We present a principled and efficient planning algorithm for cooperative multiagent dynamic systems. A striking feature of our method is that the coordination and communication between the agents is not imposed, but derived directly from the system dynamics and function approximation architecture. We view the entire multiagent system as a single, large Markov decision process (MDP), which we assume can be represented in a factored way using a dynamic Bayesian network (DBN). The action space of the resulting MDP is the joint action space of the entire set of agents. Our approach is based on the use of factored linear value functions as an approximation to the joint value function. This factorization of the value function allows the agents to coordinate their actions at runtime using a natural message passing scheme. We provide a simple and efficient method for computing such an approximate value function by solving a single linear program, whose size is determined by the interaction between the value function structure and the DBN. We thereby avoid the exponential blowup in the state and action space. We show that our approach compares favorably with approaches based on reward sharing. We also show that our algorithm is an efficient alternative to more complicated algorithms even in the single agent case.

The paper introduces an AND/OR search space perspective for graphical models that include probabilistic networks (directed or undirected) and constraint networks. In contrast to the traditional (OR) search space view, the AND/OR search tree displays some of the independencies present in the graphical model explicitly and may sometime reduce the search space exponentially. Indeed, most

Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting first-order specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poole, 2003] presented a method to perform inference directly on the first-order level, but this method is limited to special cases. In this paper we present the first exact inference algorithm that operates directly on a first-order level, and that can be applied to any first-order model (specified in a language that generalizes undirected graphical models). Our experiments show superior performance in comparison with propositional exact inference. 1

We present several new algorithms for multiagent reinforcement learning. A common feature of these algorithms is a parameterized, structured representation of a policy or value function. This structure is leveraged in an approach we call coordinated reinforcement learning, by which agents coordinate both their action selection activities and their parameter updates. Within the limits of our parametric representations, the agents will determine a jointly optimal action without explicitly considering every possible action in their exponentially large joint action space. Our methods differ from many previous reinforcement learning approaches to multiagent coordination in that structured communication and coordination between agents appears at the core of both the learning algorithm and the execution architecture. Our experimental results, comparing our approach to other RL methods, illustrate both the quality of the policies obtained and the additional benefits of coordination. 1.

Many large MDPs can be represented compactly using a dynamic Bayesian network. Although the structure of the value function does not retain the structure of the process, recent work has suggested that value functions in factored MDPs can often be approximated well using a factored value function: a linear combination of restricted basis functions, each of which refers only to a small subset of variables. An approximate factored value function for a particular policy can be computed using approximate dynamic programming, but this approach (and others) can only produce an approximation relative to a distance metric which is weighted by the stationary distribution of the current policy. This type of weighted projection is ill-suited to policy improvement.

In this paper we propose a family of algorithms combining tree-clustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing optimization tasks. By analyzing the problem structure it will be possible to select from a spectrum the algorithm that best meets a given time-space specification. 1 INTRODUCTION Topology-based algorithms for constraint satisfaction and probabilistic reasoning fall into two distinct classes. One class is centered on tree-clustering, the other on cycle-cutset decomposition. Tree-clustering involves transforming the original problem into a treelike problem that can then be solved by a specialized tree-solving algorithm [ Mackworth and Freuder, 1985; Pearl, 1986 ] . The tree-clustering algorithm is time and space exponential in the induced width (also called tree width) of the problem's graph. The transforming algorithm identifies subproblems that together ...

Abstract. This article presents a class of approximation algorithms that extend the idea of boundedcomplexity inference, inspired by successful constraint propagation algorithms, to probabilistic inference and combinatorial optimization. The idea is to bound the dimensionality of dependencies created by inference algorithms. This yields a parameterized scheme, called mini-buckets, that offers adjustable trade-off between accuracy and efficiency. The mini-bucket approach to optimization problems, such as finding the most probable explanation (MPE) in Bayesian networks, generates both an approximate solution and bounds on the solution quality. We present empirical results demonstrating successful performance of the proposed approximation scheme for the MPE task, both on randomly generated problems and on realistic domains such as medical diagnosis and probabilistic decoding.

We present an algorithm for coordinated decision making in cooperative multiagent settings, where the agents ’ value function can be represented as a sum of context-specific value rules. The task of finding an optimal joint action in this setting leads to an algorithm where the coordination structure between agents depends on the current state of the system and even on the actual numerical values assigned to the value rules. We apply this framework to the task of multiagent planning in dynamic systems, showing how a joint value function of the associated Markov Decision Process can be approximated as a set of value rules using an efficient linear programming algorithm. The agents then apply the coordination graph algorithm at each iteration of the process to decide on the highest-value joint action, potentially leading to a different coordination pattern at each step of the plan. 1

We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n2 n) time, where n is the number of attributes; the number of parents per attribute is bounded by a constant. In this paper we show that the posterior probabilities for all the n(n−1) potential edges can be computed in O(n2 n) total time. This result is achieved by a forward–backward technique and fast Möbius transform algorithms, which are of independent interest. The resulting speedup by a factor of about n 2 allows us to experimentally study the statistical power of learning moderate-size networks. We report results from a simulation study that covers data sets with 20 to 10,000 records over 5 to 25 discrete attributes. 1

Lifted inference algorithms exploit repeated structure in probabilistic models to answer queries efficiently. Previous work such as de Salvo Braz et al.’s first-order variable elimination (FOVE) has focused on the sharing of potentials across interchangeable random variables. In this paper, we also exploit interchangeability within individual potentials by introducing counting formulas, which indicate how many of the random variables in a set have each possible value. We present a new lifted inference algorithm, C-FOVE, that not only handles counting formulas in its input, but also creates counting formulas for use in intermediate potentials. C-FOVE can be described succinctly in terms of six operators, along with heuristics for when to apply them. Because counting formulas capture dependencies among large numbers of variables compactly, C-FOVE achieves asymptotic speed improvements compared to FOVE.