Probably Approximately Efficient Combinatorial Auctions via Machine Learning

A well-known problem in combinatorial auctions (CAs) is that the value space grows exponentially in the number of goods, which often puts a large burden on the bidders and on the auctioneer. In this paper, we introduce a new design paradigm for CAs based on machine learning (ML). Bidders report their values (bids) to a proxy agent by answering a small number of value queries. The proxy agent then uses an ML algorithm to generalize from those bids to the whole value space, and the efficient allocation is computed based on the generalized valuations. We introduce the concept of probably approximate efficiency (PAE) to measure the efficiency of our new ML-based auctions, and we formally show how the generelizability of an ML algorithm relates to the efficiency loss incurred by the corresponding ML-based auction. To instantiate our paradigm, we use support vector regression (SVR) as the ML algorithm, which enables us to keep the winner determination problem of the CA tractable. Different parameters of the SVR algorithm allow us to trade off the expressiveness, economic efficiency, and computational efficiency of the CA. Finally, we demonstrate experimentally that, even with a small number of bids, our ML-based auctions are highly efficient with high probability.