Minimax Quantile Lower Bounds for Interactive Statistical Decision Making with Privacy
Minimax risk and regret are expectation-based criteria and do not capture rare but consequential failures. To address this concern, we develop a $δ$-explicit minimax-quantile theory for interactive statistical decision making (ISDM). We first provide structural relations between minimax quantiles, lower minimax quantiles, and minimax risk. This includes a quantile-to-expectation conversion and an equivalence between strict and lower minimax quantiles outside a countable set of confidence levels. We then derive two converse tools for ISDM: a high-probability interactive Fano's method and a high-probability interactive Le Cam's method. Then, we show that mutual-information (MI) privacy can ...
| Authors | Raghav Bongole, Amirreza Zamani, Tobias J. Oechtering et al. |
|---|---|
| Primary category | cs.LG |
| Published | 22 June 2026 |
| Last updated at source | 22 June 2026 |
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