# Learning Losses for Strategic Classification

arXiv: https://arxiv.org/abs/2203.13421 · HTML: https://mlsanity.com/paper/2203.13421/

## Key facts

- Cited by 22 papers in the map (data through 7 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 25 Mar 2022.

## Builds on (most cited first, 13 of 13)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [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)
- [VC Classes are Adversarially Robustly Learnable, but Only Improperly](https://mlsanity.com/paper/1902.04217/) (2019)
- [The Disparate Effects of Strategic Manipulation](https://mlsanity.com/paper/1808.08646/) (2018)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [Sample compression schemes for VC classes](https://mlsanity.com/paper/1503.06960/) (2015)
- [Maximizing Welfare with Incentive-Aware Evaluation Mechanisms](https://mlsanity.com/paper/2011.01956/) (2020)
- [Decisions, Counterfactual Explanations and Strategic Behavior](https://mlsanity.com/paper/2002.04333/) (2020)
- [Adversarially Robust Learning with Unknown Perturbation Sets](https://mlsanity.com/paper/2102.02145/) (2021)

## Built on by (most cited first, 22 of 22)

- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [Strategic Classification under Unknown Personalized Manipulation](https://mlsanity.com/paper/2305.16501/) (2023)
- [Fundamental Bounds on Online Strategic Classification](https://mlsanity.com/paper/2302.12355/) (2023)
- [Learnability Gaps of Strategic Classification](https://mlsanity.com/paper/2402.19303/) (2024)
- [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)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [Learning under Imitative Strategic Behavior with Unforeseeable Outcomes](https://mlsanity.com/paper/2405.01797/) (2024)
- [Strategic Littlestone Dimension: Improved Bounds on Online Strategic Classification](https://mlsanity.com/paper/2407.11619/) (2024)
- [PAC Learning with Improvements](https://mlsanity.com/paper/2503.03184/) (2025)
- [Who's Gaming the System? A Causally-Motivated Approach for Detecting Strategic Adaptation](https://mlsanity.com/paper/2412.02000/) (2024)
- [Should Decision-Makers Reveal Classifiers in Online Strategic Classification?](https://mlsanity.com/paper/2506.01936/) (2025)
- [Strategic Classification with Randomised Classifiers](https://mlsanity.com/paper/2502.01313/) (2025)
- [Strategic Classification with Non-Linear Classifiers](https://mlsanity.com/paper/2505.23443/) (2025)
- [Adversaries With Incentives: A Strategic Alternative to Adversarial Robustness](https://mlsanity.com/paper/2406.11458/) (2024)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
- [Conservative classifiers do consistently well with improving agents: characterizing statistical and online learning](https://mlsanity.com/paper/2506.05252/) (2025)
- [PAC Learnability in the Presence of Performativity](https://mlsanity.com/paper/2510.08335/) (2025)
- [On Randomized Algorithms in Online Strategic Classification](https://mlsanity.com/paper/2602.06257/) (2026)
- [Online Learning with Improving Agents: Multiclass, Budgeted Agents and Bandit Learners](https://mlsanity.com/paper/2602.17103/) (2026)
- [Revealing Positive and Negative Role Models to Help People Make Good Decisions](https://mlsanity.com/paper/2603.02495/) (2026)
- [Strategic PAC Learnability via Geometric Definability](https://mlsanity.com/paper/2605.13426/) (2026)

## Abstract (arXiv)

Strategic classification, i.e. classification under possible strategic manipulations of features, has received a lot of attention from both the machine learning and the game theory community. Most works focus on analysing properties of the optimal decision rule under such manipulations. In our work we take a learning theoretic perspective, focusing on the sample complexity needed to learn a good decision rule which is robust to strategic manipulation. We perform this analysis by introducing a novel loss function, the strategic manipulation loss, which takes into account both the accuracy of the final decision rule and its vulnerability to manipulation. We analyse the sample complexity for a known graph of possible manipulations in terms of the complexity of the function class and the manipulation graph. Additionally, we initialize the study of learning under unknown manipulation capabilities of the involved agents. Using techniques from transfer learning theory, we define a similarity measure for manipulation graphs and show that learning outcomes are robust with respect to small changes in the manipulation graph. Lastly, we analyse the (sample complexity of) learning of the manipulation capability of agents with respect to this similarity measure, providing novel guarantees for strategic classification with respect to an unknown manipulation graph.