Dispersion for Data-Driven Algorithm Design, Online Learning, and Private Optimization

Data-driven algorithm design, that is, choosing the best algorithm for a specific application, is a crucial problem in modern data science. Practitioners often optimize over a parameterized algorithm family, tuning parameters based on problems from their domain. These procedures have historically come with no guarantees, though a recent line of work studies algorithm selection from a theoretical perspective. We advance the foundations of this field in several directions: we analyze online algorithm selection, where problems arrive one-by-one and the goal is to minimize regret, and private algorithm selection, where the goal is to find good parameters over a set of problems without revealing sensitive information contained therein. We study important algorithm families, including SDP-rounding schemes for problems formulated as integer quadratic programs, and greedy techniques for canonical subset selection problems. In these cases, the algorithm's performance is a volatile and piecewise Lipschitz function of its parameters, since tweaking the parameters can completely change the algorithm's behavior. We give a sufficient and general condition, dispersion, defining a family of piecewise Lipschitz functions that can be optimized online and privately, which includes the functions measuring the performance of the algorithms we study. Intuitively, a set of piecewise Lipschitz functions is dispersed if no small region contains many of the functions' discontinuities. We present general techniques for online and private optimization of the sum of dispersed piecewise Lipschitz functions. We improve over the best-known regret bounds for a variety of problems, prove regret bounds for problems not previously studied, and give matching lower bounds. We also give matching upper and lower bounds on the utility loss due to privacy. Moreover, we uncover dispersion in auction design and pricing problems

Differential Privacy and the Fat-Shattering Dimension of Linear Queries

In this paper, we consider the task of answering linear queries under the constraint of differential privacy. This is a general and well-studied class of queries that captures other commonly studied classes, including predicate queries and histogram queries. We show that the accuracy to which a set of linear queries can be answered is closely related to its fat-shattering dimension, a property that characterizes the learnability of real-valued functions in the agnostic-learning setting.Comment: Appears in APPROX 201

Privacy Management and Optimal Pricing in People-Centric Sensing

With the emerging sensing technologies such as mobile crowdsensing and Internet of Things (IoT), people-centric data can be efficiently collected and used for analytics and optimization purposes. This data is typically required to develop and render people-centric services. In this paper, we address the privacy implication, optimal pricing, and bundling of people-centric services. We first define the inverse correlation between the service quality and privacy level from data analytics perspectives. We then present the profit maximization models of selling standalone, complementary, and substitute services. Specifically, the closed-form solutions of the optimal privacy level and subscription fee are derived to maximize the gross profit of service providers. For interrelated people-centric services, we show that cooperation by service bundling of complementary services is profitable compared to the separate sales but detrimental for substitutes. We also show that the market value of a service bundle is correlated with the degree of contingency between the interrelated services. Finally, we incorporate the profit sharing models from game theory for dividing the bundling profit among the cooperative service providers.Comment: 16 page