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Joint research with University of Warsaw, University of Toronto Vector Institute, Polish Academy of Sciences, University of Oxford; presented at NeurIPS 2021
- In this paper, the authors implement kSubS using a transformer-based subgoal module coupled with the classical best-first search framework. kSubS achieves strong results including state-of-the-art on INT within a modest computational budget.
- Humans excel in solving complex reasoning tasks through a mental process of moving from one idea to a related one. Inspired by this, the authors propose the Subgoal Search (kSubS) method.
- kSubS is a key component of a learned subgoal generator that produces a diversity of subgoals that are both achievable and closer to the solution. Using subgoals reduces the search space and induces a high-level search graph suitable for efficient planning.
Authors: Konrad Czechowski, Tomasz Odrzygóźdź, Marek Zbysiński, Michał Zawalski, Krzysztof Olejnik, Yuhuai Wu, Łukasz Kuciński, Piotr Miłoś
Abstract
Humans excel in solving complex reasoning tasks through a mental process of
moving from one idea to a related one. Inspired by this, we propose Subgoal Search (kSubS) method. Its key component is a learned subgoal generator that produces a diversity of subgoals that are both achievable and closer to the solution. Using subgoals reduces the search space and induces a high-level search graph suitable for efficient planning. In this paper, we implement kSubS using a transformerbased subgoal module coupled with the classical best-first search framework. We show that a simple approach of generating k-th step ahead subgoals is surprisingly efficient on three challenging domains: two popular puzzle games, Sokoban and the Rubik’s Cube, and an inequality proving benchmark INT. kSubS achieves strong results including state-of-the-art on INT within a modest computational budget.
References
- Forest Agostinelli, Stephen McAleer, Alexander Shmakov, and Pierre Baldi. Solving the rubik’s cube with deep reinforcement learning and search. Nature Machine Intelligence, 1(8):356–363, 2019.
- Marcin Andrychowicz, Dwight Crow, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, and Wojciech Zaremba. Hindsight experience replay. In Advances in Neural Information Processing Systems 30: Annual Conference on Neural 10 Information Processing Systems 2017, 4-9 December 2017, Long Beach, CA, USA, pages 5048–5058, 2017.
- Masataro Asai and Alex Fukunaga. Classical planning in deep latent space: Bridging the subsymbolic-symbolic boundary. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018.
- Yoshua Bengio, Andrea Lodi, and Antoine Prouvost. Machine learning for combinatorial optimization: a methodological tour d’horizon. European Journal of Operational Research, 2020.
- Cameron B Browne, Edward Powley, Daniel Whitehouse, Simon M Lucas, Peter I Cowling, Philipp Rohlfshagen, Stephen Tavener, Diego Perez, Spyridon Samothrakis, and Simon Colton. A survey of monte carlo tree search methods. IEEE Transactions on Computational Intelligence and AI in games, 4(1):1–43, 2012.
- Elliot Chane-Sane, Cordelia Schmid, and Ivan Laptev. Goal-conditioned reinforcement learning with imagined subgoals. In International Conference on Machine Learning, pages 1430–1440. PMLR, 2021.
- Peter Dayan and Geoffrey E. Hinton. Feudal reinforcement learning. In Stephen Jose Hanson, Jack D. Cowan, and C. Lee Giles, editors, Advances in Neural Information Processing Systems 5, [NIPS Conference, Denver, Colorado, USA, November 30 – December 3, 1992], pages 271–278. Morgan Kaufmann, 1992.
- Dorit Dor and Uri Zwick. Sokoban and other motion planning problems. Computational Geometry, 13(4):215–228, 1999.
- Kuan Fang, Yuke Zhu, Animesh Garg, Silvio Savarese, and Li Fei-Fei. Dynamics learning with cascaded variational inference for multi-step manipulation. arXiv preprint arXiv:1910.13395, 2019.
- Alan Fern, Roni Khardon, and Prasad Tadepalli. The first learning track of the international planning competition. Machine Learning, 84(1-2):81–107, 2011.
- Carlos Florensa, David Held, Xinyang Geng, and Pieter Abbeel. Automatic goal generation for reinforcement learning agents. In International conference on machine learning, pages 1515–1528. PMLR, 2018.
