# Beyond Bayes-optimality: meta-learning what you know you don't know

arXiv: https://arxiv.org/abs/2209.15618 · HTML: https://mlsanity.com/paper/2209.15618/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 73 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 22 of 22)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [RL2: Fast Reinforcement Learning via Slow Reinforcement Learning](https://mlsanity.com/paper/1611.02779/) (2016)
- [Learning to reinforcement learn](https://mlsanity.com/paper/1611.05763/) (2016)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Risk-sensitive Reinforcement Learning](https://mlsanity.com/paper/1311.2097/) (2013)
- [Epistemic Neural Networks](https://mlsanity.com/paper/2107.08924/) (2021)
- [Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift](https://mlsanity.com/paper/2206.13089/) (2022)
- [Uncertainty-Aware Reinforcement Learning for Collision Avoidance](https://mlsanity.com/paper/1702.01182/) (2017)
- [Meta-learning of Sequential Strategies](https://mlsanity.com/paper/1905.03030/) (2019)
- [Risk-Averse Offline Reinforcement Learning](https://mlsanity.com/paper/2102.05371/) (2021)
- [Risk-Sensitive Reinforcement Learning: Near-Optimal Risk-Sample Tradeoff in Regret](https://mlsanity.com/paper/2006.13827/) (2020)
- [Meta-trained agents implement Bayes-optimal agents](https://mlsanity.com/paper/2010.11223/) (2020)
- [Improving Robustness via Risk Averse Distributional Reinforcement Learning](https://mlsanity.com/paper/2005.00585/) (2020)
- [Planning with Information-Processing Constraints and Model Uncertainty in Markov Decision Processes](https://mlsanity.com/paper/1604.02080/) (2016)
- [Semi-supervised novelty detection using ensembles with regularized disagreement](https://mlsanity.com/paper/2012.05825/) (2020)
- [Model-Free Risk-Sensitive Reinforcement Learning](https://mlsanity.com/paper/2111.02907/) (2021)
- [An Information-Theoretic Optimality Principle for Deep Reinforcement Learning](https://mlsanity.com/paper/1708.01867/) (2017)
- [Learning to Be Cautious](https://mlsanity.com/paper/2110.15907/) (2021)

## Built on by (most cited first, 1 of 1)

- [Next-Token Prediction Should be Ambiguity-Sensitive: A Meta-Learning Perspective](https://mlsanity.com/paper/2506.16288/) (2025)

## Abstract (arXiv)

Meta-training agents with memory has been shown to culminate in Bayes-optimal agents, which casts Bayes-optimality as the implicit solution to a numerical optimization problem rather than an explicit modeling assumption. Bayes-optimal agents are risk-neutral, since they solely attune to the expected return, and ambiguity-neutral, since they act in new situations as if the uncertainty were known. This is in contrast to risk-sensitive agents, which additionally exploit the higher-order moments of the return, and ambiguity-sensitive agents, which act differently when recognizing situations in which they lack knowledge. Humans are also known to be averse to ambiguity and sensitive to risk in ways that aren't Bayes-optimal, indicating that such sensitivity can confer advantages, especially in safety-critical situations. How can we extend the meta-learning protocol to generate risk- and ambiguity-sensitive agents? The goal of this work is to fill this gap in the literature by showing that risk- and ambiguity-sensitivity also emerge as the result of an optimization problem using modified meta-training algorithms, which manipulate the experience-generation process of the learner. We empirically test our proposed meta-training algorithms on agents exposed to foundational classes of decision-making experiments and demonstrate that they become sensitive to risk and ambiguity.