/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

The problem of privacy-preserving data analysis has a long history spanning multiple disciplines. As electronic data about individuals becomes increasingly detailed, and as technology enables ever more powerful collection and curation of these data, the need increases for a robust, meaningful, and mathematically rigorous definition of privacy, together with a computationally rich class of algorithms that satisfy this definition. Differential Privacy is such a definition.After motivating and discussing the meaning of differential privacy, the preponderance of this monograph is devoted to fundamental techniques for achieving differential privacy, and application of these techniques in creative combinations, using the query-release problem as an ongoing example. A key point is that, by rethinking the computational goal, one can often obtain far better results than would be achieved by methodically replacing each step of a non-private computation with a differentially private implementation. Despite some astonishingly powerful computational results, there are still fundamental limitations — not just on what can be achieved with differential privacy but on what can be achieved with any method that protects against a complete breakdown in privacy. Virtually all the algorithms discussed herein maintain differential privacy against adversaries of arbitrary computational power. Certain algorithms are computationally intensive, others are efficient. Computational complexity for the adversary and the algorithm are both discussed.We then turn from fundamentals to applications other than queryrelease, discussing differentially private methods for mechanism design and machine learning. The vast majority of the literature on differentially private algorithms considers a single, static, database that is subject to many analyses. Differential privacy in other models, including distributed databases and computations on data streams is discussed.Finally, we note that this work is meant as a thorough introduction to the problems and techniques of differential privacy, but is not intended to be an exhaustive survey — there is by now a vast amount of work in differential privacy, and we can cover only a small portion of it.

/pdf/the-algorithmic-foundations-of-differential-privacy-1n8bb9a7eo.pdf

The Algorithmic Foundations of Differential Privacy

Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.

/pdf/maximizing-the-spread-of-influence-through-a-social-network-47y1ehuvwi.pdf

Maximizing the Spread of Influence through a Social Network

We study the role that privacy-preserving algorithms, which prevent the leakage of specific information about participants, can play in the design of mechanisms for strategic agents, which must encourage players to honestly report information. Specifically, we show that the recent notion of differential privacv, in addition to its own intrinsic virtue, can ensure that participants have limited effect on the outcome of the mechanism, and as a consequence have limited incentive to lie. More precisely, mechanisms with differential privacy are approximate dominant strategy under arbitrary player utility functions, are automatically resilient to coalitions, and easily allow repeatability. We study several special cases of the unlimited supply auction problem, providing new results for digital goods auctions, attribute auctions, and auctions with arbitrary structural constraints on the prices. As an important prelude to developing a privacy-preserving auction mechanism, we introduce and study a generalization of previous privacy work that accommodates the high sensitivity of the auction setting, where a single participant may dramatically alter the optimal fixed price, and a slight change in the offered price may take the revenue from optimal to zero.

/pdf/mechanism-design-via-differential-privacy-z5vjyvpisy.pdf

Mechanism Design via Differential Privacy

A new era of theoretical computer science addresses fundamental problems about auctions, networks, and human behavior.

http://www.maths.lse.ac.uk/Personal/stengel/TEXTE/agt-stengel.pdf

Algorithmic Game Theory

We discuss the use of social networks in implementing viral marketing strategies. While influence maximization has been studied in this context (see Chapter 24 of [10]), we study revenue maximization, arguably, a more natural objective. In our model, a buyer's decision to buy an item is influenced by the set of other buyers that own the item and the price at which the item is offered.We focus on algorithmic question of finding revenue maximizing marketing strategies. When the buyers are completely symmetric, we can find the optimal marketing strategy in polynomial time. In the general case, motivated by hardness results, we investigate approximation algorithms for this problem. We identify a family of strategies called influence-and-exploit strategies that are based on the following idea: Initially influence the population by giving the item for free to carefully a chosen set of buyers. Then extract revenue from the remaining buyers using a 'greedy' pricing strategy. We first argue why such strategies are reasonable and then show how to use recently developed set-function maximization techniques to find the right set of buyers to influence.

