# Recent Advances in Hierarchical Reinforcement Learning

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## Abstract

Reinforcement learning is bedeviled by the curse of dimensionality: the number of parameters to be learned grows exponentially with the size of any compact encoding of a state. Recent attempts to combat the curse of dimensionality have turned to principled ways of exploiting temporal abstraction, where decisions are not required at each step, but rather invoke the execution of temporally-extended activities which follow their own policies until termination. This leads naturally to hierarchical control architectures and associated learning algorithms. We review several approaches to temporal abstraction and hierarchical organization that machine learning researchers have recently developed. Common to these approaches is a reliance on the theory of semi-Markov decision processes, which we emphasize in our review. We then discuss extensions of these ideas to concurrent activities, multiagent coordination, and hierarchical memory for addressing partial observability. Concluding remarks address open challenges facing the further development of reinforcement learning in a hierarchical setting.

## Keywords

Learning Algorithm Reinforcement Learning Recent Attempt Hierarchical Organization Control Architecture## Preview

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## References

- Andre, D., and Russell, S. J. 2001. Programmable reinforcement learning agents. In
*Advances in Neural Information Processing Systems: Proceedings of the 2000 Conference*. Cambridge, MA: MIT Press, pp. 1019–1025.Google Scholar - Barto, A. G., Bradtke, S. J., and Singh, S. P. 1995. Learning to act using real-time dynamic programming.
*Artificial Intelligence*72: 81–138.Google Scholar - Bernstein, D., Zilberstein, S., and Immerman, N. 2000. The complexity of decentralized control of markov decision processes. In
*16th Conference on Uncertainty in Artificial Intelligence*.Google Scholar - Bertsekas, D. P. 1987.
*Dynamic Programming: Deterministic and Stochastic Models*. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar - Bertsekas, D. P., and Tsitsiklis, J. N. 1996.
*Neuro-Dynamic Programming*. Belmont, MA: Athena Scientific.Google Scholar - Boyen, X., and Koller, D. 1998. Tractable inference for complex stochastic processes. In G. F. Cooper and S. Moral, editors,
*Proceedings of the Fourteenth Conference on Uncertainty in AI*. San Francisco, CA, Morgan Kaufmann, pp. 33–42.Google Scholar - Bradtke, S. J., and Duff, M. O. 1995. Reinforcement learning methods for continuous-time Markov decision problems. In G. Tesauro, D. S. Touretzky, and T. Leen, editors,
*Advances in Neural Information Processing Systems: Proceedings of the 1994 Conference*, Cambridge, MA: MIT Press, pp. 393–400.Google Scholar - Branicky, M. S., Borkar, V. S., and Mitter, S. K. 1998. A unified framework for hybrid control: Model and optimal control theory.
*IEEE Transactions on Automatic Control*43: 31–45.Google Scholar - Brooks, R. A. 1986. Achieving Artificial Intelligence through building robots. Technical Report A.I. Memo 899, Massachusetts Institute of Technology Artificial Intelligence Laboratory, Cambridge, MA.Google Scholar
- Crites, R. H. 1996.
*Large-Scale Dynamic Optimization Using Teams of Reinforcement Learning Agents*. Ph.D. thesis, Amberst, MA: University of Massachusetts.Google Scholar - Crites, R. H., and Barto, A. G. 1998. Elevator group control using multiple reinforcement learning agents.
*Machine Learning*33: 235–262.Google Scholar - Das, T. K., Gosavi, A., Mahadevan, S., and Marchalleck, N. 1999. Solving semi-Markov decision problems using average reward reinforcement learning.
*Management Science*45: 560–574.Google Scholar - Dean, T. L., and Kanazawa, K. 1989. A model for reasoning about persistence and causation.
*Computational Intelligence*5: 142–150.Google Scholar - Dietterich, T. G. 2000. Hierarchical reinforcement learning with the maxq value function decomposition.
*Journal of Artificial Intelligence Research*13: 227–303.Google Scholar - Digney, B. 1996. Emergent hierarchical control structures: Learning reactive/hierarchical relationships in reinforcement environments. In P. Meas and M. Mataric, editors,
*From Animals to Animats 4: The Fourth Conference on Simulation of Adaptive Behavior*. Cambridge, MA: MIT Press.Google Scholar - Digney, B. 1998. Learning hierarchical control structure from multiple tasks and changing environments. In
*From Animals to Animals 5: The Fifth Conference on Simulation of Adaptive Behavior*. Cambridge, MA: MIT Press.Google Scholar - Driessens, K., and Dzeroski, S. 2002. Integrating experimentation and guidance in relational reinforcement learning. In
*Machine Learning: Proceedings of the Nineteenth International Conference on Machine Learning*.Google Scholar - Fikes, R. E., Hart, P. E., and Nilsson, N. J. 1972. Learning and executing generalized robot plans.
