Distributed Constraint Optimization

Distributed Constraint Satisfaction (DisCSP) and Distributed Constraint Optimization (DCOP) are formal frameworks that can be used to model a variety of problems in which multiple decision-makers cooperate towards a common goal: from computing an equilibrium of a game, to vehicle routing problems, to combinatorial auctions. In this thesis, we independently address two important issues in such multi-agent problems: 1) how to provide strong guarantees on the protection of the privacy of the participants, and 2) how to anticipate future, uncontrollable events. On the privacy front, our contributions depart from previous work in two ways. First, we consider not only constraint privacy (the agents' private costs) and decision privacy (keeping the complete solution secret), but also two other types of privacy that have been largely overlooked in the literature: agent privacy, which has to do with protecting the identities of the participants, and topology privacy, which covers information about the agents' co-dependencies. Second, while previous work focused mainly on quantitatively measuring and reducing privacy loss, our algorithms provide stronger, qualitative guarantees on what information will remain secret. Our experiments show that it is possible to provide such privacy guarantees, while still scaling to much larger problems than the previous state of the art. When it comes to reasoning under uncertainty, we propose an extension to the DCOP framework, called DCOP under Stochastic Uncertainty (StochDCOP), which includes uncontrollable, random variables with known probability distributions that model uncertain, future events. The problem becomes one of making "optimal" offline decisions, before the true values of the random variables can be observed. We consider three possible concepts of optimality: minimizing the expected cost, minimizing the worst-case cost, or maximizing the probability of a-posteriori optimality. We propose a new family of StochDCOP algorithms, exploring the tradeoffs between solution quality, computational and message complexity, and privacy. In particular, we show how discovering and reasoning about co-dependencies on common random variables can yield higher-quality solutions.

Distributed Constraint Optimization under Stochastic Uncertainty

Boi Faltings, Thomas Léauté

In many real-life optimization problems involving multiple agents, the rewards are not necessarily known exactly in advance, but rather depend on sources of exogenous uncertainty. For instance, delivery companies might have to coordinate to choose who should serve which foreseen customer, under uncertainty in the locations of the customers. The framework of Distributed Constraint Optimization under Stochastic Uncertainty was proposed to model such problems; in this paper, we generalize this formalism by introducing the concept of evaluation functions that model various optimization criteria. We take the example of three such evaluation functions, expectation, consensus, and robustness, and we adapt and generalize two previous algorithms accordingly. Our experimental results on a class of Vehicle Routing Problems show that incomplete algorithms are not only cheaper than complete ones (in terms of simulated time, Non-Concurrent Constraint Checks, and information exchange), but they are also often able to find the optimal solution. We also show that exchanging more information about the dependencies of their respective cost functions on the sources of uncertainty can help the agents discover higher-quality solutions.

2011

A Scalable Method for Multiagent Constraint Optimization

Boi Faltings, Adrian Petcu

We present in this paper a new complete method for distributed constraint optimization. This is a utility-propagation method, inspired by the sum-product algorithm (Kschischang et al 2001). The original algorithm requires fixed message sizes, linear memory and linear time in the size of the problem. However, it is correct only for tree-shaped constraint networks. In this paper, we show how to extend that algorithm to arbitrary topologies using a pseudotree arrangement of the problem graph. We compare our algorithm with "standard" backtracking algorithms, and present experimental results. For some problem types we report orders of magnitude less messages, and even the ability to deal with arbitrary large problems. Our algorithm is formulated for optimization problems, but can be easily applied to satisfaction problems as well.

2005

Protecting Privacy through Distributed Computation in Multi-agent Decision Making

Boi Faltings, Thomas Léauté

As large-scale theft of data from corporate servers is becoming increasingly common, it becomes interesting to examine alternatives to the paradigm of centralizing sensitive data into large databases. Instead, one could use cryptography and distributed computation so that sensitive data can be supplied and processed in encrypted form, and only the final result is made known. In this paper, we examine how such a paradigm can be used to implement constraint satisfaction, a technique that can solve a broad class of AI problems such as resource allocation, planning, scheduling, and diagnosis. Most previous work on privacy in constraint satisfaction only attempted to protect specific types of information, in particular the feasibility of particular combinations of decisions. We formalize and extend these restricted notions of privacy by introducing four types of private information, including the feasibility of decisions and the final decisions made, but also the identities of the participants and the topology of the problem. We present distributed algorithms that allow computing solutions to constraint satisfaction problems while maintaining these four types of privacy. We formally prove the privacy properties of these algorithms, and show experiments that compare their respective performance on benchmark problems.

AI Access Foundation2013