Sample-Efficient Hypergradient Estimation for Decentralized Bi-Level Reinforcement Learning
arXiv:2603.14867v3 Announce Type: replace-cross Abstract: Many strategic decision-making problems, such as environment design for warehouse robots, can be naturally formulated as bi-level reinforcement learning (RL), where a leader agent optimizes its objective while a follower solves a Markov decision process (MDP) conditioned on the leader's decisions. In many situations, a fundamental challenge arises when the leader cannot intervene in the follower's optimization process; it can only observe the optimization outcome. We address this decentralized setting by deriving the hypergradient of the leader's objective, i.e., the gradient of the leader's strategy that accounts for changes in the follower's optimal policy. Unlike prior hypergradient-based methods that require extensive data for r
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Abstract:Many strategic decision-making problems, such as environment design for warehouse robots, can be naturally formulated as bi-level reinforcement learning (RL), where a leader agent optimizes its objective while a follower solves a Markov decision process (MDP) conditioned on the leader's decisions. In many situations, a fundamental challenge arises when the leader cannot intervene in the follower's optimization process; it can only observe the optimization outcome. We address this decentralized setting by deriving the hypergradient of the leader's objective, i.e., the gradient of the leader's strategy that accounts for changes in the follower's optimal policy. Unlike prior hypergradient-based methods that require extensive data for repeated state visits or rely on gradient estimators whose complexity can increase substantially with the high-dimensional leader's decision space, we leverage the Boltzmann covariance trick to derive an alternative hypergradient formulation. This enables efficient hypergradient estimation solely from interaction samples, even when the leader's decision space is high-dimensional. Additionally, to our knowledge, this is the first method that enables hypergradient-based optimization for 2-player Markov games in decentralized settings. Experiments highlight the impact of hypergradient updates and demonstrate our method's effectiveness in both discrete and continuous state tasks.
Comments: 26 pages. Accepted at ICAPS 2026
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computer Science and Game Theory (cs.GT); Multiagent Systems (cs.MA)
Cite as: arXiv:2603.14867 [cs.LG]
(or arXiv:2603.14867v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2603.14867
arXiv-issued DOI via DataCite
Submission history
From: Mikoto Kudo [view email] [v1] Mon, 16 Mar 2026 06:11:00 UTC (18,250 KB) [v2] Wed, 25 Mar 2026 09:28:45 UTC (18,250 KB) [v3] Tue, 31 Mar 2026 10:34:35 UTC (18,250 KB)
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