Select the better $5 promo-targeting model

You have two user-scoring models for a $5 coupon: M0 (current) and M1 (new), each outputting p_i = P(redeem | user i). You may send at most B promos/day. Define a decision policy that sends to the top‑K users per day so expected spend is ≤ B. a) Specify a success metric aligned to profit (e.g., expected incremental profit per user = uplift × expected GMV − $5) and justify why AUC/accuracy can be misleading for targeting. b) Using a historical randomized dataset with columns {user_id, features, assigned_treatment ∈ {coupon, control}, outcome redeem ∈ {0,1}, gmv, timestamp}, derive off‑policy estimators to compare the two policies induced by M0 and M1: inverse propensity scoring (IPS), self‑normalized IPS (SNIPS), and doubly robust (DR). Write the formulas, state assumptions for unbiasedness, and discuss variance trade‑offs and cross‑fitting. c) Describe how you would calibrate probabilities (e.g., isotonic/Platt), set a daily threshold to respect budget B under drift, and directly optimize expected profit subject to guardrails (opt‑out rate, complaint rate). d) List three concrete leakage risks (e.g., using features that reflect prior coupon exposure, post‑treatment variables, or future-engagement proxies) and how you would detect/prevent them. e) Explain handling delayed redemption labels and per‑user redemption caps in both training and evaluation to avoid bias. f) Outline a monitoring plan for non‑stationarity and cold‑start users, including shadow deployment and canarying.