Abstract
Monte Carlo Search algorithms can give excellent results for some combinatorial optimization problems and for some games. They can be parallelized efficiently on high-end CPU servers. Nested Monte Carlo Search is an algorithm that parallelizes well. We take advantage of this property to obtain large speedups running it on low cost GPUs. The combinatorial optimization problem we use for the experiments is the Snake-in-the-Box. It is a graph theory problem for which Nested Monte Carlo Search previously improved lower bounds. It has applications in electrical engineering, coding theory, and computer network topologies. Using a low cost GPU, we obtain speedups as high as 420 compared to a single CPU.
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References
Bouzy, B.: Monte-Carlo fork search for cooperative path-finding. In: Computer Games Workshop at IJCAI, pp. 1–15 (2013)
Bouzy, B.: Burnt pancake problem: new lower bounds on the diameter and new experimental optimality ratios. In: SOCS, pp. 119–120 (2016)
Brodtkorb, A., Hagen, T., Schulz, C., Hasle, G.: GPU computing in discrete optimization. Part I: Introduction to the GPU. EURO J. Transp. Logist. 2 (2013). https://doi.org/10.1007/s13676-013-0025-1
Browne, C., et al.: A survey of Monte Carlo tree search methods. IEEE Trans. Comput. Intell. AI Games 4(1), 1–43 (2012). https://doi.org/10.1109/TCIAIG.2012.2186810
Buber, E., Banu, D.: Performance analysis and CPU vs GPU comparison for deep learning. In: 2018 6th International Conference on Control Engineering & Information Technology (CEIT), pp. 1–6. IEEE (2018)
Cazenave, T.: Nested Monte-Carlo search. In: Boutilier, C. (ed.) IJCAI, pp. 456–461 (2009)
Cazenave, T.: Generalized nested rollout policy adaptation. In: Monte Search at IJCAI (2020)
Cazenave, T., Fournier, T.: Monte Carlo inverse folding. In: Monte Search at IJCAI (2020)
Cazenave, T., Lucas, J.Y., Kim, H., Triboulet, T.: Monte Carlo vehicle routing. In: ATT at ECAI 2020, Saint Jacques de Compostelle, Spain (2020). https://hal.archives-ouvertes.fr/hal-03117515
Cazenave, T., Negrevergne, B., Sikora, F.: Monte Carlo graph coloring. In: Monte Search at IJCAI (2020)
Cazenave, T., Saffidine, A., Schofield, M.J., Thielscher, M.: Nested Monte Carlo search for two-player games. In: AAAI, pp. 687–693 (2016)
Cazenave, T., Teytaud, F.: Application of the nested rollout policy adaptation algorithm to the traveling salesman problem with time windows. In: Learning and Intelligent Optimization - 6th International Conference, LION, vol. 6, pp. 42–54 (2012)
Dang, C., Bazgan, C., Cazenave, T., Chopin, M., Wuillemin, P.-H.: Monte Carlo search algorithms for network traffic engineering. In: Dong, Y., Kourtellis, N., Hammer, B., Lozano, J.A. (eds.) ECML PKDD 2021. LNCS (LNAI), vol. 12978, pp. 486–501. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-86514-6_30
Dwivedi, A.D., Morawiecki, P., Wójtowicz, S.: Finding differential paths in ARX ciphers through nested Monte-Carlo search. Int. J. Electron. Telecommun. 64(2), 147–150 (2018)
Edelkamp, S., Cazenave, T.: Improved diversity in nested rollout policy adaptation. In: Friedrich, G., Helmert, M., Wotawa, F. (eds.) KI 2016. LNCS (LNAI), vol. 9904, pp. 43–55. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46073-4_4
Edelkamp, S., Gath, M., Cazenave, T., Teytaud, F.: Algorithm and knowledge engineering for the TSPTW problem. In: 2013 IEEE Symposium on Computational Intelligence in Scheduling (SCIS), pp. 44–51. IEEE (2013)
