Design an ad-selection system across objectives

On TikTok, you must choose which of three advertiser types to show to a user at impression time. Assume objective/value schemes: Gaming (CPI, $10 per install), E‑commerce (CPA, $5 per purchase), Branding (CPM, $3 per 1000 impressions). Design an end‑to‑end ad‑selection system that maximizes expected advertiser value while respecting budgets and pacing. Specify: (1) features and models to estimate P(install | ad,user,context) and P(purchase | ·), calibration/ debiasing for auction-time use, and updating cadence; (2) how to make scores commensurate across objectives (e.g., expected value per impression, converting CPM to per‑impression value) including predicted win rate, quality thresholds, and user experience constraints; (3) exploration vs. exploitation (e.g., contextual bandits), cold‑start handling, and guardrails (frequency capping, diversity, fairness); (4) auction mechanics (second‑price/VCG), bid shading, pacing control, and multi‑objective bidding interactions; (5) offline/online evaluation, including counterfactual replay, lift tests, and success metrics (incremental ROAS, retention, long‑term engagement), and how to detect/mitigate feedback loops or gaming.