Privacy of Existence of Secrets: Introducing Steganographic DCOPs and Revisiting DCOP Frameworks

Here we identify a type of privacy concern in Distributed Constraint Optimization (DCOPs) not previously addressed in literature, despite its importance and impact on the application field: the privacy of existence of secrets. Science only starts where metrics and assumptions are clearly defined. The area of Distributed Constraint Optimization has emerged at the intersection of the multi-agent system community and constraint programming. For the multi-agent community, the constraint optimization problems are an elegant way to express many of the problems occurring in trading and distributed robotics. For the theoretical constraint programming community the DCOPs are a natural extension of their main object of study, the constraint satisfaction problem. As such, the understanding of the DCOP framework has been refined with the needs of the two communities, but sometimes without spelling the new assumptions formally and therefore making it difficult to compare techniques. Here we give a direction to the efforts for structuring concepts in this area.

Distributed Constraint Problems for Utilitarian Agents with Privacy Concerns, Recast as POMDPs

Privacy has traditionally been a major motivation for distributed problem solving. Distributed Constraint Satisfaction Problem (DisCSP) as well as Distributed Constraint Optimization Problem (DCOP) are fundamental models used to solve various families of distributed problems. Even though several approaches have been proposed to quantify and preserve privacy in such problems, none of them is exempt from limitations. Here we approach the problem by assuming that computation is performed among utilitarian agents. We introduce a utilitarian approach where the utility of each state is estimated as the difference between the reward for reaching an agreement on assignments of shared variables and the cost of privacy loss. We investigate extensions to solvers where agents integrate the utility function to guide their search and decide which action to perform, defining thereby their policy. We show that these extended solvers succeed in significantly reducing privacy loss without significant degradation of the solution quality.

DisCSPs with Privacy Recast as Planning Problems for Utility-based Agents

Privacy has traditionally been a major motivation for decentralized problem solving. However, even though several metrics have been proposed to quantify it, none of them is easily integrated with common solvers. Constraint programming is a fundamental paradigm used to approach various families of problems. We introduce Utilitarian Distributed Constraint Satisfaction Problems (UDisCSP) where the utility of each state is estimated as the difference between the the expected rewards for agreements on assignments for shared variables, and the expected cost of privacy loss. Therefore, a traditional DisCSP with privacy requirements is viewed as a planning problem. The actions available to agents are: communication and local inference. Common decentralized solvers are evaluated here from the point of view of their interpretation as greedy planners. Further, we investigate some simple extensions where these solvers start taking into account the utility function. In these extensions we assume that the planning problem is further restricting the set of communication actions to only the communication primitives present in the corresponding solver protocols. The solvers obtained for the new type of problems propose the action (communication/inference) to be performed in each situation, defining thereby the policy.

Utilitarian Distributed Constraint Optimization Problems

Privacy has been a major motivation for distributed problem optimization. However, even though several methods have been proposed to evaluate it, none of them is widely used. The Distributed Constraint Optimization Problem (DCOP) is a fundamental model used to approach various families of distributed problems. As privacy loss does not occur when a solution is accepted, but when it is proposed, privacy requirements cannot be interpreted as a criteria of the objective function of the DCOP. Here we approach the problem by letting both the optimized costs found in DCOPs and the privacy requirements guide the agents' exploration of the search space. We introduce Utilitarian Distributed Constraint Optimization Problem (UDCOP) where the costs and the privacy requirements are used as parameters to a heuristic modifying the search process. Common stochastic algorithms for decentralized constraint optimization problems are evaluated here according to how well they preserve privacy. Further, we propose some extensions where these solvers modify their search process to take into account their privacy requirements, succeeding in significantly reducing their privacy loss without significant degradation of the solution quality.