Distributed Constraint Optimization under Stochastic Uncertainty

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.

Distributed Constraint Optimization

Thomas Léauté

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.

EPFL2011

E[DPOP]: Distributed Constraint Optimization under Stochastic Uncertainty using Collaborative Sampling

Boi Faltings, Thomas Léauté

Many applications that require distributed optimization also include uncertainty about the problem and the optimization criteria themselves. However, current approaches to distributed optimization assume that the problem is entirely known before optimization is carried out, while approaches to optimization with uncertainty have been investigated for centralized algorithms. This paper introduces the framework of Distributed Constraint Optimization under Stochastic Uncertainty (StochDCOP), in which random variables with known probability distributions are used to model sources of uncertainty. Our main novel contribution is a distributed procedure called col laborative sampling, which we use to produce several new versions of the DPOP algorithm for StochDCOPs. We evaluate the benefits of collaborative sampling over the simple approach in which each agent samples the random variables independently. We also show that collaborative sampling can be used to implement a new, distributed version of the consensus algorithm, which is a well-known algorithm for centralized, online stochastic optimization in which the solution chosen is the one that is optimal in most cases, rather than the one that maximizes the expected utility.

2009

Coordinating Logistics Operations with Privacy Guarantees

Boi Faltings, Thomas Léauté

Several logistics service providers serve a certain number of customers, geographically spread over an area of operations. They would like to coordinate their operations so as to minimize overall cost. At the same time, they would like to keep information about their costs, constraints and preferences private, thus precluding conventional negotiation. We show how AI techniques, in particular Distributed Constraint Optimization (DCOP), can be integrated with cryptographic techniques to allow such coordination without revealing agents' private information. The problem of assigning customers to companies is formulated as a DCOP, for which we propose two novel, privacy-preserving algorithms. We compare their performances and privacy properties on a set of Vehicle Routing Problem benchmarks.

2011

Distributed Constraint Optimization

Thomas Léauté

EPFL2011