  Guaranteed display (GD) advertising is a critical component of advertising
since it provides publishers with stable revenue and enables advertisers to
target specific audiences with guaranteed impressions. However, smooth pacing
control for online ad delivery presents a challenge due to significant budget
disparities, user arrival distribution drift, and dynamic change between supply
and demand. This paper presents robust risk-constrained pacing (RCPacing) that
utilizes Lagrangian dual multipliers to fine-tune probabilistic throttling
through monotonic mapping functions within the percentile space of impression
performance distribution. RCPacing combines distribution drift resilience and
compatibility with guaranteed allocation mechanism, enabling us to provide
near-optimal online services. We also show that RCPacing achieves $O(\sqrt{T})$
dynamic regret where $T$ is the length of the horizon. RCPacing's effectiveness
is validated through offline evaluations and online A/B testing conducted on
Taobao brand advertising platform.
