Differentiable Bilevel Programming for Stackelberg Congestion Games

Understand

In a Stackelberg congestion game (SCG), a leader aims to maximize their own gain by anticipating and manipulating the equilibrium state at which the followers settle by playing a congestion game.

• Often formulated as bilevel programs, large-scale SCGs are well known for their intractability and complexity.
• Here, we attempt to tackle this computational challenge by marrying traditional methodologies with the latest differentiable programming techniques in machine learning.
• The core idea centers on replacing the lower-level equilibrium problem with a smooth evolution trajectory defined by the imitative logit dynamic (ILD), which we prove converges to the equilibrium of the congestion game under mild conditions.