{"type":"ScholarlyArticle","title":"Iterative Budgeted Exponential Search","authors":[{"name":"Malte Helmert","slug":"malte-helmert","given":"Malte","family":"Helmert","affiliation":"Department of Mathematics and Computer Science , University of Basel , Switzerland"},{"name":"Tor Lattimore","slug":"tor-lattimore","given":"Tor","family":"Lattimore","affiliation":"DeepMind , London , UK"},{"name":"Levi H. S. Lelis","slug":"levi-h-s-lelis","given":"Levi H. S.","family":"Lelis","affiliation":"Departamento de Informática , Universidade Federal de Viçosa , Brazil"},{"name":"Laurent Orseau","slug":"laurent-orseau","given":"Laurent","family":"Orseau","affiliation":"DeepMind , London , UK"},{"name":"Nathan R. Sturtevant","slug":"nathan-r-sturtevant","given":"Nathan R.","family":"Sturtevant","affiliation":"Department of Computing Science , University of Alberta , Edmonton , AB , Canada"}],"abstract":"We tackle two long-standing problems related to re-expansions in heuristic search algorithms. For graph search, A* can require Ω(2ⁿ) expansions, where n is the number of states within the final f bound. Existing algorithms that address this problem like B and B’ improve this bound to Ω(n²). For tree search, IDA* can also require Ω(n²) expansions. We describe a new algorithmic framework that iteratively controls an expansion budget and solution cost limit, giving rise to new graph and tree search algorithms for which the number of expansions is O(n log C*), where C* is the optimal solution cost. Our experiments show that the new algorithms are robust in scenarios where existing algorithms fail. In the case of tree search, our new algorithms have no overhead over IDA* in scenarios to which IDA* is well suited and can therefore be recommended as a general replacement for IDA*.","doi":"10.24963/ijcai.2019/174","url":"https://ijcai.org/proceedings/2019/174","pdf":"https://ijcai.org/proceedings/2019/0174.pdf","markdown":"https://ijcai.org/proceedings/2019/174.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/174","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Heuristic Search and Game Playing","track":"Main track","number":174,"pages":{"first":1249,"last":1257},"keywords":["Heuristic Search and Game Playing: Heuristic Search","Heuristic Search and Game Playing: Combinatorial Search and Optimisation"],"videos":[],"references":[{"position":1,"raw":"[Akagi et al., 2010] Yuima Akagi, Akihiro Kishimoto, and Alex Fukunaga. On transposition tables for single-agent search and planning: Summary of results. In Proceedings of the 3rd Annual Symposium on Combinatorial Search (SoCS 2010), pages 2-9, 2010.","title":"On transposition tables for single-agent search and planning: Summary of results","authors":"Akagi","year":"2010","venue":"Proceedings of the 3rd Annual Symposium on Combinatorial Search (SoCS 2010)","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bentley and Yao, 1976] Jon Louis Bentley and Andrew Chi-Chih Yao. An almost optimal algorithm for unbounded searching. Information Processing Letters, 5(3):82-87, 1976.","title":"An almost optimal algorithm for unbounded searching","authors":"Yao Bentley, Jon, Louis Bentley, Andrew Chi-Chih Yao","year":"1976","venue":"Information Processing Letters","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Burns and Ruml, 2013] Ethan Burns and Wheeler Ruml. Iterative-deepening search with on-line tree size predic- tion. Annals of Mathematics and Artificial Intelligence, 69(2):183-205, 2013.","title":"Iterative-deepening search with on-line tree size prediction","authors":"Ruml Burns, Ethan Burns, Wheeler Ruml","year":"2013","venue":"Annals of Mathematics and Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Chen et al., 2019] Jingwei Chen, Nathan R. Sturtevant, William Doyle, and Wheeler Ruml. Revisiting suboptimal search. In Proceedings of the 12th Annual Symposium on Combinatorial Search (SoCS 2019), 2019.","title":"Revisiting suboptimal search","authors":"Jingwei Chen, Nathan R Sturtevant, William Doyle, Wheeler Ruml","year":"2019","venue":"Proceedings of the 12th Annual Symposium on Combinatorial Search","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Dechter and Pearl, 1985] Rina Dechter and Judea Pearl. Generalized best-first search strategies and the optimality of A*. Journal of the ACM, 32(3):505-536, 1985.","title":"Generalized best-first search strategies and the optimality of A","authors":"Rina Dechter, Judea Pearl","year":"1985","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Doran and Michie, 1966] James E. Doran and Donald Michie. Experiments with the graph traverser program. