Abstract

Many of the recent trajectory optimization algorithms alternate between linear approximation
of the system dynamics around the mean trajectory and conservative policy update.
One way of constraining the policy change is by bounding the Kullback-Leibler (KL)
divergence between successive policies. These approaches already demonstrated great experimental
success in challenging problems such as end-to-end control of physical systems.
However, these approaches lack any improvement guarantee as the linear approximation of
the system dynamics can introduce a bias in the policy update and prevent convergence
to the optimal policy. In this article, we propose a new model-free trajectory-based policy
optimization algorithm with guaranteed monotonic improvement. The algorithm backpropagates
a local, quadratic and time-dependent Q-Function learned from trajectory data
instead of a model of the system dynamics. Our policy update ensures exact KL-constraint
satisfaction without simplifying assumptions on the system dynamics. We experimentally
demonstrate on highly non-linear control tasks the improvement in performance of our algorithm
in comparison to approaches linearizing the system dynamics. In order to show the
monotonic improvement of our algorithm, we additionally conduct a theoretical analysis of
our policy update scheme to derive a lower bound of the change in policy return between
successive iterations.