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Convert CATE Estimates Into a Budgeted, Cost-Aware Targeting Policy
A marketing team scored 200,000 customers. Predicted uplift \hat\tau (extra probability of purchase from the coupon) and predicted baseline purchase probability \hat\mu_0 by band:
| Band | Customers | \hat\tau | \hat\mu_0 |
|---|---|---|---|
| A | 20,000 | 0.12 | 0.05 |
| B | 30,000 | 0.08 | 0.10 |
| C | 50,000 | 0.04 | 0.20 |
| D | 60,000 | 0.02 | 0.30 |
| E | 40,000 | -0.01 | 0.40 |
An order earns $30 margin before the coupon. The coupon is $6, paid whenever the customer redeems it on an order, and every send also costs $0.20. Marketing can send at most 60,000 coupons.
- Write the expected profit of sending a coupon to a customer and compute it for each band.
- Build the optimal policy under the 60,000 budget. How many customers receive coupons and what are the incremental orders and profit?
- Compare with targeting by the response model (highest \hat\mu_0+\hat\tau first) using the same budget.
- The budget is cut to 25,000. What changes? What if you suspect the \hat\tau values are noisy, and how would you check the policy's value before launch?
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