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Higher-Order Approximate Relational Refinement Types for Mechanism Design and Differential Privacy
Gilles Barthe, Marco Gaboardi, Emilio Jesús Gallego Arias, Justin Hsu, Aaron Roth, Pierre-Yves Strub
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Mechanism design is the study of algorithm design in which the inputs to the algorithm are controlled by strategic agents, who must be incentivized to faithfully report them. Unlike typical programmatic properties, it is not sufficient for algorithms to merely satisfy the property---incentive properties are only useful if the strategic agents also believe this fact. Verification is an attractive way to convince agents that the incentive properties actually hold, but mechanism design poses several unique challenges: interesting properties can be sophisticated relational properties of probabilistic computations involving expected values, and mechanisms may rely on other probabilistic properties, like differential privacy, to achieve their goals. We introduce a relational refinement type system, called 𝖧𝖮𝖠𝖱𝖾², for verifying mechanism design and differential privacy. We show that 𝖧𝖮𝖠𝖱𝖾² is sound w.r.t. a denotational semantics, and correctly models (ϵ,δ)-differential privacy; moreover, we show that it subsumes DFuzz, an existing linear dependent type system for differential privacy. Finally, we develop an SMT-based implementation of 𝖧𝖮𝖠𝖱𝖾² and use it to verify challenging examples of mechanism design, including auctions and aggregative games, and new proposed examples from differential privacy.
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