mlsanityData to 14 Oct 2026

Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHF

arXiv 2402.06886 ↗First posted 10 Feb 2024cs.LG math.OC stat.MLcited by 41

On the map: LLM alignment / RLHF / preference optimisation → Reward modeling and RLHF

Abstract (arXiv)

Bilevel optimization has been recently applied to many machine learning tasks. However, their applications have been restricted to the supervised learning setting, where static objective functions with benign structures are considered. But bilevel problems such as incentive design, inverse reinforcement learning (RL), and RL from human feedback (RLHF) are often modeled as dynamic objective functions that go beyond the simple static objective structures, which pose significant challenges of using existing bilevel solutions. To tackle this new class of bilevel problems, we introduce the first principled algorithmic framework for solving bilevel RL problems through the lens of penalty formulation. We provide theoretical studies of the problem landscape and its penalty-based (policy) gradient algorithms. We demonstrate the effectiveness of our algorithms via simulations in the Stackelberg Markov game, RL from human feedback and incentive design.

Key facts. Cited by 41 papers in the map (data through 14 Oct 2026). Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation. Builds on 60 of its 94 references that are in the map. First posted on arXiv 10 Feb 2024.

Builds on

60 of 94 references.

Closest ancestors · 3

Same direction, newest first

  1. 2023PARL: A Unified Framework for Policy Alignment in Reinforcement Learning from Human Feedback3 Aug
  2. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Model29 May
  3. 2017Deep reinforcement learning from human preferences12 Jun

Other references · 57

  1. 2022Training language models to follow instructions with human feedbackcited by 15,971
  2. 2017Proximal Policy Optimization Algorithmscited by 15,215
  3. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,897
  4. 2016Asynchronous Methods for Deep Reinforcement Learningcited by 2,258
  5. 2018On First-Order Meta-Learning Algorithmscited by 1,018
  6. 2019Meta-Learning with Implicit Gradientscited by 525
  7. 2018Bilevel Programming for Hyperparameter Optimization and Meta-Learningcited by 405
  8. 2015Gradient-based Hyperparameter Optimization through Reversible Learningcited by 360
  9. 2020On the Global Convergence Rates of Softmax Policy Gradient Methodscited by 264
  10. 2018Approximation Methods for Bilevel Programmingcited by 236
  11. 2017Forward and Reverse Gradient-Based Hyperparameter Optimizationcited by 234
  12. 2016Hyperparameter optimization with approximate gradientcited by 233
38 more
  1. 2020Bilevel Optimization: Convergence Analysis and Enhanced Designcited by 222
  2. 2020Coresets via Bilevel Optimization for Continual Learning and Streamingcited by 192
  3. 2018Truncated Back-propagation for Bilevel Optimizationcited by 190
  4. 2019On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shiftcited by 177
  5. 2020Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularizationcited by 176
  6. 2021Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classescited by 156
  7. 2020On the Iteration Complexity of Hypergradient Computationcited by 155
  8. 2019Global Optimality Guarantees For Policy Gradient Methodscited by 150
  9. 2013Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimizationcited by 143
  10. 2019Global Convergence of Policy Gradient Methods to (Almost) Locally Optimal Policiescited by 124
  11. 2020A Finite Time Analysis of Two Time-Scale Actor Critic Methodscited by 122
  12. 2020Learning to Utilize Shaping Rewards: A New Approach of Reward Shapingcited by 114
  13. 2021A Near-Optimal Algorithm for Stochastic Bilevel Optimization via Double-Momentumcited by 106
  14. 2021Dueling RL: Reinforcement Learning with Trajectory Preferencescited by 106
  15. 2020A Sharp Analysis of Model-based Reinforcement Learning with Self-Playcited by 105
  16. 2022BOME! Bilevel Optimization Made Easy: A Simple First-Order Approachcited by 105
  17. 2021Independent Policy Gradient Methods for Competitive Reinforcement Learningcited by 101
  18. 2020Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexitycited by 92
  19. 2023On Penalty-based Bilevel Gradient Descent Methodcited by 87
  20. 2020Sample Efficient Reinforcement Learning with REINFORCEcited by 86
  21. 2021Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergencecited by 84
  22. 2020A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singletoncited by 79
  23. 2017A First Order Method for Solving Convex Bi-Level Optimization Problemscited by 67
  24. 2020Preference-based Reinforcement Learning with Finite-Time Guaranteescited by 65
  25. 2021Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyondcited by 63
  26. 2022Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergencecited by 57
  27. 2021A Fully Single Loop Algorithm for Bilevel Optimization without Hessian Inversecited by 53
  28. 2023On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximationcited by 51
  29. 2023First-order penalty methods for bilevel optimizationcited by 41
  30. 2022Will Bilevel Optimizers Benefit from Loopscited by 36
  31. 2019Reward Shaping via Meta-Learningcited by 32
  32. 2023Optimal Algorithms for Stochastic Bilevel Optimization under Relaxed Smoothness Conditionscited by 31
  33. 2021A General Descent Aggregation Framework for Gradient-based Bi-level Optimizationcited by 28
  34. 2023Last-Iterate Convergent Policy Gradient Primal-Dual Methods for Constrained MDPscited by 28
  35. 2020Towards Understanding Asynchronous Advantage Actor-critic: Convergence and Linear Speedupcited by 25
  36. 2022Automatic differentiation of nonsmooth iterative algorithmscited by 25
  37. 2021Tighter Analysis of Alternating Stochastic Gradient Method for Stochastic Nested Problemscited by 22
  38. 2021Adaptive Incentive Design with Multi-Agent Meta-Gradient Reinforcement Learningcited by 19

50 most cited of 57 All 57 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 10; 2025: 16; 2026: 15.

