Your Learned Constraint is Secretly a Backward Reachable Tube

TL;DR

This paper reveals that inverse constraint learning actually recovers a backward reachable tube, a set indicating states from which failure is inevitable, rather than the failure set itself, impacting safe policy search and transferability.

Contribution

The paper demonstrates that ICL recovers a backward reachable tube instead of the failure set, highlighting the importance of system dynamics in constraint inference.

Findings

ICL recovers a backward reachable tube, not the failure set.

The recovered BRT depends on the data collection system's dynamics.

Implications for sample efficiency and transferability of learned constraints.

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.