  Signal temporal logic (STL) is a powerful tool for describing complex
behaviors for dynamical systems. Among many approaches, the control problem for
systems under STL task constraints is well suited for learning-based solutions,
because STL is equipped with robustness metrics that quantify the satisfaction
of task specifications and thus serve as useful rewards. In this work, we
examine existing and potential robustness metrics specifically from the
perspective of how they can aid such learning algorithms. We show that various
desirable properties restrict the form of potential metrics, and introduce a
new one based on the results. The effectiveness of this new robustness metric
for accelerating the learning procedure is demonstrated through an insightful
case study.
