Conformal@K: Distribution-Free Top-K Miss-Risk Control for Recommendation with Overlapping-Group and Two-Stage Guarantees

We present Conformal@K , a model-agnostic calibration layer that provides distribution-free, finite-sample control of Top- \(K\) miss-risk in two-stage recommendation and retrieval. Given arbitrary retrieval and re-ranking scorers, Conformal@K selects monotone budgets so that, at level \(1-α\) , the probability that no relevant item appears in the returned Top- \(K\) is controlled whenever a feasible parameter exists; otherwise, a transparent best-effort mode reports the residual gap with actionable diagnostics. Beyond marginal validity, we introduce overlapping-group guarantees via smoothed, self-normalized estimates, joint two-stage calibration controlling both retrieve-miss and final miss@K, and importance-weighted and windowed variants for covariate shift and temporal dependence. Empirically, on MSLR-WEB10K , Conformal@K tracks target risks across \(α\) and meets global and cohort targets while preserving ranking quality. On POI recommendation ( Gowalla , Foursquare ) under an all-ranking protocol with a display cap ( \(Kₘₐₓ{=}50\) ), small \(α\) can be infeasible; our method still reduces global and worst-group miss-risk and improves HR@K, explicitly reporting infeasibility gaps. We compare against four fairness-of-exposure baselines, showing that Conformal@K and exposure-fair methods target complementary objectives and compose in practice. Shift-aware and streaming variants stabilize miss-risk under drift. The method drops into existing stacks with audit-friendly diagnostics.