Decide if ad load is optimized

Pinterest is testing different ad loads (ads per 100 content units) in the home feed. Design an analysis to determine whether the current ad load is optimized. Include: 1) Primary success function for the business that trades off user-side and ads-side (e.g., constrained optimization: maximize revenue subject to user-experience guardrails); define exact user guardrails (e.g., 7-day retention, session duration, complaint rate) and ads-side metrics (e.g., RPM, CTR, advertiser ROI). 2) Experiment design: arms, randomization unit, holdouts, duration, power, and a plan to mitigate auction interference and novelty effects; describe how you’d select long-term proxy metrics for user value and how you’d backtest their predictive validity. 3) Decision rule: formalize as an optimization problem with constraints (e.g., maximize RPM with hard constraints on relative changes in retention and time spent) and specify the statistical testing approach (sequential vs fixed-horizon) and multiple-testing control across arms. 4) Heterogeneity: how you’d segment (e.g., new vs power users, content verticals), test for interactions, and guard against Simpson’s paradox. 5) Rollout plan: ramp strategy, kill switches/guardrails, and monitoring post-launch for non-stationarity and seasonality. Provide concrete metric formulas and thresholds you would propose.