mlsanityData to 14 Oct 2026

On The Sample Complexity Bounds In Bilevel Reinforcement Learning

arXiv 2503.17644 ↗First posted 22 Mar 2025cs.LG cs.AIcited by 10

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

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 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-Lojasiewicz (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 O(ε-3) improving upon existing bounds of 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.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 40 of its 52 references that are in the map. First posted on arXiv 22 Mar 2025.

Builds on

40 of 52 references.

Closest ancestors · 3

Same direction, newest first

  1. 2024A Sharper Global Convergence Analysis for Average Reward Reinforcement Learning via an Actor-Critic Approach26 Jul
  2. 2024Bilevel reinforcement learning via the development of hyper-gradient without lower-level convexity30 May
  3. 2024Order-Optimal Regret with Novel Policy Gradient Approaches in Infinite-Horizon Average Reward MDPs2 Apr

Other references · 37

  1. 2017Deep reinforcement learning from human preferencescited by 3,912
  2. 2019Fine-Tuning Language Models from Human Preferencescited by 2,150
  3. 2018DeepMind Control Suitecited by 956
  4. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 787
  5. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 539
  6. 2017Learning Robust Rewards with Adversarial Inverse Reinforcement Learningcited by 490
  7. 2021PEBBLE: Feedback-Efficient Interactive Reinforcement Learning via Relabeling Experience and Unsupervised Pre-trainingcited by 302
  8. 2020Bilevel Optimization: Convergence Analysis and Enhanced Designcited by 222
  9. 2019Neural Policy Gradient Methods: Global Optimality and Rates of Convergencecited by 159
  10. 2020Learning to Utilize Shaping Rewards: A New Approach of Reward Shapingcited by 114
  11. 2021B-Pref: Benchmarking Preference-Based Reinforcement Learningcited by 106
  12. 2020A Sharp Analysis of Model-based Reinforcement Learning with Self-Playcited by 105
25 more
  1. 2023A Fully First-Order Method for Stochastic Bilevel Optimizationcited by 100
  2. 2023On Penalty-based Bilevel Gradient Descent Methodcited by 87
  3. 2020The Complexity of Constrained Min-Max Optimizationcited by 82
  4. 2021A Single-Timescale Method for Stochastic Bilevel Optimizationcited by 69
  5. 2022An Improved Analysis of (Variance-Reduced) Policy Gradient and Natural Policy Gradient Methodscited by 68
  6. 2020Preference-based Reinforcement Learning with Finite-Time Guaranteescited by 65
  7. 2023On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximationcited by 51
  8. 2022Maximum-Likelihood Inverse Reinforcement Learning with Finite-Time Guaranteescited by 42
  9. 2024Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHFcited by 41
  10. 2023PARL: A Unified Framework for Policy Alignment in Reinforcement Learning from Human Feedbackcited by 40
  11. 2023On Finding Small Hyper-Gradients in Bilevel Optimization: Hardness Results and Improved Analysiscited by 39
  12. 2021On the Convergence Theory for Hessian-Free Bilevel Algorithmscited by 35
  13. 2020Single-Timescale Actor-Critic Provably Finds Globally Optimal Policycited by 34
  14. 2019Reward Shaping via Meta-Learningcited by 32
  15. 2023Improved Sample Complexity Analysis of Natural Policy Gradient Algorithm with General Parameterization for Infinite Horizon Discounted Reward Markov Decision Processescited by 25
  16. 2022Decentralized Stochastic Bilevel Optimization with Improved per-Iteration Complexitycited by 21
  17. 2022Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Functioncited by 20
  18. 2024SAIL: Self-Improving Efficient Online Alignment of Large Language Modelscited by 20
  19. 2022Bilevel Optimization with a Lower-level Contraction: Optimal Sample Complexity without Warm-startcited by 17
  20. 2023Can We Find Nash Equilibria at a Linear Rate in Markov Games?cited by 9
  21. 2024Sample-Efficient Preference-based Reinforcement Learning with Dynamics Aware Rewardscited by 9
  22. 2023On the Global Convergence of Natural Actor-Critic with Two-layer Neural Network Parametrizationcited by 5
  23. 2016Caching Incentive Design in Wireless D2D Networks: A Stackelberg Game Approachcited by 3
  24. 2022On the Global Convergence of Fitted Q-Iteration with Two-layer Neural Network Parametrizationcited by 3
  25. 2024Social Environment Designcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 6.

10 papers.

  1. 2025A Technical Survey of Reinforcement Learning Techniques for Large Language Modelscited by 21
  2. 2025Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Accesscited by 2
  3. 2026Online Convex Optimization with Dueling Feedbackcited by 2
  4. 2025Primal-Only Actor Critic Algorithm for Robust Constrained Average Cost MDPscited by 1
  5. 2026Oracle-Robust Online Alignment for Large Language Modelscited by 1
  6. 2026On the Convergence of Self-Improving Online LLM Alignmentcited by 1
  7. 2025From Data to Rewards: a Bilevel Optimization Perspective on Maximum Likelihood Estimationcited by 0
  8. 2026Sample Complexity Analysis for Constrained Bilevel Reinforcement Learningcited by 0
  9. 2026Non-Expansive Two-Time-Scale Stochastic Approximation: A Fixed-Schedule One-Quarter Barrier and Bias-Corrected Accelerationcited by 0
  10. 2026Hypergradient-based Bilevel Reinforcement Learning with Improved Sample Complexitycited by 0

Similar, not cited

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  1. 2025Improving Reinforcement Learning Sample-Efficiency using Local Approximation
  2. 2025Convergence and Sample Complexity of First-Order Methods for Agnostic Reinforcement Learning
  3. 2025Near-Optimal Sample Complexity for Iterated CVaR Reinforcement Learning with a Generative Model
  4. 2026On the Stability and Generalization of First-order Bilevel Minimax Optimization
  5. 2026Bilevel Optimization over Saddle Points of Zero-Sum Markov Games
  6. 2021A Lower Bound for the Sample Complexity of Inverse Reinforcement Learning
  7. 2026Tight Sample Complexity Bounds for Entropic Best Policy Identification
  8. 2024Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPs