Risk-Aware Submodular Optimization for Multi-Robot Coordination
This work addresses risk-aware decision-making for multi-robot systems, such as mobility-on-demand and environmental monitoring, representing an incremental extension of CVaR to submodular optimization.
The paper tackles the problem of incorporating risk into combinatorial decisions under uncertainty for multi-robot coordination, formulating a discrete submodular maximization problem using Conditional-Value-at-Risk (CVaR) and proposing a Sequential Greedy Algorithm with a constant-factor approximation guarantee and polynomial runtime, demonstrated through simulations in vehicle assignment and sensor selection case studies.
We study the problem of incorporating risk while making combinatorial decisions under uncertainty. We formulate a discrete submodular maximization problem for selecting a set using Conditional-Value-at-Risk (CVaR), a risk metric commonly used in financial analysis. While CVaR has recently been used in optimization of linear cost functions in robotics, we take the first step towards extending this to discrete submodular optimization and provide several positive results. Specifically, we propose the Sequential Greedy Algorithm that provides an approximation guarantee on finding the maxima of the CVaR cost function under a matroidal constraint. The approximation guarantee shows that the solution produced by our algorithm is within a constant factor of the optimal and an additive term that depends on the optimal. Our analysis uses the curvature of the submodular set function, and proves that the algorithm runs in polynomial time. This formulates a number of combinatorial optimization problems that appear in robotics. We use two such problems, vehicle assignment under uncertainty for mobility-on-demand and sensor selection with failures for environmental monitoring, as case studies to demonstrate the efficacy of our formulation. In particular, for the mobility-on-demand study, we propose an online triggering assignment algorithm that triggers a new assignment only can potentially lead to reducing the waiting time at demand locations. We verify the performance of the Sequential Greedy Algorithm and the online triggering assignment algorithm through simulations.