Model-Free Approximate Bayesian Learning for Large-Scale Conversion
  Funnel Optimization
Garud Iyengar Raghav Singal
The flexibility of choosing the ad action as a function of the consumer state
is critical for modern-day marketing campaigns. We study the problem of
identifying the optimal sequential personalized interventions that maximize the
adoption probability for a new product. We model consumer behavior by a
conversion funnel that captures the state of each consumer (e.g., interaction
history with the firm) and allows the consumer behavior to vary as a function
of both her state and firm's sequential interventions. We show our model
captures consumer behavior with very high accuracy (out-of-sample AUC of over
0.95) in a real-world email marketing dataset. However, it results in a very
large-scale learning problem, where the firm must learn the state-specific
effects of various interventions from consumer interactions. We propose a novel
attribution-based decision-making algorithm for this problem that we call
model-free approximate Bayesian learning. Our algorithm inherits the
interpretability and scalability of Thompson sampling for bandits and maintains
an approximate belief over the value of each state-specific intervention. The
belief is updated as the algorithm interacts with the consumers. Despite being
an approximation to the Bayes update, we prove the asymptotic optimality of our
algorithm and analyze its convergence rate. We show that our algorithm
significantly outperforms traditional approaches on extensive simulations
calibrated to a real-world email marketing dataset.