A Bayesian Approach to Tackling Hard Computational Problems (Preliminary Report)

Abstract Abstract We describe research and results centering on the construction and use of Bayesian models that can predict the run time of problem solvers. Our efforts are motivated by observations of high variance in the run time uired to solve instances for several challenging problems. The methods have application to the decision-theoretic control of hard search and reasoning algorithms. We illustrate the approach with a focus on the task of predicting run time for general and domain-specific solvers on a hard class of structured constraint satisfaction problems. We describe the use of learned models to predict the ultimate length of a trial, based on observing the behavior of the search algorithm during an early phase of a problem session. Finally, we discuss how we can employ the models to inform dynamic run-time decisions. We thank Dimitris Achlioptas for his insightful contributions and feedback.

[1]  Bart Selman,et al.  Generating Satisfiable Problem Instances , 2000, AAAI/IAAI.

[2]  Michael P. Wellman,et al.  Planning and Control , 1991 .

[3]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[4]  Stuart J. Russell.  Fine-Grained Decision-Theoretic Search Control , 2013, UAI 1990.

[5]  Eric Horvitz,et al.  Reasoning under Varying and Uncertain Resource Constraints , 1988, AAAI.

[6]  Eric Horvitz,et al.  Ideal reformulation of belief networks , 1990, UAI.

[7]  Bart Selman,et al.  Boosting Combinatorial Search Through Randomization , 1998, AAAI/IAAI.

[8]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[9]  David Heckerman,et al.  Decision-theoretic troubleshooting , 1995, CACM.

[10]  David Zuckerman,et al.  Optimal Speedup of Las Vegas Algorithms , 1993, Inf. Process. Lett..

[11]  Bart Selman,et al.  Balance and Filtering in Structured Satisfiable Problems , 2001, IJCAI.

[12]  David J. Spiegelhalter,et al.  Bayesian analysis in expert systems , 1993 .

[13]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Real-World SAT Instances , 1997, AAAI/IAAI.

[14]  David Maxwell Chickering,et al.  A Bayesian Approach to Learning Bayesian Networks with Local Structure , 1997, UAI.

[15]  Dan Roth,et al.  Learning to reason , 1994, JACM.

[16]  Oren Etzioni,et al.  Integrating Abstraction and Explanation-Based Learning in PRODIGY , 1991, AAAI.

[17]  Andrew P. Sage,et al.  Uncertainty in Artificial Intelligence , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[18]  David Heckerman,et al.  Dependency Networks for Density Estimation, Collaborative Filtering, and Data Visualization , 2000 .

[19]  Oren Etzioni,et al.  Explanation-Based Learning: A Problem Solving Perspective , 1989, Artif. Intell..

[20]  Charles J. Colbourn.  The complexity of completing partial Latin squares , 1984, Discret. Appl. Math..

[21]  Bart Selman,et al.  Unifying SAT-based and Graph-based Planning , 1999, IJCAI.

[22]  Bart Selman,et al.  Problem Structure in the Presence of Perturbations , 1997, AAAI/IAAI.

[23]  Eric Horvitz,et al.  Reasoning, Metareasoning, and Mathematical Truth: Studies of Theorem Proving under Limited Resources , 1995, UAI.

[24]  Chu Min Li,et al.  Heuristics Based on Unit Propagation for Satisfiability Problems , 1997, IJCAI.