Physics-Informed Generative World Models for Real-Time Bidding: Deriving Statistical Laws from First Principles

Abstract

Reliable policy optimization in real-time bidding (RTB) demands a high-fidelity world model capable of simulating stochastic market dynamics under constraints. However, current generative simulators are limited by their reliance on deterministic point prediction objectives (e.g., mean squared error). These approaches are statistically ill-posed for auction data, failing to capture the extreme heteroscedasticity where variance scales explosively with the mean, and neglecting the structural coupling between feedback variables. In this paper, we bridge this gap through a physics-informed statistical modeling framework derived from first principles. Axiomatically, we substantiate that the marginal distributions of bidding feedback follow Poisson-lognormal and Tweedie-lognormal laws, and operationalize them into an efficient zero-inflated generalized beta of the second kind (ZI-GB2) surrogate. This physical formulation explicitly models variance scaling, naturally resolving the gradient dominance issues inherent in heteroscedastic regression. Furthermore, we identify that the asymptotic tail dependence between cost and value arises from the shared underlying winning events, necessitating a normalizing flow copula to capture these non-Gaussian co-movements. Extensive experiments on large-scale production datasets demonstrate that our framework achieves state-of-the-art distributional fidelity and exhibits clear neural scaling laws, establishing a rigorous probabilistic foundation for future constraint-aware stochastic control.