Higher-Order Approximate Relational Refinement Types for Mechanism Design and Differential Privacy

TL;DR

This paper introduces a new relational refinement type system, HOARe^2, for verifying incentive properties and differential privacy in mechanism design, enabling formal verification of complex probabilistic properties.

Contribution

The paper presents HOARe^2, a sound type system that models relational properties in probabilistic computations, including differential privacy, and demonstrates its effectiveness on complex mechanism design examples.

Findings

HOARe^2 correctly models (ε,δ)-differential privacy.

It subsumes existing systems like DFuzz.

Successfully verifies mechanisms like auctions and aggregative games.

Abstract

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 $\mathsf{HOARe}^2$, for verifying mechanism design and differential privacy. We show that $\mathsf{HOARe}^2$ 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 $\mathsf{HOARe}^2$ and use it to verify challenging examples of mechanism design, including auctions and aggregative games, and new proposed examples from differential privacy.