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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.

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References

  • Andre, D., and Russell, S. J. 2001. Programmable reinforcement learning agents. In Advances in Neural Information Processing Svstesns: Proceedings of the 2000 Conference. Cambridge, MA: MIT Press, pp. 1019-1025.

    Google Scholar 

  • Barto, A. G., Bradike, S. J., and Singh. S. P. 1995. Learning to act using real-time dynamic programming. Artificial Intelligence 72: 81-138.

    Google Scholar 

  • Bemstein, D., Zilberstein, S., and Immerman, N. 2000. The complexity of decentralized control of markov decision processes. In C. Boutilier and M. Goldszmidt (eds). Uncertainly in Artificial Intelligence: Proceedings of the 16th Conference. San Francisco CA: Morgan Kaufmann, pp. 32-37.

    Google Scholar 

  • Bertsekas, D. P. 1987. Dynamic Programming: Deterministic and Stochastic Models. Englewood Cliffs, NJ: Prentice-Hall.

    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 (eds.), Proceedings of the Fourteenth Conference on Uncertainty in Al, 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 (eds.). 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 hybnd 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 Al. Memo 899. Cambridge, MA: Massachusetts Institute of Technology Artificial Intelligence Laboratory.

    Google Scholar 

  • Cao, X. R., Ren, Z., Bhatnagar, S., Fu, M., and Marcus, S. 2002. A time aggregation approach to Markov decision processes. Automatica 38: 929-943.

    Google Scholar 

  • Crites. R. H. 1996. Large-Scale Dvnaniic Optimization Using Teams of Reinforcement Learning Agents. Ph.D. thesis. Amherst. 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 (eds.), From Animals to Animals 4: The Fourth Confe,-ence 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. Carnbndge, MA: MIT Press.

    Google Scholar 

  • Driessens, K., and Dzeroski, S. 2002. Integrating experimentation and guidance in relational reinforcement learning. In Maching Learning: Proceedings of the Nineteenth international Conference on Machine Learning. San Francisco. GA: Morgan Kaufmann. pp. 115-122.

    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 

  • Fine, S., Singer, Y., and Tishby, N. 1998. The hierarchical hidden Markov model: analysis and applications. Machine Learning 32(1). July.

  • Forestier, J.-P., and Varaiya, P. 1978. Multilayer control of large markov chains. IEEE Transactions on Automatic Control AC-23: 298-304.

    Google Scholar 

  • Ghavarnzadeh, M., and Mahadevan, S. 2001. Continuous-time hierarchical reinforcement learning. In Proceedings of the Eighteenth International conference on Machine Learning. San Francisco. CA: Morgan Kaufmann, pp. 186-193.

    Google Scholar 

  • Ghavamzadeh, M., and Mahadevan, S. 2002. Hierarchically optimal average reward reinforcement learning. In C. Sammut and M. Goldszmidt (eds). Proceedings of the Ni,ieteenth i,iternatioiial conference on Machine Learning (1LML 2002). San Francisco CA: Morgan Kaufmann, pp. 195-202.

    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.

  • Harel, D. 1987. Statecharts: Avisual formalixm for complex systems. Science of Coniputer Programming 8: 231-274.

    Google Scholar 

  • Hengst, B. 2002. Discovering hierarchy in reinforcement learning with hexq. In Maching Learning: Proceedings of the Nineteenth International Conference on Machine Learning. San Francisco, CA: Morgan Kaufmann, pp. 243-250.

    Google Scholar 

  • Hernandez, N., and Mahadevan. S. 2001. Hierarchical memory-based reinforcement learning. In Advances in Neural information Processing Systems: Proceedings of the 2000 conference. Cambridge, MA: MIT Press, pp. 1047-1053.

    Google Scholar 

  • Howard, R. A. 1971. Dynamic Probabilistic Systems: Semi-Markar 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 Autononioiis Sstems 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 li-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., Littrnan. M., and Cassandra, A. 1998. Planning and acting in partially observable stochastic domains. Artificial intelligence 101.

  • 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. 1972. Brain function and adaptive systems-a heterostatic theory. Technical Report AFCRL-72-0164, Bedford, MA: Air Force Cambridge Research Laboratories. A summary appears in Proceedings of the International Conference on Systems,Man, and Cybernetics, 1974, IEEE Systems, Man, and Cybernetics Society, Dallas, TX.

    Google Scholar 

  • Klopf, A. H. 1982. The Hedonistic Neuron: A Theory of Memory, Learning, and Intelligence. Washington, D.C.: Hemisphere.

    Google Scholar 

  • Koenig, 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 (eds.), 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. San Francisco, CA: Morgan Kaufmann, pp. 157-163.

    Google Scholar 

  • Mahadevan, S. 1996. Average reward reinforcement leaming: 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 Proceedings of the Fourteenth international Conference. San Francisco, CA: Morgan Kaufmann, pp. 202-210.

    Google Scholar 

  • Makar, R., Mahadevan, S., and Ghavamzadeh, M. 2001. Hierarchical multi-agent reinforcement learning. In J. P. Muller, E. Andre, S. Sen, and C. Frasson (eds.), Proceedings of the Fifth international Conference on Autonomous Agents. New York: ACM Press, pp. 246-253.

    Google Scholar 

  • McCalIum, A. K. 1996. Reinforcement Learning with Selective Perceptioin and Hidden State. Ph.D. thesis, University of Rochester.

