# Energy Shields for Fairness

arXiv: https://arxiv.org/abs/2605.24926 · HTML: https://mlsanity.com/paper/2605.24926/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 24 May 2026.

## Builds on (most cited first, 24 of 24)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [Algorithms for Fairness in Sequential Decision Making](https://mlsanity.com/paper/1901.08568/) (2019)
- [Safe Reinforcement Learning via Shielding under Partial Observability](https://mlsanity.com/paper/2204.00755/) (2022)
- [Probabilistic Verification of Fairness Properties via Concentration](https://mlsanity.com/paper/1812.02573/) (2018)
- [Safe Reinforcement Learning via Probabilistic Logic Shields](https://mlsanity.com/paper/2303.03226/) (2023)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [Justicia: A Stochastic SAT Approach to Formally Verify Fairness](https://mlsanity.com/paper/2009.06516/) (2020)
- [Certifying Robustness to Programmable Data Bias in Decision Trees](https://mlsanity.com/paper/2110.04363/) (2021)
- [Probabilistic Verification of Neural Networks Against Group Fairness](https://mlsanity.com/paper/2107.08362/) (2021)
- [Runtime Monitoring of Dynamic Fairness Properties](https://mlsanity.com/paper/2305.04699/) (2023)
- [Convergence Rates for Stochastic Approximation: Biased Noise with Unbounded Variance, and Applications](https://mlsanity.com/paper/2312.02828/) (2023)
- [Real-time Stream-based Monitoring](https://mlsanity.com/paper/1711.03829/) (2017)
- [Remembering to Be Fair: Non-Markovian Fairness in Sequential Decision Making](https://mlsanity.com/paper/2312.04772/) (2023)
- [Certifying the Fairness of KNN in the Presence of Dataset Bias](https://mlsanity.com/paper/2307.08722/) (2023)
- [Fairness Shields: Safeguarding against Biased Decision Makers](https://mlsanity.com/paper/2412.11994/) (2024)
- [Stream-Based Monitoring of Algorithmic Fairness](https://mlsanity.com/paper/2501.18331/) (2025)
- [Monitoring Robustness and Individual Fairness](https://mlsanity.com/paper/2506.00496/) (2025)

## Abstract (arXiv)

Runtime fairness is not a one-time constraint but a dynamic property evaluated over a sequence of decisions. To ensure fairness at runtime, it is necessary to account for past decisions, information neglected by conventional, static classifiers. Traditional fairness shields enforce runtime fairness abruptly, by intervening deterministically whenever a sequence of decisions violates the target for a running fairness measure. This motivates our emphmain conceptual contribution: energy shields. An energy shield is a novel, lightweight, adaptive controller that monitors a sequence of decisions and intervenes probabilistically to ensure runtime fairness smoothly, by utilizing physics-inspired energy functions to nudge the sequence toward fairness: the more unfair the decisions, the stronger the nudging force becomes. This makes energy shields the emphfirst fairness shields to provide both short-term safety and long-term liveness guarantees. Safety ensures that the running fairness measure stays within a running target interval with high probability, and liveness ensures that the limit of the fairness measure lies within the limit target interval. Intuitively, the short-term specifies the tolerated fairness values and the long-term specifies the desired fairness values. We also provide a synthesis procedure for constructing the least intrusive energy shield for a given target specification, and demonstrate its efficiency experimentally. We evaluate our energy shields against existing fairness shields through the lens of short- and long-term fairness.