Geometry of Policy Improvement
This work provides theoretical insights into policy optimization for decision-making agents with limited information, though it appears incremental as it builds on geometric interpretations of existing policy improvement methods.
The paper tackles the problem of optimal memoryless decision-making by analyzing the relationship between an agent's information about the system state and policy performance, showing that policies randomizing among at most k actions maximize expected long-term reward when at most k world states are consistent with observations.
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.