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We develop a versatile new methodology for multidimensional mechanism designthat incorporates side information about agent types with the bicriteria goalof generating high social welfare and high revenue simultaneously. Sideinformation can come from a variety of sources -- examples include advice froma domain expert, predictions from a machine-learning model trained onhistorical agent data, or even the mechanism designer's own gut instinct -- andin practice such sources are abundant. In this paper we adopt a prior-freeperspective that makes no assumptions on the correctness, accuracy, or sourceof the side information. First, we design a meta-mechanism that integratesinput side information with an improvement of the classical VCG mechanism. Thewelfare, revenue, and incentive properties of our meta-mechanism arecharacterized by a number of novel constructions we introduce based on thenotion of a weakest competitor, which is an agent that has the smallest impacton welfare. We then show that our meta-mechanism -- when carefully instantiated-- simultaneously achieves strong welfare and revenue guarantees that areparameterized by errors in the side information. When the side information ishighly informative and accurate, our mechanism achieves welfare and revenuecompetitive with the total social surplus, and its performance decayscontinuously and gradually as the quality of the side information decreases.Finally, we apply our meta-mechanism to a setting where each agent's type isdetermined by a constant number of parameters. Specifically, agent types lie onconstant-dimensional subspaces (of the potentially high-dimensional ambienttype space) that are known to the mechanism designer. We use our meta-mechanismto obtain the first known welfare and revenue guarantees in this setting.

Bicriteria Multidimensional Mechanism Design with Side Information