  Bayesian reinforcement learning (BRL) offers a decision-theoretic solution
for reinforcement learning. While "model-based" BRL algorithms have focused
either on maintaining a posterior distribution on models or value functions and
combining this with approximate dynamic programming or tree search, previous
Bayesian "model-free" value function distribution approaches implicitly make
strong assumptions or approximations. We describe a novel Bayesian framework,
Inferential Induction, for correctly inferring value function distributions
from data, which leads to the development of a new class of BRL algorithms. We
design an algorithm, Bayesian Backwards Induction, with this framework. We
experimentally demonstrate that the proposed algorithm is competitive with
respect to the state of the art.
