  Given recent deep learning results that demonstrate the ability to
effectively optimize high-dimensional non-convex functions with gradient
descent optimization on GPUs, we ask in this paper whether symbolic gradient
optimization tools such as Tensorflow can be effective for planning in hybrid
(mixed discrete and continuous) nonlinear domains with high dimensional state
and action spaces? To this end, we demonstrate that hybrid planning with
Tensorflow and RMSProp gradient descent is competitive with mixed integer
linear program (MILP) based optimization on piecewise linear planning domains
(where we can compute optimal solutions) and substantially outperforms
state-of-the-art interior point methods for nonlinear planning domains.
Furthermore, we remark that Tensorflow is highly scalable, converging to a
strong plan on a large-scale concurrent domain with a total of 576,000
continuous action parameters distributed over a horizon of 96 time steps and
100 parallel instances in only 4 minutes. We provide a number of insights that
clarify such strong performance including observations that despite long
horizons, RMSProp avoids both the vanishing and exploding gradient problems.
Together these results suggest a new frontier for highly scalable planning in
nonlinear hybrid domains by leveraging GPUs and the power of recent advances in
gradient descent with highly optimized toolkits like Tensorflow.
