On the Sample Complexity Bounds of Bilevel Reinforcement Learning

Bilevel reinforcement learning (BRL) has emerged as a powerful framework for aligning generative models, yet its theoretical foundations, especially sample complexity bounds, remain underexplored. In this work, we present the first sample complexity bound for BRL, establishing a rate of $\mathcal{O}({ϵ}^{-3})$ in continuous state-action spaces.

Traditional MDP analysis techniques do not extend to BRL due to its nested structure and non-convex lower-level problems. We overcome these challenges by leveraging the Polyak-Łojasiewicz (PL) condition and the MDP structure to obtain closed-form gradients, enabling tight sample complexity analysis.

Our analysis also extends to general bi-level optimization settings with non-convex lower levels, where we achieve state-of-the-art sample complexity results of $\mathcal{O}({ϵ}^{-3})$ improving upon existing bounds of $\mathcal{O}({ϵ}^{-6})$.

Additionally, we address the computational bottleneck of hypergradient estimation by proposing a fully first-order, Hessian-free algorithm suitable for large-scale problems.