How can I efficiently route multiple agents with varied costs?
Hessian Riemannian Flow For Multi-Population Wardrop Equilibrium
This paper addresses optimized routing in networks with multiple user groups (e.g., cars, trucks) having different cost functions (e.g., travel time, emissions). It proves the existence and uniqueness of an optimal equilibrium (where no individual can improve their outcome by changing their route unilaterally) under certain conditions. A novel, efficient algorithm called Hessian Riemannian Flow (HRF) is introduced to compute this equilibrium, outperforming traditional methods.
Relevant to LLM-based multi-agent systems, this research offers: 1) a framework for defining and finding stable states in multi-agent scenarios where agents have diverse objectives, and 2) a computationally efficient algorithm (HRF) for achieving this, potentially applicable to complex interactions within these systems. The concept of varying cost functions aligns with assigning different reward functions to different agents in an LLM-based multi-agent system. The distributed nature of the HRF algorithm can be seen as analogous to independent agents learning and adapting concurrently within a shared environment.