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 294(1437):235-259, 1966.","title":"Experiments with the graph traverser program","authors":"James E Doran, Donald Michie","year":"1437","venue":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Felner, 2011] Ariel Felner. Position paper: Dijkstra's algorithm versus uniform cost search or a case against dijkstra's algorithm. In Proceedings of the 4th Annual Symposium on Combinatorial Search (SoCS 2011), pages 47-51, 2011.","title":"Position paper: Dijkstra's algorithm versus uniform cost search or a case against dijkstra's algorithm","authors":"Ariel Felner, Felner","year":"2011","venue":"Proceedings of the 4th Annual Symposium on Combinatorial Search (SoCS 2011)","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hart et al., 1968] Peter E. Hart, Nils J. Nilsson, and Bertram Raphael. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics, 4(2):100-107, 1968.","title":"A formal basis for the heuristic determination of minimum cost paths","authors":"Peter E Hart, Nils J Nilsson, Bertram Raphael","year":"1968","venue":"IEEE Transactions on Systems Science and Cybernetics","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Hatem et al., 2015] Matthew Hatem, Scott Kiesel, and Wheeler Ruml. Recursive best-first search with bounded overhead. In Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI 2015), pages 1151-1157, 2015.","title":"Recursive best-first search with bounded overhead","authors":"Matthew Hatem, Scott Kiesel, Wheeler Ruml","year":"2015","venue":"Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI 2015)","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Hatem et al., 2018] Matthew Hatem, Ethan Burns, and Wheeler Ruml. Solving large problems with heuristic search: General-purpose parallel external-memory search. Journal of Artificial Intelligence Research, 62:233-268, 2018.","title":"Solving large problems with heuristic search: General-purpose parallel external-memory search","authors":"Matthew Hatem, Ethan Burns, Wheeler Ruml","year":"2018","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Helmert et al., 2019] Malte Helmert, Tor Lattimore, Levi H. S. Lelis, Laurent Orseau, and Nathan R. Sturtevant. Iterative budgeted exponential search. CoRR, 2019.","title":"Iterative budgeted exponential search","authors":"Malte Helmert, Tor Lattimore, H S Levi, Laurent Lelis, Nathan R Orseau, Sturtevant","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Holte, 2010] Robert C. Holte. Common misconceptions concerning heuristic search. In Proceedings of the 3rd Annual Symposium on Combinatorial Search (SoCS 2010), pages 46-51, 2010.","title":"Common misconceptions concerning heuristic search","authors":"C Robert, Holte","year":"2010","venue":"Proceedings of the 3rd Annual Symposium on Combinatorial Search (SoCS 2010)","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Korf, 1985] Richard E. Korf. Depth-first iterative- deepening: An optimal admissible tree search. Artificial Intelligence, 27(1):97-109, 1985.","title":"Depth-first iterativedeepening: An optimal admissible tree search","authors":"Richard E Korf","year":"1985","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Korf, 1993] Richard E. Korf. Linear-space best-first search. Artificial Intelligence, 62(1):41-78, 1993.","title":"Linear-space best-first search","authors":"Richard E Korf","year":"1993","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Lammertink, 1989] Ferdinand Lammertink. Puzzle or game having token filled track and turntable, October 3 1989. US Patent 4,871,173.","title":"Puzzle or game having token filled track and turntable","authors":"Ferdinand Lammertink","year":"1989","venue":"US Patent","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Luby et al., 1993] Michael Luby, Alistair Sinclair, and David Zuckerman. Optimal speedup of Las Vegas algorithms. Information Processing Letters, 47(4):173- 180, September 1993.","title":"Optimal speedup of Las Vegas algorithms","authors":"Michael Luby, Alistair Sinclair, David Zuckerman","year":"1993","venue":"Information Processing