Uncertainty-Aware Budget Allocation for Online User Acquisition via Behavioral Mixture Likelihoods

Online marketplaces acquire new users through uncertainty-aware bidding: programmatic advertising systems bid in proportion to each prospective user's predicted lifetime value (pLTV), estimated at the moment when the least is known about the user. Prevailing pLTV models fit a single distribution to all positive spend, leaving the behavioral heterogeneity of newly acquired users unmodeled. On real-world data from hyperlocal e-commerce, we show that spend uncertainty is structurally a two-regime behavioral mixture: trial users who transact once, and engaged users whose spend compounds over repeat orders. To address this, we introduce ZI-BMLN, a zero-inflated two-component LogNormal mixture that encodes the behavioral regime inside the likelihood through weak supervision, while retaining a closed-form expectation for bidding. We evaluate our framework on a real-world user acquisition system at Swiggy, one of India's largest hyperlocal commerce platforms. Offline, ZI-BMLN outperforms baselines in two different business verticals with Gini coefficients reaching 0.896 (Instamart) and 0.789 (food delivery) and improving spend ranking among paying users by up to 1.3% over ZILN, the strongest baseline. A six-week geo-randomized live experiment confirms the allocation gain with up to +2.4pp uplift in retention, after which the model was ramped to full production for uncertainty-aware decision-making.