Gradient-Based Mixed Planning with Discrete and Continuous Actions
  Dealing with planning problems with both discrete logical relations and
continuous numeric changes in real-world dynamic environments is challenging.
Existing numeric planning systems for the problem often discretize numeric
variables or impose convex quadratic constraints on numeric variables, which
harms the performance when solving the problem. In this paper, we propose a
novel algorithm framework to solve the numeric planning problems mixed with
discrete and continuous actions based on gradient descent. We cast the numeric
planning with discrete and continuous actions as an optimization problem by
integrating a heuristic function based on discrete effects. Specifically, we
propose a gradient-based framework to simultaneously optimize continuous
parameters and actions of candidate plans. The framework is combined with a
heuristic module to estimate the best plan candidate to transit initial state
to the goal based on relaxation. We repeatedly update numeric parameters and
compute candidate plan until it converges to a valid plan to the planning
problem. In the empirical study, we exhibit that our algorithm framework is
both effective and efficient, especially when solving non-convex planning
problems.
