# A Unified Linear Programming Framework for Offline Reward Learning from Human Demonstrations and Feedback

arXiv: https://arxiv.org/abs/2405.12421 · HTML: https://mlsanity.com/paper/2405.12421/

## Key facts

- Cited by 4 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 35 of its 47 references that are in the map.
- First posted on arXiv 20 May 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)
- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)

## Builds on (most cited first, 30 of 35)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Guided Cost Learning: Deep Inverse Optimal Control via Policy Optimization](https://mlsanity.com/paper/1603.00448/) (2016)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Reward learning from human preferences and demonstrations in Atari](https://mlsanity.com/paper/1811.06521/) (2018)
- [Recursively Summarizing Books with Human Feedback](https://mlsanity.com/paper/2109.10862/) (2021)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Extrapolating Beyond Suboptimal Demonstrations via Inverse Reinforcement Learning from Observations](https://mlsanity.com/paper/1904.06387/) (2019)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [IQ-Learn: Inverse soft-Q Learning for Imitation](https://mlsanity.com/paper/2106.12142/) (2021)
- [AlgaeDICE: Policy Gradient from Arbitrary Experience](https://mlsanity.com/paper/1912.02074/) (2019)
- [Imitation Learning via Off-Policy Distribution Matching](https://mlsanity.com/paper/1912.05032/) (2019)
- [Maximum Entropy Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/1507.04888/) (2015)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Interactive Learning from Policy-Dependent Human Feedback](https://mlsanity.com/paper/1701.06049/) (2017)
- [Chain of Hindsight Aligns Language Models with Feedback](https://mlsanity.com/paper/2302.02676/) (2023)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [OptiDICE: Offline Policy Optimization via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2106.10783/) (2021)
- [RLHF from Heterogeneous Feedback via Personalization and Preference Aggregation](https://mlsanity.com/paper/2405.00254/) (2024)
- [Reinforcement Learning with Human Feedback: Learning Dynamic Choices via Pessimism](https://mlsanity.com/paper/2305.18438/) (2023)
- [Benchmarks and Algorithms for Offline Preference-Based Reward Learning](https://mlsanity.com/paper/2301.01392/) (2023)
- [Dual RL: Unification and New Methods for Reinforcement and Imitation Learning](https://mlsanity.com/paper/2302.08560/) (2023)
- [Offline Reinforcement Learning Under Value and Density-Ratio Realizability: The Power of Gaps](https://mlsanity.com/paper/2203.13935/) (2022)
- [Optimal Conservative Offline RL with General Function Approximation via Augmented Lagrangian](https://mlsanity.com/paper/2211.00716/) (2022)
- [Active Exploration for Inverse Reinforcement Learning](https://mlsanity.com/paper/2207.08645/) (2022)

## Built on by (most cited first, 4 of 4)

- [Beyond RLHF and NLHF: Population-Proportional Alignment under an Axiomatic Framework](https://mlsanity.com/paper/2506.05619/) (2025)
- [Inverse Reinforcement Learning without an Optimal Demonstrator: A Feasible Reward Set Approach](https://mlsanity.com/paper/2605.30903/) (2026)
- [Specifying Reward Functions for RL Without Environment Sampling](https://mlsanity.com/paper/2609.15544/) (2026)
- [PHIRL: Aligning Learned Rewards with Task Progress for Inverse Reinforcement Learning](https://mlsanity.com/paper/2609.31855/) (2026)

## Abstract (arXiv)

Inverse Reinforcement Learning (IRL) and Reinforcement Learning from Human Feedback (RLHF) are pivotal methodologies in reward learning, which involve inferring and shaping the underlying reward function of sequential decision-making problems based on observed human demonstrations and feedback. Most prior work in reward learning has relied on prior knowledge or assumptions about decision or preference models, potentially leading to robustness issues. In response, this paper introduces a novel linear programming (LP) framework tailored for offline reward learning. Utilizing pre-collected trajectories without online exploration, this framework estimates a feasible reward set from the primal-dual optimality conditions of a suitably designed LP, and offers an optimality guarantee with provable sample efficiency. Our LP framework also enables aligning the reward functions with human feedback, such as pairwise trajectory comparison data, while maintaining computational tractability and sample efficiency. We demonstrate that our framework potentially achieves better performance compared to the conventional maximum likelihood estimation (MLE) approach through analytical examples and numerical experiments.