Iterative Scarcity-Guided Exploration: Bootstrapping Generative Auto-bidding from Narrow Support

Auto-bidding is a core algorithmic component in online advertising auctions. In practical cold-start settings, iterative training is commonly used to compensate for low-quality, narrowly supported historical data. Unfortunately, in iterative training, representative diffusion-based AI-Generated Bidding (AIGB) methods fail to sustain extrapolation beyond the narrow data support and stagnate at a suboptimal level. In this paper, we theoretically attribute this stagnation to Signal-to-Noise Ratio (SNR) collapse: the weak radial return signal is overwhelmed by a curvature-induced penalty. To break this stagnation, we propose \textbf{Iterative Scarcity-Guided Exploration (ISGE)}, which introduces a guidance handoff: as the return signal collapses, scarcity subsequently takes over as an exploratory signal to elevate the SNR above a critical threshold. Specifically, ISGE iteratively alternates between a \emph{Judger} that assigns scarcity scores to trajectories and an \emph{Explorer} that performs guided generation of high-scarcity and high-return trajectories, thereby bootstrapping from the narrow support with such self-generated trajectories. Extensive experiments on the industrial AuctionNet benchmark demonstrate that ISGE, starting from cold-start datasets, effectively surpasses the performance of the Full-Dataset baseline within three iterations.