Low-rank State-action Value-function Approximation
  Value functions are central to Dynamic Programming and Reinforcement Learning
but their exact estimation suffers from the curse of dimensionality,
challenging the development of practical value-function (VF) estimation
algorithms. Several approaches have been proposed to overcome this issue, from
non-parametric schemes that aggregate states or actions to parametric
approximations of state and action VFs via, e.g., linear estimators or deep
neural networks. Relevantly, several high-dimensional state problems can be
well-approximated by an intrinsic low-rank structure. Motivated by this and
leveraging results from low-rank optimization, this paper proposes different
stochastic algorithms to estimate a low-rank factorization of the $Q(s, a)$
matrix. This is a non-parametric alternative to VF approximation that
dramatically reduces the computational and sample complexities relative to
classical $Q$-learning methods that estimate $Q(s,a)$ separately for each
state-action pair.