Letters","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Martelli, 1977] Alberto Martelli. On the complexity of admissible search algorithms. Artificial Intelligence, 8(1):1-13, 1977.","title":"On the complexity of admissible search algorithms","authors":"Alberto Martelli","year":"1977","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Mérõ, 1984] László Mérõ. A heuristic search algorithm with modifiable estimate. Artificial Intelligence, 23(1):13- 27, 1984.","title":"László Mérõ. A heuristic search algorithm with modifiable estimate","authors":"Mérõ","year":"1984","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Orseau et al., 2018] Laurent Orseau, Levi H. S. Lelis, Tor Lattimore, and Theophane Weber. Single-agent policy tree search with guarantees. In Proceedings of the 31st Annual Conference on Neural Information Processing Systems (NeurIPS 2018), pages 3205-3215, 2018.","title":"Single-agent policy tree search with guarantees","authors":"Laurent Orseau, H S Levi, Tor Lelis, Theophane Lattimore, Weber","year":"2018","venue":"Proceedings of the 31st Annual Conference on Neural Information Processing Systems (NeurIPS 2018)","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Orseau et al., 2019] Laurent Orseau, Tor Lattimore, and Levi H. S. Lelis. Zooming cautiously: Linear-memory heuristic search with node expansion guarantees. CoRR, abs/1906.03242, 2019.","title":"Zooming cautiously: Linear-memory heuristic search with node expansion guarantees","authors":"Laurent Orseau, Tor Lattimore, Levi H S Lelis","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Press et al., 1992] William H. Press, Saul A. Teukolsky, William Vetterling, and Brian P. Flannery. Numerical recipes in C. Cambridge University Press, 1992.","title":"Numerical recipes in C","authors":"H William, Saul A Press, William Teukolsky, Brian P Vetterling, Flannery","year":"1992","venue":null,"doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Russell and Norvig, 2009] Stuart Russell and Peter Norvig. Artificial Intelligence: A Modern Approach. Prentice Hall Press, Upper Saddle River, NJ, USA, 3rd edition, 2009.","title":"Artificial Intelligence: A Modern Approach","authors":"Stuart Russell, Peter Norvig","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Sarkar et al., 1991] U. K. Sarkar, P. P. Chakrabarti, S. Ghose, and S. C. De Sarkar. Reducing reexpansions in iterative-deepening search by controlling cutoff bounds. Artificial Intelligence, 50(2):207-221, 1991.","title":"Reducing reexpansions in iterative-deepening search by controlling cutoff bounds","authors":"U K Sarkar, P P Chakrabarti, S Ghose, S C De Sarkar","year":"1991","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Sharon et al., 2014] Guni Sharon, Ariel Felner, and Nathan R. Sturtevant. Exponential deepening A* for real-time agent-centered search. In Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI 2014), pages 871-877, 2014.","title":"Exponential deepening A* for real-time agent-centered search","authors":"Guni Sharon, Ariel Felner, Nathan R Sturtevant","year":"2014","venue":"Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI 2014)","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Sturtevant and Helmert, 2019] Nathan R. Sturtevant and Malte Helmert. Exponential-binary state-space search. CoRR, abs/1906.02912, 2019.","title":"Exponential-binary state-space search","authors":"Nathan R Sturtevant, Malte Helmert","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Wah and Shang, 1994] Benjamin W. Wah and Yi Shang. Comparision and evaluation of a class of IDA* algorithms. International Journal on Artificial Intelligence Tools, 3(4):493-524, 1994.","title":"Comparision and evaluation of a class of IDA* algorithms","authors":"Benjamin W Wah, Yi Shang","year":"1994","venue":"International Journal on Artificial Intelligence Tools","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Zhou and Hansen, 2004] Rong Zhou and Eric A. Hansen. Structured duplicate detection in external-memory graph search. In Proceedings of the 19th National Conference on Artificial Intelligence (AAAI 2004), pages 683-689, 2004.","title":"Structured duplicate detection in external-memory graph search","authors":"Rong Zhou, Eric A Hansen","year":"2004","venue":"Proceedings of the 19th National Conference on Artificial Intelligence (AAAI 2004)","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}