Problem
Research questions and friction points this paper is trying to address.
Voronoi regions
agent utility
utility gradient
Cost-Induced Voronoi
state space
Agent Utilities over Generalized Voronoi Regions and their Gradients
🤖 AI Summary
This work addresses the problem of differentiable spatial coverage under mismatched state and partition spaces by introducing Cost-Induced Voronoi (CIV) regions, wherein each agent’s utility is defined as the integral of a utility density over its CIV region. By integrating Linear Quadratic Regulator (LQR) optimal control to construct CIV partitions, the study extends Voronoi tessellations to heterogeneous space scenarios for the first time. A key innovation lies in the application of the Reynolds transport theorem to analytically derive utility gradients, enabling efficient optimization. Evaluated in a two-team soccer simulation, the proposed method achieves gradient accuracy comparable to finite differences while reducing computational time by nearly an order of magnitude.
📝 Abstract
In this paper, we generalize the concept of Voronoi regions, define agent utility as the integral of a utility density over the corresponding Voronoi region, derive gradients of the utility, and illustrate the approach in a two-team example from soccer.
The generalization of Voronoi regions is in the form of so-called Cost-Induced Voronoi (CIV) regions, where the agent state space may differ from the space being partitioned. One example of such regions is when the cost is given by the optimal solution of an LQR control problem. Then the agent states include position as well as velocity, while the partitioned space only includes positions.
The agent utility is defined by integrating some utility density over the CIV region of the agent. This utility density might be the probability density of some beneficial event, such as receiving a pass in soccer. The utility is then the overall probability of receiving a pass and the gradient represents a way to improve that probability. We show how this utility gradient can be computed using the Reynolds Transport Theorem from fluid mechanics, and that this approach achieves similar accuracy while reducing computation time by about an order of magnitude compared to a baseline finite-difference approximation.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Cost-Induced Voronoi
Utility Gradient
Reynolds Transport Theorem
Generalized Voronoi Regions
LQR-based Cost
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