- Guillem Frances, Miquel Ramírez Jávega, Nir Lipovetzky, and Hector Geffner. Purely declarative action descriptions are overrated: Classical planning with simulators. In IJCAI Twenty-Sixth International Joint Conference on Artificial Intelligence; 2017 Aug 19-25; Melbourne, Australia.[California]: IJCAI; 2017. p. 4294-301. International Joint Conferences on Artificial Intelligence Organization (IJCAI), 2017.
- Thomas Gabor, Jan Peter, Thomy Phan, Christian Meyer, and Claudia Linnhoff-Popien. Subgoalbased temporal abstraction in Monte-Carlo Tree Search. In IJCAI, pages 5562–5568, 2019.
- Wei Gao, David Hsu, Wee Sun Lee, Shengmei Shen, and Karthikk Subramanian. Intention-net: Integrating planning and deep learning for goal-directed autonomous navigation. In 1st Annual Conference on Robot Learning, CoRL 2017, Mountain View, California, USA, November 13-15, 2017, Proceedings, volume 78 of Proceedings of Machine Learning Research, pages 185–194. PMLR, 2017.
- Timothy Gowers. The importance of mathematics. Springer-Verlag, 2000.
- Arthur Guez, Mehdi Mirza, Karol Gregor, Rishabh Kabra, Sébastien Racanière, Théophane Weber, David Raposo, Adam Santoro, Laurent Orseau, Tom Eccles, et al. An investigation of model-free planning. In International Conference on Machine Learning, pages 2464–2473.
PMLR, 2019. - Jessica B. Hamrick, Abram L. Friesen, Feryal Behbahani, Arthur Guez, Fabio Viola, Sims Witherspoon, Thomas Anthony, Lars Holger Buesing, Petar Velickovic, and Theophane Weber. On the role of planning in model-based deep reinforcement learning. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net, 2021.
- Demis Hassabis, Dharshan Kumaran, Christopher Summerfield, and Matthew Botvinick. Neuroscience-inspired artificial intelligence. Neuron, 95(2):245–258, 2017.11
- Hado Hasselt. Double q-learning. Advancesin neural information processing systems, 23:2613–2621, 2010.
- Jeffrey R Hollerman, Leon Tremblay, and Wolfram Schultz. Involvement of basal ganglia and orbitofrontal cortex in goal-directed behavior. Progress in brain research, 126:193–215, 2000.
- Dinesh Jayaraman, Frederik Ebert, Alexei A. Efros, and Sergey Levine. Time-agnostic prediction: Predicting predictable video frames. In 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6-9, 2019. OpenReview.net, 2019.
- Leslie Pack Kaelbling. Learning to achieve goals. In Ruzena Bajcsy, editor, Proceedings of the 13th International Joint Conference on Artificial Intelligence. Chambéry, France, August 28 -September 3, 1993, pages 1094–1099. Morgan Kaufmann, 1993.
- Taesup Kim, Sungjin Ahn, and Yoshua Bengio. Variational temporal abstraction. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d’Alché-Buc, Emily B. Fox, and Roman Garnett, editors, Advances in Neural Information Processing Systems 32: Annual
Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pages 11566–11575, 2019. - Thanard Kurutach, Aviv Tamar, Ge Yang, Stuart J. Russell, and Pieter Abbeel. Learning plannable representations with causal infogan. In Samy Bengio, Hanna M. Wallach, Hugo Larochelle, Kristen Grauman, Nicolò Cesa-Bianchi, and Roman Garnett, editors, Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montréal, Canada, pages 8747–8758, 2018.
- Nir Lipovetzky and Hector Geffner. Width and serialization of classical planning problems. In ECAI 2012, pages 540–545. IOS Press, 2012.
- Kara Liu, Thanard Kurutach, Christine Tung, Pieter Abbeel, and Aviv Tamar. Hallucinative topological memory for zero-shot visual planning. In Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13-18 July 2020, Virtual Event, volume 119 of Proceedings of Machine Learning Research, pages 6259–6270. PMLR, 2020.
- Yinhan Liu, Jiatao Gu, Naman Goyal, Xian Li, Sergey Edunov, Marjan Ghazvininejad, Mike Lewis, and Luke Zettlemoyer. Multilingual denoising pre-training for neural machine translation. CoRR, abs/2001.08210, 2020.
