Towards a theory of incentives in machine learning

Abstract

The connection between machine learning and economics is, I feel, quite natural. There is a growing body of work that lies at the intersection of the two fields, but most of this work focuses on applying machine learning paradigms to economic problems. Examples include prediction of consumer behavior [Kalai 2003; Beigman and Vohra 2006], automated design of voting rules [Procaccia et al. 2007; Procaccia et al. 2008], and reduction of mechanism design problems to standard algorithmic questions [Balcan et al. 2005]. Nevertheless, there are preciously few papers investigating the incentives that, in some settings, govern the learning process itself (see, e.g., Perote and PerotePena [2004], Dalvi et al. [2004]); none of them do so in a general machine learning framework. Where, indeed, do strategic considerations come into play in the learning world? In general, a machine learning algorithm receives a (small but hopefully representative) training set consisting of points sampled from an input space and labeled according to some target function; the algorithm outputs a hypothesis that is presumably close to the target function. For simplicity, consider a basic setup where n selfish agents control n disjoint subsets of the input space. The label of each point in the training set is reported by the agent that controls it (whereas the identities of the points controlled by an agent are common knowledge). Crucially, each agent is interested only in the accuracy of the generated hypothesis on its own part of the input space. An agent can influence the outcome of the learning process by misreporting the labels of the points under its control. The above strategic setup seems relevant, for instance, in the context of decisions taken by a central bank, such as the European Central Bank (ECB). The governing council of the central bank collects information from national bankers (the agents), who in turn gather data on different economic parameters by means of their own institutions. The central bank decides on an economic policy (hypothesis) by using, say, regression learning on the examples provided by the national bankers. The national bankers may thus be motivated to manipulate their portion of the data