Distributed Private Constraint Optimization

IEEE Transactions on Automatic Control, 2016

Many resource allocation problems can be formulated as an optimization problem whose constraints contain sensitive information about participating users. This paper concerns solving this kind of optimization problem in a distributed manner while protecting the privacy of user information. Without privacy considerations, existing distributed algorithms normally consist in a central entity computing and broadcasting certain public coordination signals to participating users. However, the coordination signals often depend on user information, so that an adversary who has access to the coordination signals can potentially decode information on individual users and put user privacy at risk. We present a distributed optimization algorithm that preserves differential privacy, which is a strong notion that guarantees user privacy regardless of any auxiliary information an adversary may have. The algorithm achieves privacy by perturbing the public signals with additive noise, whose magnitude is determined by the sensitivity of the projection operation onto user-specified constraints. By viewing the differentially private algorithm as an implementation of stochastic gradient descent, we are able to derive a bound for the suboptimality of the algorithm. We illustrate the implementation of our algorithm via a case study of electric vehicle charging. Specifically, we derive the sensitivity and present numerical simulations for the algorithm. Through numerical simulations, we are able to investigate various aspects of the algorithm when being used in practice, including the choice of step size, number of iterations, and the trade-off between privacy level and suboptimality.

2020

Privacy has traditionally been a major motivation of distributed problem solving. In this paper, we focus on privacy issues when solving Distributed Constraint Optimization Problems (DCOPs) using a local search approach. Two such popular algorithms exist to find good solutions to DCOP: DSA and GDBA. However, these were not designed with privacy in mind. In this paper, we propose DSAB, a new algorithm that merges ideas from both algorithms to allow extensive handling of constraint privacy. We also study how algorithms behave when solving Utilitarian DCOPs, where utilitarian agents want to reach an agreement while reducing the privacy loss. We show experimentally that this allows us reductions of domain privacy loss by a factor 2 to 3 with no significant impact on the quality of the solution.

Annals of Mathematics and Artificial Intelligence, 2019

In this work, we approach the issue of privacy in distributed constraint reasoning by studying how agents compromise solution quality for preserving privacy, using utility and game theory. We propose a utilitarian definition of privacy in the context of distributed constraint reasoning, detail its different implications, and present a model and solvers, as well as their properties. We then show how important steps in a distributed constraint optimization with privacy requirements can be modeled as a planning problem, and more specifically as a stochastic game. We present experiments validating the interest of our approach, according to several criteria.

2018

Privacy has been a major concern for agents in distributed constraint reasoning. In this work, we approach this issue in distributed constraint reasoning by letting agents compromise solution quality for preserving privacy, using utility theory. We formalize privacy in the context of distributed constraint reasoning, detail its different aspects, and present model and solvers, as well as their properties. We then show how distributed constraint reasoning with privacy requirements can be modelled as a planning problem, and more specifically as

2002

This paper develops a secure distributed Constraint Satisfaction algorithm. A Distributed Constraint Satisfaction Problem (DisCSP) is a CSP in which variables and constraints are distributed among multiple agents. A major motivation for solving a DisCSP without gathering all information in one server is the concern about privacy/security. However, existing DisCSP algorithms leak some information during the search process and privacy/security issues are not dealt with formally. Our newly developed algorithm utilizes a public key encryption scheme. In this algorithm, multiple servers, which receive encrypted information from agents, cooperatively perform a search process that is equivalent to a standard chronological backtracking. This algorithm does not leak any private information, i.e., neither agents nor servers can obtain any additional information on the value assignment of variables that belong to other agents.

arXiv (Cornell University), 2012

Ensuring privacy of sensitive data is essential in many contexts, such as healthcare data, banks, ecommerce, wireless sensor networks, and social networks. It is common that different entities coordinate or want to rely on a third party to solve a specific problem. At the same time, no entity wants to publish its problem data during the solution procedure unless there is a privacy guarantee. Unlike cryptography and differential privacy based approaches, the methods based on optimization lack a quantification of the privacy they can provide. The main contribution of this paper is to provide a mechanism to quantify the privacy of a broad class of optimization approaches. In particular, we formally define a one-tomany relation, which relates a given adversarial observed message to an uncertainty set of the problem data. This relation quantifies the potential ambiguity on problem data due to the employed optimization approaches. The privacy definitions are then formalized based on the uncertainty sets. The properties of the proposed privacy measure is analyzed. The key ideas are illustrated with examples, including localization, average consensus, among others.