41 papers.

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  1. 2024SEAL: Safety-enhanced Aligned LLM Fine-tuning via Bilevel Data Selectioncited by 64
  2. 2025Beyond Two-Stage Training: Cooperative SFT and RL for LLM Reasoningcited by 30
  3. 2024SAIL: Self-Improving Efficient Online Alignment of Large Language Modelscited by 20
  4. 2024Self-Play with Adversarial Critic: Provable and Scalable Offline Alignment for Language Modelscited by 16
  5. 2025Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontierscited by 16
  6. 2024Contextual Bilevel Reinforcement Learning for Incentive Alignmentcited by 14
  7. 2024Understanding Forgetting in LLM Supervised Fine-Tuning and Preference Learning -- A Convex Optimization Perspectivecited by 12
  8. 2024Bilevel reinforcement learning via the development of hyper-gradient without lower-level convexitycited by 10
  9. 2025On The Sample Complexity Bounds In Bilevel Reinforcement Learningcited by 10
  10. 2025Stackelberg Learning from Human Feedback: Preference Optimization as a Sequential Gamecited by 10
  11. 2025Direct Prediction Set Minimization via Bilevel Conformal Classifier Trainingcited by 8
  12. 2026Safety at One Shot: Patching Fine-Tuned LLMs with A Single Instancecited by 8
29 more
  1. 2024A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraintscited by 7
  2. 2025A First-order Generative Bilevel Optimization Framework for Diffusion Modelscited by 4
  3. 2026Explaining and Preventing Alignment Collapse in Iterative RLHFcited by 4
  4. 2024On The Global Convergence Of Online RLHF With Neural Parametrizationcited by 3
  5. 2024Unlocking TriLevel Learning with Level-Wise Zeroth Order Constraints: Distributed Algorithms and Provable Non-Asymptotic Convergencecited by 3
  6. 2025A Fully First-Order Layer for Differentiable Optimizationcited by 3
  7. 2024Learning to Steer Markovian Agents under Model Uncertaintycited by 2
  8. 2025Adversarial Policy Optimization for Offline Preference-based Reinforcement Learningcited by 2
  9. 2025Learning Explainable Dense Reward Shapes via Bayesian Optimizationcited by 2
  10. 2025Multi-Objective Bilevel Learningcited by 2
  11. 2026Deep Incentive Design with Differentiable Equilibrium Blockscited by 2
  12. 2026Sample-Efficient Hypergradient Estimation for Decentralized Bi-Level Reinforcement Learningcited by 2
  13. 2026CoNav-UAV: Cooperative Dual-Altitude Aerial Navigation via Stackelberg Learningcited by 2
  14. 2025Nonconvex Decentralized Stochastic Bilevel Optimization under Heavy-Tailed Noisecited by 1
  15. 2025Alchemist: Unlocking Efficiency in Text-to-Image Model Training via Meta-Gradient Data Selectioncited by 1
  16. 2026Oracle-Robust Online Alignment for Large Language Modelscited by 1
  17. 2026A Tale of Two Problems: Multi-Task Bilevel Learning Meets Equality Constrained Multi-Objective Optimizationcited by 1
  18. 2026On the Convergence of Self-Improving Online LLM Alignmentcited by 1
  19. 2025Enhanced Penalty-based Bidirectional Reinforcement Learning Algorithmscited by 0
  20. 2025A Provably Convergent Plug-and-Play Framework for Stochastic Bilevel Optimizationcited by 0
  21. 2025HERAKLES: Hierarchical Skill Compilation for Open-ended LLM Agentscited by 0
  22. 2025From Data to Rewards: a Bilevel Optimization Perspective on Maximum Likelihood Estimationcited by 0
  23. 2026Sample Complexity Analysis for Constrained Bilevel Reinforcement Learningcited by 0
  24. 2026On the Stability and Generalization of First-order Bilevel Minimax Optimizationcited by 0
  25. 2026Sharper Analysis of Single-Loop Methods for Bilevel Optimizationcited by 0
  26. 2026Hypergradient-based Bilevel Reinforcement Learning with Improved Sample Complexitycited by 0
  27. 2026Efficient Hypergradient Descent for Inverse Reinforcement Learningcited by 0
  28. 2026Active Inference as Context Acquisition for AI Agentscited by 0
  29. 2026Scalable, Transferable Meta-network for Data Selection Requires a Different Loss (and Why the Obvious Choice is Problematic)cited by 0

Similar, not cited

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  1. 2026Bilevel Optimization over Saddle Points of Zero-Sum Markov Games
  2. 2024Exploration-Driven Policy Optimization in RLHF: Theoretical Insights on Efficient Data Utilization
  3. 2025Reinforcement Learning from Human Feedback
  4. 2025One Framework to Rule Them All: Unifying RL-Based and RL-Free Methods in RLHF
  5. 2023Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint
  6. 2023Is RLHF More Difficult than Standard RL?
  7. 2024Towards Sample-Efficiency and Generalization of Transfer and Inverse Reinforcement Learning: A Comprehensive Literature Review
  8. 2025Bi-Level Policy Optimization with Nystr"om Hypergradients