# Strategic Classification with Randomised Classifiers

arXiv: https://arxiv.org/abs/2502.01313 · HTML: https://mlsanity.com/paper/2502.01313/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 14 of 14)

- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [The Disparate Effects of Strategic Manipulation](https://mlsanity.com/paper/1808.08646/) (2018)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [Strategic Classification Made Practical](https://mlsanity.com/paper/2103.01826/) (2021)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [The Role of Randomness and Noise in Strategic Classification](https://mlsanity.com/paper/2005.08377/) (2020)
- [Randomization matters. How to defend against strong adversarial attacks](https://mlsanity.com/paper/2002.11565/) (2020)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Learning Losses for Strategic Classification](https://mlsanity.com/paper/2203.13421/) (2022)
- [Strategic Classification with Graph Neural Networks](https://mlsanity.com/paper/2205.15765/) (2022)
- [One-Shot Strategic Classification Under Unknown Costs](https://mlsanity.com/paper/2311.02761/) (2023)
- [Bayesian Strategic Classification](https://mlsanity.com/paper/2402.08758/) (2024)

## Built on by (most cited first, 4 of 4)

- [Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification](https://mlsanity.com/paper/2505.05594/) (2025)
- [Ambiguous Strategic Classification](https://mlsanity.com/paper/2606.10137/) (2026)
- [Non-Linear Strategic Classification Made Practical](https://mlsanity.com/paper/2606.28204/) (2026)
- [Robust Strategic Classification under Decision-Dependent Cost Uncertainty](https://mlsanity.com/paper/2606.30136/) (2026)

## Abstract (arXiv)

We consider the problem of strategic classification, where a learner must build a model to classify agents based on features that have been strategically modified. Previous work in this area has concentrated on the case when the learner is restricted to deterministic classifiers. In contrast, we perform a theoretical analysis of an extension to this setting that allows the learner to produce a randomised classifier. We show that, under certain conditions, the optimal randomised classifier can achieve better accuracy than the optimal deterministic classifier, but under no conditions can it be worse. When a finite set of training data is available, we show that the excess risk of Strategic Empirical Risk Minimisation over the class of randomised classifiers is bounded in a similar manner as the deterministic case. In both the deterministic and randomised cases, the risk of the classifier produced by the learner converges to that of the corresponding optimal classifier as the volume of available training data grows. Moreover, this convergence happens at the same rate as in the i.i.d. case. Our findings are compared with previous theoretical work analysing the problem of strategic classification. We conclude that randomisation has the potential to alleviate some issues that could be faced in practice without introducing any substantial downsides.