Human-in-the-Loop Multi-Robot Information Gathering with Inverse Submodular Maximization

We consider a new type of inverse combinatorial optimization, Inverse Submodular Maximization (ISM), for its application in human-in-the-loop multi-robot information gathering.Forward combinatorial optimization - solving a combinatorial problem given the reward (cost)-related parameters - is widely used in multi-robot coordination. In the standard pipeline, domain experts design the reward (cost)-related parameters offline. These parameters are utilized for coordinating robots online. What if non-expert human supervisors desire to change these parameters during task execution to adapt to some new requirements? We are interested in the case where human supervisors can suggest what path primitives to take, and the robots need to change the internal decision-making parameters accordingly. We study such problems from the perspective of inverse combinatorial optimization, i.e., the process of finding parameters that give certain solutions to the problem. Specifically, we propose a new formulation for ISM for a family of multi-robot information gathering scenarios, in which we aim to find a new set of parameters that minimally deviates from the current parameters while causing a greedy algorithm to output path primitives that are the same as those desired by the human supervisors. We show that for the case with a single suggestion, such problems can be formulated as a Mixed Integer Quadratic Program (MIQP), which is intractable for existing solvers when the problem size is large. We propose a new Branch $\&$ Bound algorithm to solve such problems. For the case with multiple suggestions from several human supervisors, the problem can be cast as a multi-objective optimization and can be solved using Pareto Monte Carlo Tree Search. In numerical simulations, we demonstrate how to use ISM in multi-robot scientific data collection and event detection-driven coverage control.