As data-driven methods are deployed in real-world settings, the processes that generate the observed data will often react to the decisions of the learner. For example, a data source may have some incentive for the algorithm to provide a particular label (e.g. approve a bank loan), and manipulate their features accordingly. Work in strategic classification and decision-dependent distributions seeks to characterize the closed-loop behavior of deploying learning algorithms by explicitly considering the effect of the classifier on the underlying data distribution. More recently, works in performative prediction seek to classify the closed-loop behavior by considering general properties of the mapping from classifier to data distribution, rather than an explicit form. Building on this notion, we analyze repeated risk minimization as the perturbed trajectories of the gradient flows of performative risk minimization. We consider the case where there may be multiple local minimizers of performative risk, motivated by real world situations where the initial conditions may have significant impact on the long-term behavior of the system. As a motivating example, we consider a company whose current employee demographics affect the applicant pool they interview: the initial demographics of the company can affect the long-term hiring policies of the company. We provide sufficient conditions to characterize the region of attraction for the various equilibria in this settings. Additionally, we introduce the notion of performative alignment, which provides a geometric condition on the convergence of repeated risk minimization to performative risk minimizers.
翻译:随着数据驱动方法在现实世界环境中的部署,生成观察到的数据的过程往往会对学习者的决定作出反应。例如,数据源可能会对算法提供特定标签(例如批准银行贷款)并相应调整其特征具有一定的动力。战略分类和根据决定的分布工作试图通过明确考虑分类者对基本数据分布的影响来说明部署学习算法的闭路行为。最近,实绩预测工作试图通过考虑从分类到数据分布的绘图的一般特性而不是明确的形式来分类闭路行为。基于这一概念,我们分析反复的风险最小化,作为递增递增递增风险风险最小化的轨迹(例如,批准银行贷款),并相应调整其特征。我们考虑的情况是,可能存在多种当地最低性风险最小化风险最小化行为,其动机是明确考虑分类者对系统长期最小化行为的影响。作为一个激励性的例子,我们认为,一个其当前雇员人口构成影响其面试对象群群的一般特性的公司:公司初始人口统计学状况可以影响长期风险趋同度,从而影响企业的吸引力。我们考虑,因此,在公司中引入了长期的弹性组合政策。