The choice to participate in a data-driven service, often made on the basis of quality of that service, influences the ability of the service to learn and improve. We study the participation and retraining dynamics that arise when both the learners and sub-populations of users are \emph{risk-reducing}, which cover a broad class of updates including gradient descent, multiplicative weights, etc. Suppose, for example, that individuals choose to spend their time amongst social media platforms proportionally to how well each platform works for them. Each platform also gathers data about its active users, which it uses to update parameters with a gradient step. For this example and for our general class of dynamics, we show that the only asymptotically stable equilibria are segmented, with sub-populations allocated to a single learner. Under mild assumptions, the utilitarian social optimum is a stable equilibrium. In contrast to previous work, which shows that repeated risk minimization can result in representation disparity and high overall loss for a single learner \citep{hashimoto2018fairness,miller2021outside}, we find that repeated myopic updates with multiple learners lead to better outcomes. We illustrate the phenomena via a simulated example initialized from real data.

翻译：参与数据驱动服务的选择（通常基于该服务质量）会影响服务学习与改进的能力。我们研究了当学习器与用户子群体均为"风险降低"（涵盖梯度下降、乘法权重等广泛更新类别）时所引发的参与与重训练动态。例如，假设个体根据社交媒体平台对其工作效果的优劣比例分配时间。每个平台同时收集其活跃用户的数据，并通过梯度步骤更新参数。针对此例及我们的一般动态类别，我们证明唯一渐近稳定的均衡是细分状态，即子群体被分配到单一学习器。在温和假设下，功利主义社会最优解是一个稳定均衡。与以往表明重复风险最小化可能导致单个学习器出现表征差异和高总体损失的研究不同 \citep{hashimoto2018fairness,miller2021outside}，我们发现多个学习器重复短视更新能带来更优结果。我们通过基于真实数据初始化的模拟示例说明了这一现象。