- Piotr Miłos, Łukasz Kuci ´ nski, Konrad Czechowski, Piotr Kozakowski, and Maciek Klimek. Uncertainty-sensitive learning and planning with ensembles. arXiv preprint arXiv:1912.09996, 2019.
- Suraj Nair and Chelsea Finn. Hierarchical foresight: Self-supervised learning of longhorizon tasks via visual subgoal generation. In 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26-30, 2020. OpenReview.net, 2020.
- Soroush Nasiriany, Vitchyr Pong, Steven Lin, and Sergey Levine. Planning with goalconditioned policies. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d’Alché-Buc, Emily B. Fox, and Roman Garnett, editors, Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pages 14814–14825, 2019.
- Giambattista Parascandolo, Lars Buesing, Josh Merel, Leonard Hasenclever, John Aslanides, Jessica B Hamrick, Nicolas Heess, Alexander Neitz, and Theophane Weber. Divide-and-conquer monte carlo tree search for goal-directed planning. arXiv preprint arXiv:2004.11410, 2020.
- Sujoy Paul, Jeroen Vanbaar, and Amit Roy-Chowdhury. Learning from trajectories via subgoal discovery. Advances in Neural Information Processing Systems, 32:8411–8421, 2019.
- Karl Pertsch, Oleh Rybkin, Frederik Ebert, Shenghao Zhou, Dinesh Jayaraman, Chelsea Finn, and Sergey Levine. Long-horizon visual planning with goal-conditioned hierarchical predictors. In Hugo Larochelle, Marc’Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and HsuanTien Lin, editors, Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020.12
- Karl Pertsch, Oleh Rybkin, Jingyun Yang, Shenghao Zhou, Konstantinos G. Derpanis, Kostas Daniilidis, Joseph J. Lim, and Andrew Jaegle. Keyframing the future: Keyframe discovery for visual prediction and planning. In Alexandre M. Bayen, Ali Jadbabaie, George J. Pappas, Pablo A.Parrilo, Benjamin Recht, Claire J. Tomlin, and Melanie N. Zeilinger, editors, Proceedings of the 2nd Annual Conference on Learning for Dynamics and Control, L4DC 2020, Online Event, Berkeley, CA, USA, 11-12 June 2020, volume 120 of Proceedings of Machine Learning Research, pages 969–979. PMLR, 2020.
- Silviu Pitis, Harris Chan, Stephen Zhao, Bradly C. Stadie, and Jimmy Ba. Maximum entropy gain exploration for long horizon multi-goal reinforcement learning. In Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13-18 July 2020, Virtual Event, volume 119 of Proceedings of Machine Learning Research, pages 7750–7761. PMLR, 2020.
- Stanislas Polu and Ilya Sutskever. Generative language modeling for automated theorem proving. arXiv preprint arXiv:2009.03393, 2020.
- Sébastien Racanière, Theophane Weber, David P. Reichert, Lars Buesing, Arthur Guez, Danilo Jimenez Rezende, Adrià Puigdomènech Badia, Oriol Vinyals, Nicolas Heess, Yujia Li, Razvan Pascanu, Peter Battaglia, Demis Hassabis, David Silver, and Daan Wierstra. Imagination-augmented agents for deep reinforcement learning. In NIPS, 2017.
- Tomas Rokicki and M Davidson. God’s number is 26 in the quarter-turn metric, 2014.
- Stuart Russell and Peter Norvig. Artificial intelligence: A modern approach. ed. 3. 2010.
- Nikolay Savinov, Alexey Dosovitskiy, and Vladlen Koltun. Semi-parametric topological memory for navigation. In 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 – May 3, 2018, Conference Track Proceedings. OpenReview.net, 2018.
- David Silver, Aja Huang, Chris J Maddison, Arthur Guez, Laurent Sifre, George Van Den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, et al. Mastering the game of go with deep neural networks and tree search. nature, 529(7587):484–489, 2016.
- David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Thore Graepel, Timothy Lillicrap, Karen Simonyan, and Demis Hassabis. A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science, 1144:1140–1144, 2018.
