  Reinforcement Learning (RL) algorithms allow artificial agents to improve
their action selections so as to increase rewarding experiences in their
environments. Deep Reinforcement Learning algorithms require solving a
nonconvex and nonlinear unconstrained optimization problem. Methods for solving
the optimization problems in deep RL are restricted to the class of first-order
algorithms, such as stochastic gradient descent (SGD). The major drawback of
the SGD methods is that they have the undesirable effect of not escaping saddle
points and their performance can be seriously obstructed by ill-conditioning.
Furthermore, SGD methods require exhaustive trial and error to fine-tune many
learning parameters. Using second derivative information can result in improved
convergence properties, but computing the Hessian matrix for large-scale
problems is not practical. Quasi-Newton methods require only first-order
gradient information, like SGD, but they can construct a low rank approximation
of the Hessian matrix and result in superlinear convergence. The limited-memory
Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) approach is one of the most popular
quasi-Newton methods that construct positive definite Hessian approximations.
In this paper, we introduce an efficient optimization method, based on the
limited memory BFGS quasi-Newton method using line search strategy -- as an
alternative to SGD methods. Our method bridges the disparity between first
order methods and second order methods by continuing to use gradient
information to calculate a low-rank Hessian approximations. We provide formal
convergence analysis as well as empirical results on a subset of the classic
ATARI 2600 games. Our results show a robust convergence with preferred
generalization characteristics, as well as fast training time and no need for
the experience replaying mechanism.
