# Split the Differences, Pool the Rest: Provably Efficient Multi-Objective Imitation

arXiv: https://arxiv.org/abs/2605.12000 · HTML: https://mlsanity.com/paper/2605.12000/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 41 of its 65 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 30 of 41)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Open X-Embodiment: Robotic Learning Datasets and RT-X Models](https://mlsanity.com/paper/2310.08864/) (2023)
- [DROID: A Large-Scale In-The-Wild Robot Manipulation Dataset](https://mlsanity.com/paper/2403.12945/) (2024)
- [BridgeData V2: A Dataset for Robot Learning at Scale](https://mlsanity.com/paper/2308.12952/) (2023)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [Social Bias Frames: Reasoning about Social and Power Implications of Language](https://mlsanity.com/paper/1911.03891/) (2019)
- [Pretraining Language Models with Human Preferences](https://mlsanity.com/paper/2302.08582/) (2023)
- [A Survey of Multi-Objective Sequential Decision-Making](https://mlsanity.com/paper/1402.0590/) (2014)
- [A Generalized Algorithm for Multi-Objective Reinforcement Learning and Policy Adaptation](https://mlsanity.com/paper/1908.08342/) (2019)
- [Behavior Generation with Latent Actions](https://mlsanity.com/paper/2403.03181/) (2024)
- [Multi-Agent Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1807.09936/) (2018)
- [Toward the Fundamental Limits of Imitation Learning](https://mlsanity.com/paper/2009.05990/) (2020)
- [Of Moments and Matching: A Game-Theoretic Framework for Closing the Imitation Gap](https://mlsanity.com/paper/2103.03236/) (2021)
- [Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning](https://mlsanity.com/paper/2407.15007/) (2024)
- [Coordinated Multi-Agent Imitation Learning](https://mlsanity.com/paper/1703.03121/) (2017)
- [Multi-Agent Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1907.13220/) (2019)
- [Model-Free Imitation Learning with Policy Optimization](https://mlsanity.com/paper/1605.08478/) (2016)
- [Online Apprenticeship Learning](https://mlsanity.com/paper/2102.06924/) (2021)
- [Proximal Point Imitation Learning](https://mlsanity.com/paper/2209.10968/) (2022)
- [Imitating Language via Scalable Inverse Reinforcement Learning](https://mlsanity.com/paper/2409.01369/) (2024)
- [Provably Efficient Adversarial Imitation Learning with Unknown Transitions](https://mlsanity.com/paper/2306.06563/) (2023)
- [Imitation Learning in Discounted Linear MDPs without exploration assumptions](https://mlsanity.com/paper/2405.02181/) (2024)
- [Optimistically Optimistic Exploration for Provably Efficient Infinite-Horizon Reinforcement and Imitation Learning](https://mlsanity.com/paper/2502.13900/) (2025)

## Abstract (arXiv)

This work investigates multi-objective imitation learning: the problem of recovering policies that lie on the Pareto front given demonstrations from multiple Pareto-optimal experts in a Multi-Objective Markov Decision Process (MOMDP). Standard imitation approaches are ill-equipped for this regime, as naively aggregating conflicting expert trajectories can result in dominated policies. To address this, we introduce Multi-Output Augmented Behavioral Cloning (MA-BC), an algorithm that systematically partitions divergent expert data while pooling state-action pairs where no behavior conflict is observed. Theoretically, we prove that MA-BC converges to Pareto-optimal policies at a faster statistical rate than any learner that considers each expert dataset independently. Furthermore, we establish a novel lower bound for multi-objective imitation learning, demonstrating that MA-BC is minimax optimal. Finally, we empirically validate our algorithm across diverse discrete environments and, guided by our theoretical insights, extend and evaluate MA-BC on a continuous Linear Quadratic Regulator (LQR) control task.