*Artificial Intelligence*3: 251–288.Google Scholar - Finc, S., Singer, Y., and Tishby, N. 1998. The hierarchical hidden Markov model: analysis and applications.
*Machine Learning*32(1): July.Google Scholar - Forestier, J.-P., and Varaiya, P. 1978. Multilayer control of large Markov chains.
*IEEE Transactions on Automatic Control AC-*23: 298–304.Google Scholar - Ghavamzadeh, M., and Mahadevan, S. 2001. Continuous-time hierarchical reinforcement learning. In
*Proceedings of the Eighteenth International Conference on Machine Learning*.Google Scholar - Grudic, G. Z., and Ungar, L. H. 2000. Localizing search in reinforcement learning. In
*Proceedings of the 18th National Conference on Artificial Intelligence (AAAI-00)*, pp. 590–595.Google Scholar - Harel, D. 1987. Statecharts: A visual formalixm for complex systems.
*Science of Computer Programming*8: 231–274.Google Scholar - Hengst, B. 2002. Discovering hierarchy in reinforcement learning with hexq. In
*Machine Learning: Proceedings of the Nineteenth International Conference on Machine Learning*.Google Scholar - Hernandez, N., and Mahadevan, S. 2001. Hierarchical memory-based reinforcement learning.
*Proceedings of Neural Information Processing Systems*.Google Scholar - Howard, R. A. 1971.
*Dynamic Probabilistic Systems: Semi-Markov and Decision Processes*. New York: Wiley.Google Scholar - Huber, M., and Grupen, R. A. 1997. A feedback control structure for on-line learning tasks.
*Robotics and Autonomous Systems*22: 303–315.Google Scholar - Iba, G. A. 1989. A heuristic approach to the discovery of macro-operators.
*Machine Learning*3: 285–317.Google Scholar - Jaakkola, T., Jordan, M. I., and Singh, S. P. 1994. On the convergence of stochastic iterative dynamic programming algorithms.
*Neural Computation*6: 1185–1201.Google Scholar - Jonsson, A., and Barto, A. G. 2001. Automated state abstraction for options using the U-tree algorithm. In
*Advances in Neural Information Processing Systems: Proceedings of the 2000 Conference*, Cambridge, MA: MIT Press, pp. 1054–1060.Google Scholar - Kaelbling, L., Littman, M., and Cassandra A. 1998. Planning and acting in partially observable stochastic domains.
*Artificial Intelligence*101.Google Scholar - Kaelbling, L. P., Littman, M. L., and Moore, A. W. 1996. Reinforcement learning: A survey.
*Journal of Artificial Intelligence Research*4: 237–285.Google Scholar - Klopf, A. H. 1974. Brain function and adaptive systems-ÐA heterostatic theory. Technical Report AFCRL–72–0164, Air Force Cambridge Research Laboratories, Bedford, MA, 1972. A summary appears in
*Proceedings of the International Conference on Systems, Man, and Cybernetics*, IEEE Systems, Man, and Cybernetics Society, Dallas, TXGoogle Scholar - Klopf, A. H. 1982.
*The Hedonistic Neuron: A Theory of Memory, Learning, and Intelligence*. Washington, D.C.: Hemisphere.Google Scholar - Koening, S., and Simmons, R. 1997. Xavier: A robot navigation architecture based on partially observable Markov decision process models. In D. Kortenkamp, P. Bonasso, and R. Murphy, editors,
*Al-based Mobile Robots: Case-studies of Successful Robot Systems*. Cambridge, MA: MIT Press.Google Scholar - Kokotovic, P. V., Khalil, H. K., and O'Reilly, J. 1986. Singular Perturbation Methods in Control:
*Analysis and Design*. London: Academic Press.Google Scholar - Korf, R. E. 1985. Learning to Solve Problems by Searching for Macro-Operators. Boston, MA: Pitman.Google Scholar
- Littman, M. 1994. Markov games as a framework for multi-agent reinforcement learning. In
*Proceedings of the Eleventh International Conference on Machine Learning*, pp. 157–163.Google Scholar - Mahadevan, S. 1996. Average reward reinforcement learning: Foundations, algorithms, and empirical results.
*Machine Learning*22: 159–196.Google Scholar - Mahadevan, S., Marchalleck, N., Das, T., and Gosavi, A. 1997. Self-improving factory simulation using continuous-time average-reward reinforcement learning. In
*Machine Learning: Proceedings of the Fourteenth International Conference*.Google Scholar - Makar, R., Mahadevan, S., and Ghavamzadeh, M. 2001. Hierarchical multi-agent reinforcement learning. In J. P. MuÈller, E. Andre, S. Sen, and C. Frasson, editors,
*Proceedings of the Fifth International Conference on Autonomous Agents*, pp. 246–253.Google Scholar - McCallum, A. K. 1996.