/pdf/optimal-marketing-strategies-over-social-networks-484c6jyzva.pdf

Optimal marketing strategies over social networks

We study the classic mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known distribution. In single parameter settings (i.e., where each agent's preference is given by a single private value for being served and zero for not being served) this problem is solved [20]. Unfortunately, these single parameter optimal mechanisms are impractical and rarely employed [1], and furthermore the underlying economic theory fails to generalize to the important, relevant, and unsolved multi-dimensional setting (i.e., where each agent's preference is given by multiple values for each of the multiple services available) [25].In contrast to the theory of optimal mechanisms we develop a theory of sequential posted price mechanisms, where agents in sequence are offered take-it-or-leave-it prices. We prove that these mechanisms are approximately optimal in single-dimensional settings. These posted-price mechanisms avoid many of the properties of optimal mechanisms that make the latter impractical. Furthermore, these mechanisms generalize naturally to multi-dimensional settings where they give the first known approximations to the elusive optimal multi-dimensional mechanism design problem. In particular, we solve multi-dimensional multi-unit auction problems and generalizations to matroid feasibility constraints. The constant approximations we obtain range from 1.5 to 8. For all but one case, our posted price sequences can be computed in polynomial time.This work can be viewed as an extension and improvement of the single-agent algorithmic pricing work of [9] to the setting of multiple agents where the designer has combinatorial feasibility constraints on which agents can simultaneously obtain each service.

/pdf/multi-parameter-mechanism-design-and-sequential-posted-2u6j018uhp.pdf

Multi-parameter mechanism design and sequential posted pricing

The monopolist's theory of optimal single-item auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bidder and run the Vickrey auction than to run the optimal auction. These results hold for single-item auctions under the assumption that the agents' valuations are independently and identically drawn from a distribution that satisfies a natural (and prevalent) regularity condition.These fundamental guarantees for the Vickrey auction fail to hold in general single-parameter agent mechanism design problems. We give precise (and weak) conditions under which approximate analogs of these two results hold, thereby demonstrating that simple mechanisms remain almost optimal in quite general single-parameter agent settings.

/pdf/simple-versus-optimal-mechanisms-3a8ial4oqu.pdf

Simple versus optimal mechanisms

We consider the classical mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known distribution. In single-parameter settings (i.e., where each agent's preference is given by a single private value for being served and zero for not being served) this problem is solved. Unfortunately, these single parameter optimal mechanisms are impractical and rarely employed, and furthermore the underlying economic theory fails to generalize to the important, relevant, and unsolved multi-dimensional setting (i.e., where each agent's preference is given by multiple values for each of the multiple services available). In contrast to the theory of optimal mechanisms we develop a theory of sequential posted price mechanisms, where agents in sequence are offered take-it-or-leave-it prices. We prove that these mechanisms are approximately optimal in single-dimensional settings. These posted-price mechanisms avoid many of the properties of optimal mechanisms that make the latter impractical. Furthermore, these mechanisms generalize naturally to multidimensional settings where they give the first known approximations to the elusive optimal multi-dimensional mechanism design problem.

/pdf/multi-parameter-mechanism-design-and-sequential-posted-2id5js9sgw.pdf

We study the problem of pricing items for sale to consumers so as to maximize the seller's revenue. We assume that for each consumer, we know the maximum amount he would be willing to pay for each bundle of items, and want to find pricings of the items with corresponding allocations that maximize seller profit and at the same time are envy-free, which is a natural fairness criterion requiring that consumers are maximally happy with the outcome they receive given the pricing. We study this problem for two important classes of inputs: unit demand consumers, who want to buy at most one item from among a selection they are interested in, and single-minded consumers, who want to buy one particular subset, but only if they can afford it.We show that computing envy-free prices to maximize the seller's revenue is APX-hard in both of these cases, and give a logarithmic approximation algorithm for them. For several interesting special cases, we derive polynomial-time algorithms. Furthermore, we investigate some connections with the corresponding mechanism design problem, in which the consumer's preferences are private values: for this case, we give a log-competitive truthful mechanism.

Jason D. Hartline

Papers

Optimal marketing strategies over social networks

Multi-parameter mechanism design and sequential posted pricing

Simple versus optimal mechanisms

Multi-parameter mechanism design and sequential posted pricing

On profit-maximizing envy-free pricing