The privacy of individuals is an increasing concern in a time where a large amount of data is recorded and stored by different actors all around us. The collected data is for instance electricity and water consumption from individual households, the GPS location of smart phones, public transportation routines, and shopping from digital payment methods. Thus, it is not a wonder why people may start to feel monitored. Nonetheless, the recorded data is extremely valuable for instance in the efforts of reducing pollution and CO2 emissions and increasing user experiences and living standards. It is therefore highly relevant to study how privacy sensitive data can be recorded and included in computations without violating the privacy of individuals. This thesis is one such study. The angle of investigation is how cryptographic methods can be used to keep data private (or hidden) even when it is desired to perform computations on it. Said more straight forward, the thesis is concerned with how computations can be made on encrypted data, without needing to decrypt or in other ways reveal the data. The applied methods to protect the data are based on secure multiparty computation and secret sharing, while the objective is to apply optimization algorithms on the secret data. The main contribution of the work is insights into the challenges of using cipher texts in algorithms and a novel real number secret sharing scheme that proposes a trade-off between privacy and usability of the scheme. The latter contribution challenges the generally accepted idea that the cryptographic techniques should ensure 100 percent privacy also when applied to real world problems. iii Resumé I en tid hvor data opsamles overalt i samfundet af forskellige aktører, er mange bekymret for den enkeltes privatliv. Det opsamlede data kan eksempelvis vaere elektricitet og vand forbrug, GPS lokationen af smartphones, offentlig transport rutiner og shopping ved brug af digitale betalings metoder. Det er derfor ikke maerkeligt, at mange kan føle sig overvåget. På den anden side er det opsamlede data yderst vaerdifuldt i udviklingen af teknologier, der reducerer forurening og udledning af CO2 og forbedrer bruger oplevelser og levevilkår. Det er derfor relevant at undersøge, hvordan data sikkerhed og privatliv kan forenes med opsamling og brug af sensitivt data. Denne afhandling er netop sådan en undersøgelse. Udgangspunktet for studiet er brugen af kryptografiske metoder til at holde data hemmeligt, selv når beregninger skal laves på dataet. Sagt med andre ord undersøger afhandlingen, hvordan beregninger kan udføres på krypteret data uden at dekryptere eller på andre måder afsløre dataet. De anvendte metoder til at beskytte data er baseret på secure multiparty computation og secret sharing, mens formålet er at anvende optimerings algoritmer på det hemmelige data. Resultatet af arbejdet er hovedsageligt en større forståelse af udfordringerne ved at bruge krypteret data i algoritmer og en ny secret sharing metode til reelle tal som giver en afvejning mellem privathed og praktisk brug af metoden. Det sidste resultat udfordrer den generelle accept af at kryptografiske metoder skal sikre privatliv 100 procent selv når de anvendes i praktiske problemstillinger.

Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems, 2006

Distributed constraint optimization (DCOP) has emerged as a useful technique for multiagent coordination. While previous DCOP work focuses on optimizing a single team objective, in many domains, agents must satisfy additional constraints on resources consumed locally (due to interactions within their local neighborhoods). Such resource constraints may be required to be private or shared for efficiency's sake. This paper provides a novel multiply-constrained DCOP algorithm for addressing these domains which is based on mutually-intervening search, i.e. using local resource constraints to intervene in the search for the optimal solution and vice versa. It is realized through three key ideas: (i) transforming n-ary constraints to maintain privacy; (ii) dynamically setting upper bounds on joint resource consumption with neighbors; and (iii) identifying if the local DCOP graph structure allows agents to compute exact resource bounds for additional efficiency. These ideas are implemented by modifying Adopt, one of the most efficient DCOP algorithms. Both detailed experimental results as well as proofs of correctness are presented.

Computational Intelligence, 2004

In this paper, we consider multi-agent constraint systems with preferences, modeled as soft constraint systems in which variables and constraints are distributed among multiple autonomous agents. We assume that each agent can set some preferences over its local data, and we consider two different criteria for finding optimal global solutions: fuzzy and Pareto optimality. We propose a general graph-based framework to describe the problem to be solved in its generic form. As a case study, we consider a distributed meeting scheduling problem where each agent has a preexisting schedule and the agents must decide on a common meeting that satisfies a given optimality condition. For this scenario we consider the topics of solution quality, search efficiency, and privacy loss, where the latter pertains to information about an agent's pre-existing meetings and available time-slots. We also develop and test strategies that trade efficiency for solution quality and strategies that minimize information exchange, including some that do not require inter-agent comparisons of utilities. Our experimental results demonstrate some of the relations among solution quality, efficiency, and privacy loss, and provide useful hints on how to reach a tradeoff among these three factors. In this work, we show how soft constraint formalisms can be used to incorporate preferences into multi-agent problem solving along with other facets of the problem, such as time and distance constraints. This work also shows that the notion of privacy loss can be made concrete so that it can be treated as a distinct, manipulable factor in the context of distributed decision making.

Constraints - An International Journal, 2009

Distributed constraint satisfaction problems (DisCSPs) are composed of agents connected by constraints. The standard model for DisCSP search algorithms uses messages containing assignments of agents. It assumes that constraints are checked by one of the two agents involved in a binary constraint, hence the constraint is fully known to both agents. This paper presents a new DisCSP model in which constraints are kept private and are only partially known to agents. In addition, value assignments can also be kept private to agents and not be circulated in messages. Two versions of a new asynchronous backtracking algorithm that work with partially known constraints (PKC) are presented. One is a two-phase asynchronous backtracking algorithm and the other uses only a single phase. Another new algorithm preserves the privacy of assignments by performing distributed forward-checking (DisFC). We propose to use entropy as quantitative measure for privacy. An extensive experimental evaluation demonstrates a trade-off between preserving privacy and the efficiency of search, among the different algorithms.