# Model-Value Inconsistency as a Signal for Epistemic Uncertainty

arXiv: https://arxiv.org/abs/2112.04153 · HTML: https://mlsanity.com/paper/2112.04153/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 106 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 30 of 61)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Unifying Count-Based Exploration and Intrinsic Motivation](https://mlsanity.com/paper/1606.01868/) (2016)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Leveraging Procedural Generation to Benchmark Reinforcement Learning](https://mlsanity.com/paper/1912.01588/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Reinforcement Learning with Unsupervised Auxiliary Tasks](https://mlsanity.com/paper/1611.05397/) (2016)
- [dm_control: Software and Tasks for Continuous Control](https://mlsanity.com/paper/2006.12983/) (2020)
- [Planning to Explore via Self-Supervised World Models](https://mlsanity.com/paper/2005.05960/) (2020)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [Self-Supervised Exploration via Disagreement](https://mlsanity.com/paper/1906.04161/) (2019)
- [Safe and Efficient Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1606.02647/) (2016)
- [Stochastic Latent Actor-Critic: Deep Reinforcement Learning with a Latent Variable Model](https://mlsanity.com/paper/1907.00953/) (2019)
- [Model-Ensemble Trust-Region Policy Optimization](https://mlsanity.com/paper/1802.10592/) (2018)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Action-Conditional Video Prediction using Deep Networks in Atari Games](https://mlsanity.com/paper/1507.08750/) (2015)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [Sample-Efficient Reinforcement Learning with Stochastic Ensemble Value Expansion](https://mlsanity.com/paper/1807.01675/) (2018)
- [Model-Based Value Estimation for Efficient Model-Free Reinforcement Learning](https://mlsanity.com/paper/1803.00101/) (2018)

## Built on by (most cited first, 6 of 6)

- [Human-Timescale Adaptation in an Open-Ended Task Space](https://mlsanity.com/paper/2301.07608/) (2023)
- [Cross-Domain Policy Adaptation via Value-Guided Data Filtering](https://mlsanity.com/paper/2305.17625/) (2023)
- [Learning General World Models in a Handful of Reward-Free Deployments](https://mlsanity.com/paper/2210.12719/) (2022)
- [ReLU to the Rescue: Improve Your On-Policy Actor-Critic with Positive Advantages](https://mlsanity.com/paper/2306.01460/) (2023)
- [Biased Dreams: Limitations to Epistemic Uncertainty Quantification in Latent Dynamics Models](https://mlsanity.com/paper/2604.25416/) (2026)
- [Contextual Similarity Distillation: Ensemble Uncertainties with a Single Model](https://mlsanity.com/paper/2503.11339/) (2025)

## Abstract (arXiv)

Using a model of the environment and a value function, an agent can construct many estimates of a state's value, by unrolling the model for different lengths and bootstrapping with its value function. Our key insight is that one can treat this set of value estimates as a type of ensemble, which we call an implicit value ensemble (IVE). Consequently, the discrepancy between these estimates can be used as a proxy for the agent's epistemic uncertainty; we term this signal model-value inconsistency or self-inconsistency for short. Unlike prior work which estimates uncertainty by training an ensemble of many models and/or value functions, this approach requires only the single model and value function which are already being learned in most model-based reinforcement learning algorithms. We provide empirical evidence in both tabular and function approximation settings from pixels that self-inconsistency is useful (i) as a signal for exploration, (ii) for acting safely under distribution shifts, and (iii) for robustifying value-based planning with a learned model.