  • McGovern, A. 2002. Autonomous Discovers of Temporal Abstractions from interaction with An Environment. Ph.D. thesis. University of Massachusetts.

  • McGovern, A., and Barb, A. 2001. Automatic discovery of subgoals in reinforcement learning using diverse density. In 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.

  • 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. PhD 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. 2001. Lyapunov-constrained action sets for reinforcement learning. In C. Brodley and A. Danyluk (eds.). Proceedings of the Eighteenth international Conference on Machine Learning.San Francisco, CA: Morgan Kaufmann. pp. 409-416.

    Google Scholar 

  • Perkins, T. J., and Barb, A. G. 2002. Lyapunov design for safe reinforcement learning. Journal of Machine Learning Research 3: 803-832.

    Google Scholar 

  • Precup, D. 2000. Temporal Abstraction in Reinforcentent 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 Machime Learning, ECML-98. Springer Verlag, pp. 382-393.

  • Puterman, M. L. 1994. Markov Decision Problems. Wiley, NY.

    Google Scholar 

  • Rohanimanesh, K., and Mahadevan, S. 2002 Learning to take concurrent actions. In Advances in Neural Information Processing Systems: Proceedings of the 2002 Conference. Cambridge: MIT Press. In press.

    Google Scholar 

  • Rohanimanesh, K., and Mahadevan, S. Structured approximation of stochastic temporally extended actions. In preparation.

  • Rohanimanesh, K., and Mahadevan, S. 2001. Decision-theoretic planning with concurrent temporally extended actions. InProceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence.

  • Ross. S. 1983. Introduction to Stochastic Dynamic Programming. New York: Academic Press.

    Google Scholar 

  • Rummery, G. A., and Niranjan, M. 1994. On-line q-learrnng using connectionist systems. Technical Report CUED/F-INFENG/'FR 166, Cambridge University Engineering Department.

  • Samuel. A. L. 1963. Some studies in machine learning using the game of checkers. IBM Journal on Research and Developntent 3: 211-229, 1959. Reprinted in E. A. Feigenbaurn and J. Feldman (eds.), Computers and Thought. New York: McGraw-Hill, pp. pp71-105.

    Google Scholar 

  • Samuel. A. L. 1967. Some studies in machine learning using the game of checkers. Il-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.

  • Shatkay, H., and Kaelbling. L. P. 1997. Learning topological maps with weak local odometric information. In IJC4I (2). 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, pp. 974-980.

    Google Scholar 

  • Singh, S., Jaakkola, T., Littman, M. L., and Szepesvári. 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 Notional 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 (eds.), 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 leaming: Successful examples using sparse coarse coding. In D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo (eds.). Advances in Neural Information Processing Svstenis: Proceedings of the 1995 Conference. Cambridge. MA: MIT Press. pp. 1038-1044.

    Google Scholar 

  • Sutton, R. S., and Barto, A. G. 1981. Toward a modem 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 leaming: Independent vs. cooperative agents. In Proceedings of the Tenth International Conference on Mac/tine Learning. San Francisco, CA: Morgan Kaufmann, pp. 330-337.

    Google Scholar 

  • Tesauro, G. J. 1992. Practical issues in temporal difference leaming. Machine Learning 8: 257-277.

    Google Scholar 

  • Tesauro, G. J. 1994. TD-gammon, a self-teaching backgammon program, achieves master-level play. Neural Coniputation 6(2): 215-219.

    Google Scholar 

  • Theocharous, G. 2002. Hierarchical Learning and Planning in Partially Observable Markov Derision Processes. Ph.D. Thesis, Michigan State University.

  • Theocharous, G., and Mahadevan. S. 2002. Approximate planning with hierarchical partially observable markov decision processs for robot navigation. In Proceedings of the IEEE International Conference on Robotics and Autontation (ICRA).

  • Theocharous, G., Rohanimanesh. K., and Mahadevan, S. 2001. Learning hierarchical partially observable markov decision processs for robot navigation. In Proceedings of the IEEE International Conference o,i Robotics and Automation (ICRA).

  • Thrun, S. B., and Schwartz, A. 1995. Finding structure in reinforcement learning. In G. Tesauro, D. S. Touretzky, and T. Leen (eds.), Advances tn Neural Information Processing Systems: Proceedings of the 1994 Conference. Cambridge, MA: MIT Press, PP. 385-392.

    Google Scholar 

  • Tsitsikhs, 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 front Delayed Rewards. Ph.D. thesis, Cambridge, England: 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 (eds.), Handbook of Intelligent Control: Neural, Fuzzy.and Adaptive Approaches. New York: Van Nostrand Reinhold, pp. 493-325.

    Google Scholar 

  • Woods, W. A. 1970. Transition network grammars for natural language analysis.Comntunications of the ACM 13: 591-606.

    Google Scholar 

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  1. Autonomous Learning Laboratory, Department of Computer Science, University of Massachusetts, Amherst, MA, 01003

    Andrew G. Barto & Sridhar Mahadevan

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  1. Andrew G. Barto
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Barto, A.G., Mahadevan, S. Recent Advances in Hierarchical Reinforcement Learning. Discrete Event Dynamic Systems 13, 341–379 (2003). https://doi.org/10.1023/A:1025696116075

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