R-MAX - A general polynomial time algorithm for near-optimal reinforcement learning

Ronen I. Brafman, Moshe Tennenholtz

Research output: Contribution to journalArticlepeer-review

590 Scopus citations


R-MAX is a very simple model-based reinforcement learning algorithm which can attain near-optimal average reward in polynomial time. In R-MAX, the agent always maintains a complete, but possibly inaccurate model of its environment and acts based on the optimal policy derived from this model. The model is initialized in an optimistic fashion: all actions in all states return the maximal possible reward (hence the name). During execution, it is updated based on the agent's observations. R-MAX improves upon several previous algorithms: (1) It is simpler and more general than Kearns and Singh's E3 algorithm, covering zero-sum stochastic games. (2) It has a built-in mechanism for resolving the exploration vs. exploitation dilemma. (3) It formally justifies the "optimism under uncertainty" bias used in many RL algorithms. (4) It is simpler, more general, and more efficient than Brafman and Tennenholtz's LSG algorithm for learning in single controller stochastic games. (5) It generalizes the algorithm by Monderer and Tennenholtz for learning in repeated games. (6) It is the only algorithm for learning in repeated games, to date, which is provably efficient, considerably improving and simplifying previous algorithms by Banos and by Megiddo.

Original languageEnglish
Pages (from-to)213-231
Number of pages19
JournalJournal of Machine Learning Research
Issue number2
StatePublished - 15 Feb 2003


  • Learning in Games
  • Markov Decision Processes
  • Provably Efficient Learning
  • Reinforcement Learning
  • Stochastic Games

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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