- David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy P. Lillicrap, Karen Simonyan, and Demis Hassabis. Mastering chess and shogi by self-play with a general reinforcement learning algorithm. ArXiv, abs/1712.01815, 2017.
- David Silver, Julian Schrittwieser, Karen Simonyan, Ioannis Antonoglou, Aja Huang, Arthur Guez, Thomas Hubert, Lucas Baker, Matthew Lai, Adrian Bolton, Yutian Chen, Timothy Lillicrap, Fan Hui, Laurent Sifre, George Van Den Driessche, Thore Graepel, and Demis
Hassabis. Mastering the game of Go without human knowledge. Nature, 2017. - Gregory J. Stein, Christopher Bradley, and Nicholas Roy. Learning over subgoals for efficient navigation of structured, unknown environments. In 2nd Annual Conference on Robot Learning, CoRL 2018, Zürich, Switzerland, 29-31 October 2018, Proceedings, volume 87 of Proceedings of Machine Learning Research, pages 213–222. PMLR, 2018.
- Richard S. Sutton, Joseph Modayil, Michael Delp, Thomas Degris, Patrick M. Pilarski, Adam White, and Doina Precup. Horde: a scalable real-time architecture for learning knowledge from unsupervised sensorimotor interaction. In Liz Sonenberg, Peter Stone, Kagan Tumer, and Pinar Yolum, editors, 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), Taipei, Taiwan, May 2-6, 2011, Volume 1-3, pages 761–768. IFAAMAS, 2011.
- Richard S. Sutton, Doina Precup, and Satinder P. Singh. Between mdps and semi-mdps: A framework for temporal abstraction in reinforcement learning. Artif. Intell., 112(1-2):181–211, 1999.
- Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Isabelle Guyon, Ulrike von Luxburg, Samy Bengio, Hanna M. Wallach, Rob Fergus, S. V. N. Vishwanathan, and Roman 13 Garnett, editors, Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, USA, pages 5998–6008, 2017.
- Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Isabelle Guyon, Ulrike von Luxburg, Samy Bengio, Hanna M. Wallach, Rob Fergus, S. V. N. Vishwanathan, and Roman
Garnett, editors, Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, USA, pages 5998–6008, 2017. - Alexander Sasha Vezhnevets, Simon Osindero, Tom Schaul, Nicolas Manfred Otto Heess, Max Jaderberg, David Silver, and Koray Kavukcuoglu. Feudal networks for hierarchical reinforcement learning. ArXiv, abs/1703.01161, 2017.
- Oriol Vinyals, Igor Babuschkin, Wojciech M. Czarnecki, Michaël Mathieu, Andrew Dudzik, Junyoung Chung, David H. Choi, Richard Powell, Timo Ewalds, Petko Georgiev, Junhyuk Oh, Dan Horgan, Manuel Kroiss, Ivo Danihelka, Aja Huang, Laurent Sifre, Trevor Cai, John P. Agapiou, Max Jaderberg, Alexander S. Vezhnevets, Rémi Leblond, Tobias Pohlen, Valentin Dalibard, David Budden, Yury Sulsky, James Molloy, Tom L. Paine, Caglar Gulcehre, Ziyu Wang, Tobias Pfaff, Yuhuai Wu, Roman Ring, Dani Yogatama, Dario Wünsch, Katrina McKinney, Oliver Smith, Tom Schaul, Timothy Lillicrap, Koray Kavukcuoglu, Demis Hassabis, Chris Apps, and David Silver. Grandmaster level in starcraft ii using multi-agent reinforcementlearning. Nature, 575(7782):350–354, Nov 2019.
- David Wilkins. Using patterns and plans in chess. Artif. Intell., 14(2):165–203, 1980.
- Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, and Jamie Brew. Huggingface’s transformers: State-of-the-art natural language processing. CoRR, abs/1910.03771, 2019.
- Yuhuai Wu, Albert Jiang, Jimmy Ba, and Roger Grosse. Int: An inequality benchmark for evaluating generalization in theorem proving. arXiv preprint arXiv:2007.02924, 2020.
- Lunjun Zhang, Ge Yang, and Bradly C. Stadie. World model as a graph: Learning latent landmarks for planning. CoRR, abs/2011.12491, 2020.