Large-scale inverse learning of user equilibrium via multiconvex optimization

This study proposes a scalable inverse learning framework for constructing context-dependent, nonparametric network equilibrium models from multiday noisy link-flow observations. Specifically, the potential function is parameterized as a nonnegative linear combination of convex bases. With a sufficiently rich set of basis functions, learning the nonnegative combination weights infers the functional form of the potential function directly from data. By replacing the context-dependent equilibrium constraints with well-defined, value-function-based suboptimality gap functions, this convex-basis-based parametrization allows a multiconvex inverse learning reformulation that can be decomposed and solved via a GPU-accelerated block coordinate descent algorithm. Moreover, the parametrized potential function incorporates context features (e.g., day of week, weather) and the learned model predicts user equilibria that vary with context rather than collapsing to a single average travel pattern. Under appropriate assumptions, this framework achieves asymptotically minimal fitting error and consistent parameter estimation. Synthetic and empirical experiments demonstrate the proposed framework's consistency and scalability.