We initiate a principled study of algorithmic collective action on digital platforms that deploy machine learning algorithms. We propose a simple theoretical model of a collective interacting with a firm's learning algorithm. The collective pools the data of participating individuals and executes an algorithmic strategy by instructing participants how to modify their own data to achieve a collective goal. We investigate the consequences of this model in three fundamental learning-theoretic settings: the case of a nonparametric optimal learning algorithm, a parametric risk minimizer, and gradient-based optimization. In each setting, we come up with coordinated algorithmic strategies and characterize natural success criteria as a function of the collective's size. Complementing our theory, we conduct systematic experiments on a skill classification task involving tens of thousands of resumes from a gig platform for freelancers. Through more than two thousand model training runs of a BERT-like language model, we see a striking correspondence emerge between our empirical observations and the predictions made by our theory. Taken together, our theory and experiments broadly support the conclusion that algorithmic collectives of exceedingly small fractional size can exert significant control over a platform's learning algorithm.

翻译：我们启动了对部署机器学习算法的数字平台上算法集体行动的严谨研究。我们提出了一个简单的理论模型，其中集体与公司的学习算法进行互动。该集体汇集参与个体的数据，并通过指导参与者如何修改自身数据以达成集体目标来执行算法策略。我们在三个基础学习理论场景中考察了该模型的后果：非参数最优学习算法、参数风险最小化以及基于梯度的优化。在每个场景中，我们设计了协调的算法策略，并刻画了作为集体规模函数的自然成功标准。为补充理论，我们在一项涉及自由职业者平台数万份简历的技能分类任务上进行了系统性实验。通过超过两千次BERT类语言模型的模型训练运行，我们的实证观察与理论预测之间呈现出显著的一致性。综合来看，我们的理论和实验广泛支持以下结论：具有极小比例的算法集体可以显著控制平台的学习算法。