Incentive-Aware Learning for Large Markets

In a typical learning problem, one key step is to use training data to pick one model from a collection of models that optimizes an objective function. In many multi-agent settings, the training data is generated through the actions of the agents, and the model is used to make a decision (e.g., how to sell an item) that affects the agents. An illustrative example of this is the problem of learning the reserve price in an auction. In such cases, the agents have an incentive to influence the training data (e.g., by manipulating their bids in the case of an auction) to game the system and achieve a more favorable outcome. In this paper, we study such incentive-aware learning problem in a general setting and show that it is possible to approximately optimize the objective function under two assumptions: (i) each individual agent is a "small" (part of the market); and (ii) there is a cost associated with manipulation. For our illustrative application, this nicely translates to a mechanism for setting approximately optimal reserve prices in auctions where no individual agent has significant market share. For this application, we also show that the second assumption (that manipulations are costly) is not necessary since we can "perturb" any auction to make it costly for the agents to manipulate.