Experiments with Distributed Anytime Inferencing: Working with Cooperative Algorithms

Anytime algorithms have demonstrated their usefulness in solving many classes of intractable and NPhard problems. This approach allows the potential for improvement in the quality of the solution to be balanced against the cost of generating that improvement, both in time and system resources. While significant work has been accomplished on characterizing individual algorithms and sequences of algorithms, the same has not been done for collections of algorithms. Our research extends the anytime concept by providing feedback to algorithms operating concurrently in a distributed cooperative environment. Traditional anytime algorithms execute individually, taking all their input from the problem being solved; the monitoring task plays little part in the problem solving process. We step beyond this paradigm by not only using multiple concurrent anytime algorithms, but also by providing the capability for these algorithms to interact. The anytime solutions obtained from the individual algorithms are available to the collection; the capability of each algorithm to utilize this feedback to improve its performance is called the anywhere property. The introduction of the anywhere property to inference algorithms gives us the capability of run-time control over the tasks. A controller can determine which task(s) are suitable for a given problem based on the characteristics of that specific problem. During runtime it can monitor and control the processes to guide the convergence towards the optimal solution, determining when tasks are non-productive so they may be terminated and possibly replaced with more appropriate tasks. To do this, however, it needs models of the algorithms’ performance. We develop these models, taking into consideration not only the characteristics of the problem, but also the effects of receiving the anytime solutions produced by other algorithms. Using combinations of algorithms can lead to an improved performance profile for the composite system. One class of problems that can benefit from this strategy is probabilistic reasoning; in particular, Bayesian Networks (Pearl 1988). Unfortunately, exact inference using Bayesian Networks is NP-hard (Shimony 1994) in general; though certain classes of networks (e.g. polytrees) are solvable in polynomial time. Approximation techniques also fall into this category (Dagum ~ Luby 1993). We have found, as have others, that characteristics of Bayesian Networks have a significant effect on the performance of the inferencing process. Network density and the distribution of the conditional probability tables are examples of these characteristics; but different algorithms can respond differently to the same characteristics. This paper explores models of algorithm performance and the interactions between them, producing a composite system model. Early experiments on Bayesian Networks with different combinations of algorithms in a static system configuration show promising results.