Sample Complexity Analysis for Constrained Bilevel Reinforcement Learning
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915764483653632 |
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| author | Saxena, Naman Aggarwal, Vaneet |
| author_facet | Saxena, Naman Aggarwal, Vaneet |
| contents | Several important problem settings within the literature of reinforcement learning (RL), such as meta-learning, hierarchical learning, and RL from human feedback (RL-HF), can be modelled as bilevel RL problems. A lot has been achieved in these domains empirically; however, the theoretical analysis of bilevel RL algorithms hasn't received a lot of attention. In this work, we analyse the sample complexity of a constrained bilevel RL algorithm, building on the progress in the unconstrained setting. We obtain an iteration complexity of $O(ε^{-2})$ and sample complexity of $\tilde{O}(ε^{-4})$ for our proposed algorithm, Constrained Bilevel Subgradient Optimization (CBSO). We use a penalty-based objective function to avoid the issue of primal-dual gap and hyper-gradient in the context of a constrained bilevel problem setting. The penalty-based formulation to handle constraints requires analysis of non-smooth optimization. We are the first ones to analyse the generally parameterized policy gradient-based RL algorithm with a non-smooth objective function using the Moreau envelope. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_00282 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sample Complexity Analysis for Constrained Bilevel Reinforcement Learning Saxena, Naman Aggarwal, Vaneet Machine Learning Artificial Intelligence Several important problem settings within the literature of reinforcement learning (RL), such as meta-learning, hierarchical learning, and RL from human feedback (RL-HF), can be modelled as bilevel RL problems. A lot has been achieved in these domains empirically; however, the theoretical analysis of bilevel RL algorithms hasn't received a lot of attention. In this work, we analyse the sample complexity of a constrained bilevel RL algorithm, building on the progress in the unconstrained setting. We obtain an iteration complexity of $O(ε^{-2})$ and sample complexity of $\tilde{O}(ε^{-4})$ for our proposed algorithm, Constrained Bilevel Subgradient Optimization (CBSO). We use a penalty-based objective function to avoid the issue of primal-dual gap and hyper-gradient in the context of a constrained bilevel problem setting. The penalty-based formulation to handle constraints requires analysis of non-smooth optimization. We are the first ones to analyse the generally parameterized policy gradient-based RL algorithm with a non-smooth objective function using the Moreau envelope. |
| title | Sample Complexity Analysis for Constrained Bilevel Reinforcement Learning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.00282 |