# Bayesian Strategic Classification

arXiv: https://arxiv.org/abs/2402.08758 · HTML: https://mlsanity.com/paper/2402.08758/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [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)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [The Strategic Perceptron](https://mlsanity.com/paper/2008.01710/) (2020)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [Maximizing Welfare with Incentive-Aware Evaluation Mechanisms](https://mlsanity.com/paper/2011.01956/) (2020)
- [The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally](https://mlsanity.com/paper/1910.04123/) (2019)
- [The Role of Randomness and Noise in Strategic Classification](https://mlsanity.com/paper/2005.08377/) (2020)
- [Stateful Strategic Regression](https://mlsanity.com/paper/2106.03827/) (2021)
- [Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents](https://mlsanity.com/paper/2306.02704/) (2023)
- [Strategyproof Linear Regression in High Dimensions](https://mlsanity.com/paper/1805.10693/) (2018)
- [Optimal Decision Making Under Strategic Behavior](https://mlsanity.com/paper/1905.09239/) (2019)
- [Manipulation-Proof Machine Learning](https://mlsanity.com/paper/2004.03865/) (2020)
- [Bayesian Persuasion for Algorithmic Recourse](https://mlsanity.com/paper/2112.06283/) (2021)
- [Truthful Linear Regression](https://mlsanity.com/paper/1506.03489/) (2015)
- [Optimal approximation for unconstrained non-submodular minimization](https://mlsanity.com/paper/1905.12145/) (2019)
- [Screening with Disadvantaged Agents](https://mlsanity.com/paper/2305.18068/) (2023)

## Built on by (most cited first, 13 of 13)

- [The Double-Edged Sword of Behavioral Responses in Strategic Classification: Theory and User Studies](https://mlsanity.com/paper/2410.18066/) (2024)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
- [Strategic Classification with Randomised Classifiers](https://mlsanity.com/paper/2502.01313/) (2025)
- [Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification](https://mlsanity.com/paper/2505.05594/) (2025)
- [Explanation Design in Strategic Learning: Sufficient Explanations that Induce Non-harmful Responses](https://mlsanity.com/paper/2502.04058/) (2025)
- [The Disparate Effects of Partial Information in Bayesian Strategic Learning](https://mlsanity.com/paper/2506.00627/) (2025)
- [Revealing Positive and Negative Role Models to Help People Make Good Decisions](https://mlsanity.com/paper/2603.02495/) (2026)
- [Learning with Conflicts of Interest](https://mlsanity.com/paper/2605.15504/) (2026)
- [Off-Policy Evaluation with Strategic Agents via Local Disclosure](https://mlsanity.com/paper/2606.07308/) (2026)
- [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)
- [Information Design Against Gaming and Learning Adversaries](https://mlsanity.com/paper/2609.31643/) (2026)

## Abstract (arXiv)

In strategic classification, agents modify their features, at a cost, to ideally obtain a positive classification from the learner's classifier. The typical response of the learner is to carefully modify their classifier to be robust to such strategic behavior. When reasoning about agent manipulations, most papers that study strategic classification rely on the following strong assumption: agents fully know the exact parameters of the deployed classifier by the learner. This often is an unrealistic assumption when using complex or proprietary machine learning techniques in real-world prediction tasks. We initiate the study of partial information release by the learner in strategic classification. We move away from the traditional assumption that agents have full knowledge of the classifier. Instead, we consider agents that have a common distributional prior on which classifier the learner is using. The learner in our model can reveal truthful, yet not necessarily complete, information about the deployed classifier to the agents. The learner's goal is to release just enough information about the classifier to maximize accuracy. We show how such partial information release can, counter-intuitively, benefit the learner's accuracy, despite increasing agents' abilities to manipulate. We show that while it is intractable to compute the best response of an agent in the general case, there exist oracle-efficient algorithms that can solve the best response of the agents when the learner's hypothesis class is the class of linear classifiers, or when the agents' cost function satisfies a natural notion of submodularity as we define. We then turn our attention to the learner's optimization problem and provide both positive and negative results on the algorithmic problem of how much information the learner should release about the classifier to maximize their expected accuracy.