Higher-Order Approximate Relational Refinement Types for Mechanism Design and Differential Privacy
- 14 January 2015
- conference paper
- conference paper
- Published by Association for Computing Machinery (ACM) in Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Abstract
Mechanism design is the study of algorithm design where 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 (epsilon,delta)-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.Keywords
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Funding Information
- Seventh Framework Programme (272487)
- Division of Computer and Network Systems (CNS-1065060)
- Ministerio de Economía y Competitividad (TIN2012-39391-C04-01)
- Fundación Caja Madrid (S2009TIC-1465)
This publication has 49 references indexed in Scilit:
- Idris, a general-purpose dependently typed programming language: Design and implementationJournal of Functional Programming, 2013
- Privacy and mechanism designACM SIGecom Exchanges, 2013
- Embedded Probabilistic ProgrammingLecture Notes in Computer Science, 2009
- Reducing mechanism design to algorithm design via machine learningJournal of Computer and System Sciences, 2008
- Truthful approximation mechanisms for restricted combinatorial auctionsGames and Economic Behavior, 2008
- Differential Privacy: A Survey of ResultsPublished by Springer Science and Business Media LLC ,2008
- Differential PrivacyLecture Notes in Computer Science, 2006
- Calibrating Noise to Sensitivity in Private Data AnalysisLecture Notes in Computer Science, 2006
- Epigram: Practical Programming with Dependent TypesLecture Notes in Computer Science, 2005
- A categorical approach to probability theoryPublished by Springer Science and Business Media LLC ,1982