# On Feasible Rewards in Multi-Agent Inverse Reinforcement Learning

arXiv: https://arxiv.org/abs/2411.15046 · HTML: https://mlsanity.com/paper/2411.15046/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Inverse reinforcement learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 25 of its 52 references that are in the map.
- First posted on arXiv 22 Nov 2024.

## Placed in

- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)

## Builds on (most cited first, 25 of 25)

- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [The StarCraft Multi-Agent Challenge](https://mlsanity.com/paper/1902.04043/) (2019)
- [Emergent Tool Use From Multi-Agent Autocurricula](https://mlsanity.com/paper/1909.07528/) (2019)
- [Safe, Multi-Agent, Reinforcement Learning for Autonomous Driving](https://mlsanity.com/paper/1610.03295/) (2016)
- [Inverse Reward Design](https://mlsanity.com/paper/1711.02827/) (2017)
- [SMARTS: Scalable Multi-Agent Reinforcement Learning Training School for Autonomous Driving](https://mlsanity.com/paper/2010.09776/) (2020)
- [Multi-Agent Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1807.09936/) (2018)
- [Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2007.07461/) (2020)
- [Adaptive Reward-Free Exploration](https://mlsanity.com/paper/2006.06294/) (2020)
- [Real-Time Bidding with Multi-Agent Reinforcement Learning in Display Advertising](https://mlsanity.com/paper/1802.09756/) (2018)
- [Multi-Agent Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1907.13220/) (2019)
- [Identifiability in inverse reinforcement learning](https://mlsanity.com/paper/2106.03498/) (2021)
- [Pessimistic Minimax Value Iteration: Provably Efficient Equilibrium Learning from Offline Datasets](https://mlsanity.com/paper/2202.07511/) (2022)
- [Large-Scale Traffic Signal Control Using a Novel Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1908.03761/) (2019)
- [Scaling up Mean Field Games with Online Mirror Descent](https://mlsanity.com/paper/2103.00623/) (2021)
- [Active Exploration for Inverse Reinforcement Learning](https://mlsanity.com/paper/2207.08645/) (2022)
- [Exploration-Exploitation in Multi-Agent Competition: Convergence with Bounded Rationality](https://mlsanity.com/paper/2106.12928/) (2021)
- [Towards Theoretical Understanding of Inverse Reinforcement Learning](https://mlsanity.com/paper/2304.12966/) (2023)
- [Identifiability and generalizability from multiple experts in Inverse Reinforcement Learning](https://mlsanity.com/paper/2209.10974/) (2022)
- [Multi-Agent Imitation Learning: Value is Easy, Regret is Hard](https://mlsanity.com/paper/2406.04219/) (2024)
- [On Imitation in Mean-field Games](https://mlsanity.com/paper/2306.14799/) (2023)
- [Offline Inverse RL: New Solution Concepts and Provably Efficient Algorithms](https://mlsanity.com/paper/2402.15392/) (2024)
- [Inverse Game Theory for Stackelberg Games: the Blessing of Bounded Rationality](https://mlsanity.com/paper/2210.01380/) (2022)
- [How does Inverse RL Scale to Large State Spaces? A Provably Efficient Approach](https://mlsanity.com/paper/2406.03812/) (2024)
- [Multi-agent Inverse Reinforcement Learning for Certain General-sum Stochastic Games](https://mlsanity.com/paper/1806.09795/) (2018)

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

- [Improving Zero-Shot Offline RL via Behavioral Task Sampling](https://mlsanity.com/paper/2604.25496/) (2026)
- [DIML: Differentiable Inverse Mechanism Learning from Behaviors of Multi-Agent Learning Trajectories](https://mlsanity.com/paper/2601.17678/) (2026)
- [Matching Multiple Experts: On the Exploitability of Multi-Agent Imitation Learning](https://mlsanity.com/paper/2602.21020/) (2026)
- [Inverse Reinforcement Learning without an Optimal Demonstrator: A Feasible Reward Set Approach](https://mlsanity.com/paper/2605.30903/) (2026)

## Abstract (arXiv)

Multi-agent Inverse Reinforcement Learning (MAIRL) aims to recover agent reward functions from expert demonstrations. We characterize the feasible reward set in Markov games, identifying all reward functions that rationalize a given equilibrium. However, equilibrium-based observations are often ambiguous: a single Nash equilibrium can correspond to many reward structures, potentially changing the game's nature in multi-agent systems. We address this by introducing entropy-regularized Markov games, which yield a unique equilibrium while preserving strategic incentives. For this setting, we provide a sample complexity analysis detailing how errors affect learned policy performance. Our work establishes theoretical foundations and practical insights for MAIRL.