The Strategic Perceptron

TL;DR

This paper introduces a modified Perceptron algorithm that effectively learns linear classifiers in strategic settings where agents can manipulate their positions, ensuring bounded mistakes despite strategic behavior and unknown manipulation costs.

Contribution

It proposes a new Perceptron-style algorithm that handles strategic manipulation with bounded mistakes, even when manipulation costs are unknown and must be learned.

Findings

The modified algorithm achieves bounded mistakes with known manipulation costs.

It extends to scenarios with unknown costs by learning and refining cost estimates.

Demonstrates failure of classical Perceptron under strategic manipulation.

Abstract

The classical Perceptron algorithm provides a simple and elegant procedure for learning a linear classifier. In each step, the algorithm observes the sample's position and label and updates the current predictor accordingly if it makes a mistake. However, in presence of strategic agents that desire to be classified as positive and that are able to modify their position by a limited amount, the classifier may not be able to observe the true position of agents but rather a position where the agent pretends to be. Unlike the original setting with perfect knowledge of positions, in this situation the Perceptron algorithm fails to achieve its guarantees, and we illustrate examples with the predictor oscillating between two solutions forever, making an unbounded number of mistakes even though a perfect large-margin linear classifier exists. Our main contribution is providing a modified Perceptron-style algorithm which makes a bounded number of mistakes in presence of strategic agents with both $\ell_2$ and weighted $\ell_1$ manipulation costs. In our baseline model, knowledge of the manipulation costs (i.e., the extent to which an agent may manipulate) is assumed. In our most general model, we relax this assumption and provide an algorithm which learns and refines both the classifier and its cost estimates to achieve good mistake bounds even when manipulation costs are unknown.