  Current state-of-the-art model-based reinforcement learning algorithms use
trajectory sampling methods, such as the Cross-Entropy Method (CEM), for
planning in continuous control settings. These zeroth-order optimizers require
sampling a large number of trajectory rollouts to select an optimal action,
which scales poorly for large prediction horizons or high dimensional action
spaces. First-order methods that use the gradients of the rewards with respect
to the actions as an update can mitigate this issue, but suffer from local
optima due to the non-convex optimization landscape. To overcome these issues
and achieve the best of both worlds, we propose a novel planner, Cross-Entropy
Method with Gradient Descent (CEM-GD), that combines first-order methods with
CEM. At the beginning of execution, CEM-GD uses CEM to sample a significant
amount of trajectory rollouts to explore the optimization landscape and avoid
poor local minima. It then uses the top trajectories as initialization for
gradient descent and applies gradient updates to each of these trajectories to
find the optimal action sequence. At each subsequent time step, however, CEM-GD
samples much fewer trajectories from CEM before applying gradient updates. We
show that as the dimensionality of the planning problem increases, CEM-GD
maintains desirable performance with a constant small number of samples by
using the gradient information, while avoiding local optima using initially
well-sampled trajectories. Furthermore, CEM-GD achieves better performance than
CEM on a variety of continuous control benchmarks in MuJoCo with 100x fewer
samples per time step, resulting in around 25% less computation time and 10%
less memory usage. The implementation of CEM-GD is available at
$\href{https://github.com/KevinHuang8/CEM-GD}{\text{https://github.com/KevinHuang8/CEM-GD}}$.
