Your Learned Constraint is Secretly a Backward Reachable Tube

Mohamad Qadri, Gokul Swamy, Jonathan Francis, Michael Kaess, Andrea Bajcsy

Keywords: Constraint Inference, Learning from Demonstration, Safe Control

TL;DR: We show that the mathematical set encoded by Inverse Constraint Learning is a dynamics-dependent Backward Reachable Tube (BRT) and not the dynamics independent Failure Set.

Abstract: Inverse Constraint Learning (ICL) is the problem of inferring constraints from safe (i.e., constraint-satisfying) demonstrations. The hope is that these inferred constraints can then be used downstream to search for safe policies for new tasks and, potentially, under different dynamics. Our paper explores the question of what mathematical entity ICL recovers. Somewhat surprisingly, we show that both in theory and in practice, ICL recovers the set of states where failure is inevitable, rather than the set of states where failure has already happened. In the language of safe control, this means we recover a backwards reachable tube (BRT) rather than a failure set. In contrast to the failure set, the BRT depends on the dynamics of the data collection system. We discuss the implications of the dynamics-conditionedness of the recovered constraint on both the sample-efficiency of policy search and the transferability of learned constraints.

Submission Number: 40