Geometry of Policy Improvement

  • Guido MontúfarEmail author
  • Johannes Rauh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10589)


We investigate the geometry of optimal memoryless time independent decision making in relation to the amount of information that the acting agent has about the state of the system. We show that the expected long term reward, discounted or per time step, is maximized by policies that randomize among at most k actions whenever at most k world states are consistent with the agent’s observation. Moreover, we show that the expected reward per time step can be studied in terms of the expected discounted reward. Our main tool is a geometric version of the policy improvement lemma, which identifies a polyhedral cone of policy changes in which the state value function increases for all states.


Partially Observable Markov Decision Process Reinforcement learning Memoryless stochastic policy Policy gradient theorem 



We thank Nihat Ay for support and insightful comments.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Departments of Mathematics and StatisticsUCLALos AngelesUSA

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