# Meta-trained agents implement Bayes-optimal agents

arXiv: https://arxiv.org/abs/2010.11223 · HTML: https://mlsanity.com/paper/2010.11223/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2020.

## Built on by (most cited first, 30 of 38)

- [Human-Timescale Adaptation in an Open-Ended Task Space](https://mlsanity.com/paper/2301.07608/) (2023)
- [General-Purpose In-Context Learning by Meta-Learning Transformers](https://mlsanity.com/paper/2212.04458/) (2022)
- [Alchemy: A benchmark and analysis toolkit for meta-reinforcement learning agents](https://mlsanity.com/paper/2102.02926/) (2021)
- [LMAct: A Benchmark for In-Context Imitation Learning with Long Multimodal Demonstrations](https://mlsanity.com/paper/2412.01441/) (2024)
- [Learning Universal Predictors](https://mlsanity.com/paper/2401.14953/) (2024)
- [Bayes in the age of intelligent machines](https://mlsanity.com/paper/2311.10206/) (2023)
- [Memory-Based Meta-Learning on Non-Stationary Distributions](https://mlsanity.com/paper/2302.03067/) (2023)
- [In-context learning agents are asymmetric belief updaters](https://mlsanity.com/paper/2402.03969/) (2024)
- [Recurrent networks, hidden states and beliefs in partially observable environments](https://mlsanity.com/paper/2208.03520/) (2022)
- [What Should Embeddings Embed? Autoregressive Models Represent Latent Generating Distributions](https://mlsanity.com/paper/2406.03707/) (2024)
- [Learning Robust Real-Time Cultural Transmission without Human Data](https://mlsanity.com/paper/2203.00715/) (2022)
- [Simplex Neural Population Learning: Any-Mixture Bayes-Optimality in Symmetric Zero-sum Games](https://mlsanity.com/paper/2205.15879/) (2022)
- [In-context learning and Occam's razor](https://mlsanity.com/paper/2410.14086/) (2024)
- [Model-Free Risk-Sensitive Reinforcement Learning](https://mlsanity.com/paper/2111.02907/) (2021)
- [Learning Causal Overhypotheses through Exploration in Children and Computational Models](https://mlsanity.com/paper/2202.10430/) (2022)
- [Minimax-Bayes Reinforcement Learning](https://mlsanity.com/paper/2302.10831/) (2023)
- [MONGOOSE: Path-wise Smooth Bayesian Optimisation via Meta-learning](https://mlsanity.com/paper/2302.11533/) (2023)
- [Understanding Prompt Tuning and In-Context Learning via Meta-Learning](https://mlsanity.com/paper/2505.17010/) (2025)
- [Transformers for Supervised Online Continual Learning](https://mlsanity.com/paper/2403.01554/) (2024)
- [ATLAS: Active Theory Learning for Automated Science](https://mlsanity.com/paper/2606.12386/) (2026)
- [Planning to the Information Horizon of BAMDPs via Epistemic State Abstraction](https://mlsanity.com/paper/2210.16872/) (2022)
- [BAMDP Shaping: a Unified Framework for Intrinsic Motivation and Reward Shaping](https://mlsanity.com/paper/2409.05358/) (2024)
- [Why is prompting hard? Understanding prompts on binary sequence predictors](https://mlsanity.com/paper/2502.10760/) (2025)
- [On Uncertainty Quantification for Near-Bayes Optimal Algorithms](https://mlsanity.com/paper/2403.19381/) (2024)
- [Position: agentic AI orchestration should be Bayes-consistent](https://mlsanity.com/paper/2605.00742/) (2026)
- [Emergent behavior and neural dynamics in artificial agents tracking turbulent plumes](https://mlsanity.com/paper/2109.12434/) (2021)
- [Doing the right thing for the right reason: Evaluating artificial moral cognition by probing cost insensitivity](https://mlsanity.com/paper/2305.18269/) (2023)
- [Modeling Human Behavior Part I -- Learning and Belief Approaches](https://mlsanity.com/paper/2205.06485/) (2022)
- [Beyond Bayes-optimality: meta-learning what you know you don't know](https://mlsanity.com/paper/2209.15618/) (2022)
- [A Metalearned Neural Circuit for Nonparametric Bayesian Inference](https://mlsanity.com/paper/2311.14601/) (2023)

## Abstract (arXiv)

Memory-based meta-learning is a powerful technique to build agents that adapt fast to any task within a target distribution. A previous theoretical study has argued that this remarkable performance is because the meta-training protocol incentivises agents to behave Bayes-optimally. We empirically investigate this claim on a number of prediction and bandit tasks. Inspired by ideas from theoretical computer science, we show that meta-learned and Bayes-optimal agents not only behave alike, but they even share a similar computational structure, in the sense that one agent system can approximately simulate the other. Furthermore, we show that Bayes-optimal agents are fixed points of the meta-learning dynamics. Our results suggest that memory-based meta-learning might serve as a general technique for numerically approximating Bayes-optimal agents - that is, even for task distributions for which we currently don't possess tractable models.