Payment Rules through Discriminant-Based Classifiers

In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex post regret, we are able to adapt statistical machine learning techniques to the design of payment rules. This computational approach to mechanism design is applicable to domains with multi-dimensional types and situations where computational efficiency is a concern. Specifically, given an outcome rule and access to a type distribution, we train a support vector machine with a specific structure imposed on the discriminant function, such that it implicitly learns a corresponding payment rule with desirable incentive properties. We extend the framework to adopt succinct k-wise dependent valuations, leveraging a connection with maximum a posteriori assignment on Markov networks to enable training to scale up to settings with a large number of items; we evaluate this construction in the case where k=2. We present applications to multiparameter combinatorial auctions with approximate winner determination, and the assignment problem with an egalitarian outcome rule. Experimental results demonstrate that the construction produces payment rules with low ex post regret, and that penalizing classification error is effective in preventing failures of ex post individual rationality.