Payment Rules for Combinatorial Auctions via Structural Support Vector Machines

Given an optimal solution to the winner determination problem of a combinatorial auction, standard approaches provide exact incentive compatibility. Even here, significant economic concerns typically preclude these approaches. For large combinatorial auction problems, however, winner determination can only be solved approximately due to its high computational complexity, and the design of appropriate payment rules for suboptimal winner determination remains a significant open problem. In this paper, we advocate the use of structural support vector machines to solve this pricing problem. The output of a winner determination algorithm, i.e., the allocation rule, is viewed as training data for a classification problem with distinct classes, each corresponding to the different bundles that can be allocated to an agent. The decision boundaries of a trained classifier are then used to construct a payment rule. An exact classifier produces a payment rule that together with the allocation rule yields a dominant-strategy incentive compatible mechanism. Moreover, minimizing regularized empirical error in training corresponds to minimizing a regularized upper bound on ex post regret for truthful bidding, allowing the approach to extend to non-implementable allocation rules.