackles the problem of learning an ε-optimal policy for discounted Markov Decision Processes, providing a model-free algorithm with sample complexity Õ(SA/(ε²(1-γ)^5.5)) and an improved version for small ε with complexity Õ(SA/(ε²(1-γ)^3)), matching the information-theoretic lower bound up to logarithmic factors.
In this paper we consider the problem of learning an $ε$-optimal policy for a discounted Markov Decision Process (MDP). Given an MDP with $S$ states, $A$ actions, the discount factor $γ\in (0,1)$, and an approximation threshold $ε> 0$, we provide a model-free algorithm to learn an $ε$-optimal policy with sample complexity $\tilde{O}(\frac{SA\ln(1/p)}{ε^2(1-γ)^{5.5}})$ (where the notation $\tilde{O}(\cdot)$ hides poly-logarithmic factors of $S,A,1/(1-γ)$, and $1/ε$) and success probability $(1-p)$. For small enough $ε$, we show an improved algorithm with sample complexity $\tilde{O}(\frac{SA\ln(1/p)}{ε^2(1-γ)^{3}})$. While the first bound improves upon all known model-free algorithms and model-based ones with tight dependence on $S$, our second algorithm beats all known sample complexity bounds and matches the information theoretic lower bound up to logarithmic factors.