# A Deeper Understanding of State-Based Critics in Multi-Agent Reinforcement Learning

arXiv: https://arxiv.org/abs/2201.01221 · HTML: https://mlsanity.com/paper/2201.01221/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 3 Jan 2022.

## Builds on (most cited first, 12 of 12)

- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [The StarCraft Multi-Agent Challenge](https://mlsanity.com/paper/1902.04043/) (2019)
- [Learning to Communicate with Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1605.06676/) (2016)
- [Emergent Tool Use From Multi-Agent Autocurricula](https://mlsanity.com/paper/1909.07528/) (2019)
- [Off-Policy Multi-Agent Decomposed Policy Gradients](https://mlsanity.com/paper/2007.12322/) (2020)
- [Shapley Q-value: A Local Reward Approach to Solve Global Reward Games](https://mlsanity.com/paper/1907.05707/) (2019)
- [Deep Implicit Coordination Graphs for Multi-agent Reinforcement Learning](https://mlsanity.com/paper/2006.11438/) (2020)
- [Contrasting Centralized and Decentralized Critics in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2102.04402/) (2021)
- [Value-Decomposition Multi-Agent Actor-Critics](https://mlsanity.com/paper/2007.12306/) (2020)
- [R-MADDPG for Partially Observable Environments and Limited Communication](https://mlsanity.com/paper/2002.06684/) (2020)
- [Multi-Agent Common Knowledge Reinforcement Learning](https://mlsanity.com/paper/1810.11702/) (2018)

## Built on by (most cited first, 10 of 10)

- [An Introduction to Centralized Training for Decentralized Execution in Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2409.03052/) (2024)
- [Towards a Standardised Performance Evaluation Protocol for Cooperative MARL](https://mlsanity.com/paper/2209.10485/) (2022)
- [PMIC: Improving Multi-Agent Reinforcement Learning with Progressive Mutual Information Collaboration](https://mlsanity.com/paper/2203.08553/) (2022)
- [Informed POMDP: Leveraging Additional Information in Model-Based RL](https://mlsanity.com/paper/2306.11488/) (2023)
- [On Centralized Critics in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2408.14597/) (2024)
- [Off-the-Grid MARL: Datasets with Baselines for Offline Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2302.00521/) (2023)
- [Optimistic critics can empower small actors](https://mlsanity.com/paper/2506.01016/) (2025)
- [LLM-Enhanced Multi-Agent Reinforcement Learning with Expert Workflow for Real-Time P2P Energy Trading](https://mlsanity.com/paper/2507.14995/) (2025)
- [Reinformed Dreamer: An Asymmetric World Model Efficiently Trained through Latent Guidance](https://mlsanity.com/paper/2607.26040/) (2026)
- [Memory-State Critic for Asymmetric Actor-Critic with Application to Vision-Based Pursuit-Evasion](https://mlsanity.com/paper/2610.03830/) (2026)

## Abstract (arXiv)

Centralized Training for Decentralized Execution, where training is done in a centralized offline fashion, has become a popular solution paradigm in Multi-Agent Reinforcement Learning. Many such methods take the form of actor-critic with state-based critics, since centralized training allows access to the true system state, which can be useful during training despite not being available at execution time. State-based critics have become a common empirical choice, albeit one which has had limited theoretical justification or analysis. In this paper, we show that state-based critics can introduce bias in the policy gradient estimates, potentially undermining the asymptotic guarantees of the algorithm. We also show that, even if the state-based critics do not introduce any bias, they can still result in a larger gradient variance, contrary to the common intuition. Finally, we show the effects of the theories in practice by comparing different forms of centralized critics on a wide range of common benchmarks, and detail how various environmental properties are related to the effectiveness of different types of critics.