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This research introduces a Hessian-free bilevel reinforcement learning algorithm that achieves state-of-the-art sample complexity by leveraging the optimality of Boltzmann policies in entropy-regularized settings. By removing restrictive assumptions like the Polyak-Lojasiewicz condition, it offers improved scalability for meta-learning and RLHF applications without relying on computationally expensive second-order derivatives.
Hypergradient-based Bilevel Reinforcement Learning with Improved Sample Complexity
arXiv:2607.28849v1 Announce Type: new Abstract: Bilevel reinforcement learning (RL) is an important framework within the literature of RL that can be used to formalize various categories of problems, such as meta-learning, hierarchical task decomposition, and reinforcement learning from human feedback (RL-HF). Most of the bilevel RL algorithms are either not scalable because of using hypergradient with Hessian, or they suffer from high sample complexity because of using penalty-based approximation methods. In this work, we propose a hypergradient-based bilevel RL algorithm using the optimality of the Boltzmann policy for the entropy regularized discounted RL objective function. Our proposed algorithm is Hessian-free and obtains an iteration complexity of $O(\epsilon^{-1})$ and state-of-the-art sample complexity of $\tilde{O}(\epsilon^{-2})$ under mild regularity conditions. Further, in our convergence analysis, we are able to remove the assumption of the Polyak-Lojasiewicz (PL) condition on the outer-level objective function present in the prior state-of-the-art sample complexity work.
Abstract:Bilevel reinforcement learning (RL) is an important framework within the literature of RL that can be used to formalize various categories of problems, such as meta-learning, hierarchical task decomposition, and reinforcement learning from human feedback (RL-HF). Most of the bilevel RL algorithms are either not scalable because of using hypergradient with Hessian, or they suffer from high sample complexity because of using penalty-based approximation methods. In this work, we propose a hypergradient-based bilevel RL algorithm using the optimality of the Boltzmann policy for the entropy regularized discounted RL objective function. Our proposed algorithm is Hessian-free and obtains an iteration complexity of $O(\epsilon^{-1})$ and state-of-the-art sample complexity of $\tilde{O}(\epsilon^{-2})$ under mild regularity conditions. Further, in our convergence analysis, we are able to remove the assumption of the Polyak-Lojasiewicz (PL) condition on the outer-level objective function present in the prior state-of-the-art sample complexity work.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2607.28849 [cs.LG]
(or arXiv:2607.28849v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.28849 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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