Extreme State Aggregation beyond MDPs

  • Marcus Hutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8776)

Abstract

We consider a Reinforcement Learning setup without any (esp. MDP) assumptions on the environment. State aggregation and more generally feature reinforcement learning is concerned with mapping histories/raw-states to reduced/aggregated states. The idea behind both is that the resulting reduced process (approximately) forms a small stationary finite-state MDP, which can then be efficiently solved or learnt. We considerably generalize existing aggregation results by showing that even if the reduced process is not an MDP, the (q-)value functions and (optimal) policies of an associated MDP with same state-space size solve the original problem, as long as the solution can approximately be represented as a function of the reduced states. This implies an upper bound on the required state space size that holds uniformly for all RL problems. It may also explain why RL algorithms designed for MDPs sometimes perform well beyond MDPs.

Keywords

State aggregation reinforcement learning non-MDP 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [FK01]
    Fazekas, I., Klesov, O.: A general approach to the strong law of large numbers. Theory of Probability & Its Applications 45(3), 436–449 (2001)MathSciNetCrossRefGoogle Scholar
  2. [FPP04]
    Ferns, N., Panangaden, P., Precup, D.: Metrics for finite Markov decision processes. In: Proc. 20th Conf. on Uncertainty in Artificial Intelligence (UAI 2004), pp. 162–169 (2004)Google Scholar
  3. [GDG03]
    Givan, R., Dean, T., Greig, M.: Equivalence notions and model minimization in Markov decision processes. Artificial Intelligence 147(1–2), 163–223 (2003)MathSciNetCrossRefMATHGoogle Scholar
  4. [Hut05]
    Hutter, M.: Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability. Springer, Berlin (2005)Google Scholar
  5. [Hut09a]
    Hutter, M.: Feature dynamic Bayesian networks. In: Proc. 2nd Conf. on Artificial General Intelligence (AGI 2009), vol. 8, pp. 67–73. Atlantis Press (2009)Google Scholar
  6. [Hut09b]
    Hutter, M.: Feature reinforcement learning: Part I: Unstructured MDPs. Journal of Artificial General Intelligence 1, 3–24 (2009)CrossRefGoogle Scholar
  7. [Hut14]
    Hutter, M.: Extreme state aggregation beyond MDPs. Technical report (2014), http://www.hutter1.net/publ/exsaggx.pdf
  8. [JOA10]
    Jaksch, T., Ortner, R., Auer, P.: Near-optimal regret bounds for reinforcement learning. Journal of Machine Learning Research 11, 1563–1600 (2010)MathSciNetMATHGoogle Scholar
  9. [LH12]
    Lattimore, T., Hutter, M.: PAC bounds for discounted MDPs. In: Bshouty, N.H., Stoltz, G., Vayatis, N., Zeugmann, T. (eds.) ALT 2012. LNCS (LNAI), vol. 7568, pp. 320–334. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. [LH14]
    Lattimote, T., Hutter, M.: General time consistent discounting. Theoretical Computer Science 519, 140–154 (2014)MathSciNetCrossRefGoogle Scholar
  11. [LHS13]
    Lattimore, T., Hutter, M., Sunehag, P.: The sample-complexity of general reinforcement learning. Journal of Machine Learning Research, W&CP: ICML 28(3), 28–36 (2013)Google Scholar
  12. [McC96]
    McCallum, A.K.: Reinforcement Learning with Selective Perception and Hidden State. PhD thesis, Department of Computer Science, University of Rochester (1996)Google Scholar
  13. [MMR11]
    Maillard, O.-A., Munos, R., Ryabko, D.: Selecting the state-representation in reinforcement learning. In: Advances in Neural Information Processing Systems (NIPS 2011), vol. 24, pp. 2627–2635 (2011)Google Scholar
  14. [Ngu13]
    Nguyen, P.: Feature Reinforcement Learning Agents. PhD thesis, Research School of Computer Science, Australian National University (2013)Google Scholar
  15. [NMRO13]
    Nguyen, P., Maillard, O., Ryabko, D., Ortner, R.: Competing with an infinite set of models in reinforcement learning. JMLR WS&CP AISTATS 31, 463–471 (2013)Google Scholar
  16. [NOR13]
    Maillard, O.-A., Nguyen, P., Ortner, R., Ryabko, D.: Optimal regret bounds for selecting the state representation in reinforcement learning. JMLR W&CP ICML 28(1), 543–551 (2013)Google Scholar
  17. [NSH11]
    Nguyen, P., Sunehag, P., Hutter, M.: Feature reinforcement learning in practice. In: Sanner, S., Hutter, M. (eds.) EWRL 2011. LNCS, vol. 7188, pp. 66–77. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. [Put94]
    Puterman, M.L.: Markov Decision Processes — Discrete Stochastic Dynamic Programming. Wiley, New York (1994)MATHGoogle Scholar
  19. [RN10]
    Russell, S.J., Norvig, P.: Artificial Intelligence. A Modern Approach, 3rd edn. Prentice-Hall, Englewood Cliffs (2010)Google Scholar
  20. [SB98]
    Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998)Google Scholar
  21. [SH10]
    Sunehag, P., Hutter, M.: Consistency of feature Markov processes. In: Hutter, M., Stephan, F., Vovk, V., Zeugmann, T. (eds.) ALT 2010. LNCS (LNAI), vol. 6331, pp. 360–374. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  22. [SLL09]
    Strehl, A.L., Li, L., Littman, M.L.: Reinforcement learning in finite MDPs: PAC analysis. Journal of Machine Learning Research 10, 2413–2444 (2009)MathSciNetMATHGoogle Scholar
  23. [VGS05]
    Vovk, V., Gammerman, A., Shafer, G.: Algorithmic Learning in a Random World. Springer, New York (2005)MATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Marcus Hutter
    • 1
  1. 1.Research School of Computer ScienceAustralian National UniversityCanberraAustralia

Personalised recommendations