*Reinforcement Learning with Selective Perception and Hidden State*. Ph.D. thesis, University of Rochester.Google Scholar - McGovern, A. 2002.
*Autonomous Discovery of Temporal Abstractions from Interaction with An Environment*. Ph.D. thesis, University of Massachusetts.Google Scholar - McGovern, A., and Barto, A. 2001. Automatic discovery of subgoals in reinforcement learning using diverse density. In C. Brodley and A. Danyluk, editors,
*Proceedings of the Eighteenth International Conference on Machine Learning*, San Francisco, CA: Morgan Kaufmann, pp. 361–368.Google Scholar - Minsky, M. L. 1954.
*Theory of Neural-Analog Reinforcement Systems and its Application to the Brain-Model Problem*. Ph.D. thesis, Princeton University.Google Scholar - Naidu, D. S. 1988.
*Singular Perturbation Methodology in Control Systems*. London: Peter Peregrinus Ltd.Google Scholar - Nourbakhsh, I., Powers, R., and Birchfield, S. 1995. Dervish: An office-navigation robot.
*Al Magazine*16(2): 53–60.Google Scholar - Parr, R. 1998.
*Hierarchical Control and Learning for Markov Decision Processes*. Ph.D. Thesis, Berkeley CA: University of California.Google Scholar - Parr, R., and Russell, S. 1998. Reinforcement learning with hierarchies of machines. In
*Advances in Neural Information Processing Systems: Proceedings of the 1997 Conference*. Cambridge, MA: MIT Press.Google Scholar - Perkins, T. J., and Barto, A. G. Lyapunov design for safe reinforcement learning.
*Journal of Machine Learning Research*. To appear.Google Scholar - Perkins, T. J., and Barto, A. G. 2001. Lyapunov-constrained action sets for reinforcement learning. In C. Brodley and A. Danyluk, editors.
*Proceedings of the Eighteenth International Conference on Machine Learning*. San Francisco, CA: Morgan Kaufmann, pp. 409–416.Google Scholar - Precup, D. 2000.
*Temporal Abstraction in Reinforcement Learning*. Ph.D. thesis, Amherst, MA: University of Massachusetts.Google Scholar - Precup, D., and Sutton, R. S. 1998. Multi-time models for temporally abstract planning. In:
*Advances in Neural Information Processing Systems: Proceedings of the 1997 Conference*. Cambridge MA: MIT Press, pp. 1050–1056.Google Scholar - Precup, D., Sutton, R. S., and Singh, S. 1998. Theoretical results on reinforcement learning with temporally abstract options. In
*Proceedings of the 10th European Conference on Machine Learning, ECML-98*. Springer Verlag, pp. 382–393.Google Scholar - Puterman, M. L. 1994.
*Markov Decision Problems*. New York: Wiley.Google Scholar - Rohanimanesh, K., and Mahadevan, S. Structured approximation of stochastic temporally extended actions. In preparation.Google Scholar
- Rohanimanesh, K., and Mahadevan, S.2001. Decision-theoretic planning with concurrent temporally extended actions. In
*Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence*.Google Scholar - Ross, S. 1983.
*Introduction to Stochastic Dynamic Programming*. New York: Academic Press.Google Scholar - Rummery, G. A., and Niranjan, M. 1994. On-line q-learning using connectionist systems. Technical Report CUED/F-INFENG/TR 166, Cambridge University Engineering Department.Google Scholar
- Samuel, A. L. 1959. Some studies in machine learning using the game of checkers.
*IBM Journal on Research and Development*3: 211–229. Reprinted in E. A. Feigenbaum and J. Feldman, editors, Computers and Thought, New York: McGraw-Hill, pp. 71–105.Google Scholar - Samuel, A. L. 1967. Some studies in machine learning using the game of checkers. II—Recent progress.
*IBM Journal on Research and Development*11: 601–617.Google Scholar - Schwartz, A. 1993. A reinforcement learning method for maximizing undiscounted rewards. In
*Proceedings of the Tenth International Conference on Machine Learning*. Morgan Kaufmann, pp. 298–305.Google Scholar - Shatkay, H., and Kaelbling, L. P. 1997. Learning topological maps with weak local odometric information. In IJCAI 2), pp. 920–929.Google Scholar
- Singh, S., and Bertsekas, D. 1997. Reinforcement learning for dynamic channel allocation in cellular telephone systems. In
*Advances in Neural Information Processing Systems: Proceedings of the 1996 Conference*. Cambridge, MA: MIT Press.Google Scholar - Singh, S., Jaakkola, T., Littman, M. L., and SzepesvaÂri. C. 2000. Convergence results for single-step on-policy reinforcement-learning algorithms.
