# The Value of Mechanistic Priors in Sequential Decision Making

arXiv: https://arxiv.org/abs/2605.10018 · HTML: https://mlsanity.com/paper/2605.10018/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 16 of 16)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Meta-Thompson Sampling](https://mlsanity.com/paper/2102.06129/) (2021)
- [Thompson Sampling for Complex Bandit Problems](https://mlsanity.com/paper/1311.0466/) (2013)
- [LISA: Learning Interpretable Skill Abstractions from Language](https://mlsanity.com/paper/2203.00054/) (2022)
- [On the Prior Sensitivity of Thompson Sampling](https://mlsanity.com/paper/1506.03378/) (2015)
- [On Bits and Bandits: Quantifying the Regret-Information Trade-off](https://mlsanity.com/paper/2405.16581/) (2024)

## Abstract (arXiv)

Hybrid mechanistic models, physical priors with learned residuals, promise to reduce the data required for good decisions, but have no computable criterion to test this. We characterize the value of mechanistic priors in sequential decision-making within both asymptotic and burn-in regimes. To formalize this, we introduce the mechanistic information of a model: the mutual information between the model's recommended policy hatπ and the true optimal policy π^*, bounded via a centered, occupancy-weighted bias. In the asymptotic regime (large N), matched bounds reveal that Bayesian regret scales with the residual entropy Hmech, delivering a theoretical sample complexity reduction of H(μ)/Hmech compared to an uninformed baseline. We further provide a computable pre-trial model certificate. Complementarily, in the clinically relevant burn-in regime (small N), we establish a lower bound on the penalty incurred by confidently wrong priors. We demonstrate both the asymptotic and burn-in bounds on an illustrative in-silico 5-fluorouracil (5-FU) chemotherapy plant whose structure follows published FOLFOX pharmacokinetics. The hybrid prior reduces cumulative regret by 1.79× relative to standard body-surface-area dosing and 1.85× relative to an uninformed learner, and remains below both under every calibration bias tested. Finally, we show that priors sensitive to distribution shift can lose half of their mechanistic information under a small distribution shift, motivating physically grounded priors for safety-critical applications.