Edelkamp, S., Gath, M., Greulich, C., Humann, M., Herzog, O., Lawo, M.: Monte-Carlo tree search for logistics. In: Clausen, U., Friedrich, H., Thaller, C., Geiger, C. (eds.) Commercial Transport. LNL, pp. 427–440. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-21266-1_28
Edelkamp, S., Gath, M., Rohde, M.: Monte-Carlo tree search for 3D packing with object orientation. In: Lutz, C., Thielscher, M. (eds.) KI 2014. LNCS (LNAI), vol. 8736, pp. 285–296. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11206-0_28
Edelkamp, S., Greulich, C.: Solving physical traveling salesman problems with policy adaptation. In: 2014 IEEE Conference on Computational Intelligence and Games (CIG), pp. 1–8. IEEE (2014)
Edelkamp, S., Tang, Z.: Monte-Carlo tree search for the multiple sequence alignment problem. In: Proceedings of the Eighth Annual Symposium on Combinatorial Search, SOCS 2015, pp. 9–17. AAAI Press (2015)
Fawzi, A., et al.: Discovering faster matrix multiplication algorithms with reinforcement learning. Nature 610(7930), 47–53 (2022)
Kinny, D.: A new approach to the snake-in-the-box problem. In: ECAI 2012. Frontiers in Artificial Intelligence and Applications, vol. 242, pp. 462–467. IOS Press (2012)
Li, F., Ye, Y., Tian, Z., Zhang, X.: CPU versus GPU: which can perform matrix computation faster-performance comparison for basic linear algebra subprograms. Neural Comput. Appl. 31(8), 4353–4365 (2019)
Méhat, J., Cazenave, T.: Combining UCT and Nested Monte Carlo Search for single-player general game playing. IEEE Trans. Comput. Intell. AI Games 2(4), 271–277 (2010)
Mei, X., Zhao, K., Liu, C., Chu, X.: Benchmarking the memory hierarchy of modern GPUs. In: Hsu, C.-H., Shi, X., Salapura, V. (eds.) NPC 2014. LNCS, vol. 8707, pp. 144–156. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44917-2_13
NVIDIA: Cuda C++ programming guide (2022). https://docs.NVIDIA.com/cuda/cuda-c-programming-guide, section: arithmetic-instructions
Portela, F.: An unexpectedly effective Monte Carlo technique for the RNA inverse folding problem. BioRxiv, p. 345587 (2018)
Poulding, S.M., Feldt, R.: Generating structured test data with specific properties using nested Monte-Carlo search. In: GECCO, pp. 1279–1286 (2014)
Poulding, S.M., Feldt, R.: Heuristic model checking using a Monte-Carlo tree search algorithm. In: GECCO, pp. 1359–1366 (2015)
Rimmel, A., Teytaud, F., Cazenave, T.: Optimization of the nested Monte-Carlo algorithm on the traveling salesman problem with time windows. In: Di Chio, C., et al. (eds.) EvoApplications 2011. LNCS, vol. 6625, pp. 501–510. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20520-0_51
Rosin, C.D.: Nested rollout policy adaptation for Monte Carlo Tree Search. In: IJCAI, pp. 649–654 (2011)
Silver, D., et al.: Mastering the game of go with deep neural networks and tree search. Nature 529, 484–489 (2016)
Silver, D., et al.: A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science 362(6419), 1140–1144 (2018)
Wong, H., Papadopoulou, M., Sadooghi-Alvandi, M., Moshovos, A.: Demystifying GPU microarchitecture through microbenchmarking. In: 2010 IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS), pp. 235–246. IEEE (2010)
Wu, D.J.: Accelerating self-play learning in go. arXiv preprint arXiv:1902.10565 (2019)
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Buzer, L., Cazenave, T. (2023). GPU for Monte Carlo Search. In: Sellmann, M., Tierney, K. (eds) Learning and Intelligent Optimization. LION 2023. Lecture Notes in Computer Science, vol 14286. Springer, Cham. https://doi.org/10.1007/978-3-031-44505-7_13
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DOI: https://doi.org/10.1007/978-3-031-44505-7_13
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