Minimax Quantile Lower Bounds for Interactive Statistical Decision Making with Privacy (opens in new tab)

Minimax risk and regret are expectation-based criteria and do not capture rare but consequential failures. To address this concern, we develop a $\delta$-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...