  SDYNA is a general framework designed to address large stochastic
reinforcement learning problems. Unlike previous model based methods in FMDPs,
it incrementally learns the structure and the parameters of a RL problem using
supervised learning techniques. Then, it integrates decision-theoric planning
algorithms based on FMDPs to compute its policy. SPITI is an instanciation of
SDYNA that exploits ITI, an incremental decision tree algorithm, to learn the
reward function and the Dynamic Bayesian Networks with local structures
representing the transition function of the problem. These representations are
used by an incremental version of the Structured Value Iteration algorithm. In
order to learn the structure, SPITI uses Chi-Square tests to detect the
independence between two probability distributions. Thus, we study the relation
between the threshold used in the Chi-Square test, the size of the model built
and the relative error of the value function of the induced policy with respect
to the optimal value. We show that, on stochastic problems, one can tune the
threshold so as to generate both a compact model and an efficient policy. Then,
we show that SPITI, while keeping its model compact, uses the generalization
property of its learning method to perform better than a stochastic classical
tabular algorithm in large RL problem with an unknown structure. We also
introduce a new measure based on Chi-Square to qualify the accuracy of the
model learned by SPITI. We qualitatively show that the generalization property
in SPITI within the FMDP framework may prevent an exponential growth of the
time required to learn the structure of large stochastic RL problems.