*Machine Learning*38: 287–308.Google Scholar - Singh, S. P. 1992. Reinforcement learning with a hierarchy of abstract models. In
*Proceedings of the Tenth National Conference on Artificial Intelligence*. Menlo Park, CA: AAAI Press/MIT Press, pp. 202–207.Google Scholar - Singh, S. P. 1992. Scaling reinforcement learning algorithms by learning variable temporal resolution models. In
*Proceedings of the Ninth International Machine Learning Conference*. San Mateo, CA: Morgan Kaufmann, pp. 406–415.Google Scholar - Stone, P., and Sutton, R. S. 2001. Scaling reinforcement learning toward RoboCup soccer. In C. Brodley and A. Danyluk, editors,
*Proceedings of the Eighteenth International Conference on Machine Learning*. San Francisco, CA: Morgan Kaufmann, pp. 537–544.Google Scholar - Sugawara, T. and Lesser. V. 1998. Learning to improve coordinated actions in cooperative distributed problem-solving environments.
*Machine Learning*33: 129–154.Google Scholar - Sutton, R. S. 1996. Generalization in reinforcement learning: Successful examples using sparse coarse coding. In D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, editors,
*Advances in Neural Information Processing Systems: Proceedings of the 1995 Conference*. Cambridge, MA: MIT Press, pp. 1038–1044.Google Scholar - Sutton, R. S., and Barto, A. G. 1981. Toward a modern theory of adaptive networks: Expectation and prediction.
*Psychological Review*88: 135–170.Google Scholar - Sutton, R. S., and Barto, A. G. 1998.
*Reinforcement Learning: An Introduction*. Cambridge, MA: MIT Press.Google Scholar - Sutton, R. S., Precup, D., and Singh, S. 1999. Between mdps and semi-mdps: A framework for temporal abstraction in reinforcement learning.
*Artificial Intelligence*112: 181–211.Google Scholar - Tan, M. 1993. Multi-agent reinforcement learning: Independent vs. cooperative agents. In
*Proceedings of the Tenth International Conference on Machine Learning*, pp. 330–337.Google Scholar - Tesauro, G. J. 1992. Practical issues in temporal difference learning.
*Machine Learning*8: 257–277.Google Scholar - Tesauro, G. J. 1994. TD-gammon, a self-teaching backgammon program, achieves master-level play.
*Neural Computation*6(2): 215–219.Google Scholar - Theocharous, G. 2002.
*Hierarchical Learning and Planning in Partially Observable Markov Decision Processes*. Ph.D. Thesis, Michigan State University.Google Scholar - Theocharous, G., and Mahadevan, S. 2002. Approximate planning with hierarchical partially observable Markov decision process for robot navigation. In
*Proceedings of the IEEE International Conference on Robotics and Automation (ICRA)*.Google Scholar - Theocharous, G., Rohanimanesh, K., and Mahadevan, S. 2001. Learning hierarchical partially observable markov decision processes for robot navigation. In
*Proceedings of the IEEE International Conference on Robotics and Automation (ICRA)*.Google Scholar - Thrun, S. B., and Schwartz, A. 1995. Finding structure in reinforcement learning. In G. Tesauro, D. S. Touretzky, and T. Leen, editors,
*Advances in Neural Information Processing Systems: Proceedings of the 1994 Conference*. Cambridge MA: MIT Press, pp. 385–392.Google Scholar - Tsitsiklis, J. N., and Van Roy, B. 1997.
*An analysis of temporal-difference learning with function approximation. IEEE Transactions on Automatic Control*42: 674–690.Google Scholar - Watkins, C. J. C. H. 1989.
*Learning from Delayed Rewards*. Ph.D. thesis. Cambridge, U.K.: Cambridge University.Google Scholar - Watkins, C. J. C. H., and Dayan, P. 1992. Q-learning.
*Machine Learning*8: 279–292.Google Scholar - Weiss, G. 1999.
*Multiagent Systems: A Modern Approach to Distributed Artificial Intelligence*. Cambridge, MA: MIT Press.Google Scholar - Werbos, P. J. 1977. Advanced forecasting methods for global crisis warning and models of intelligence.
*General Systems Yearbook*22: 25–38.Google Scholar - Werbos, P. J. 1987. Building and understanding adaptive systems: A statistical/numerical approach to factory automation and brain research.
*IEEE Transactions on Systems, Man, and Cybernetics*17: 7–20.Google Scholar - Werbos, P. J. 1992. Approximate dynamic programming for real-time control and neural modeling. In D. A. White and D. A. Sofge, editors,
*Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches*. New York: Van Nostrand Reinhold, pp. 493–525.Google Scholar - Woods, W. A. 1970. Transition network grammars for natural language analysis.
*Communications of the ACM*13: 591–606.Google Scholar