Large-scale inverse learning of user equilibrium via multiconvex optimization
提出一种可扩展的逆向学习框架，利用多天有噪声的链路流量观测数据构建上下文相关的非参数网络均衡模型，通过多凸优化和GPU加速算法实现高效求解，并预测随上下文变化的用户均衡模式。
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.