Monitoring for Shifts at Unknown Times: Parameter-Free Conditional Conformal Martingales

Tuo Liu, Drew Prinster, Francesco Orabona

Conditional conformal test martingales provide sequential tests for detecting distribution shifts, using a fixed reference dataset to avoid contamination from test-time samples. Prior work used a penalized betting function via online optimization with smoothing, clipping, and other hyperparameters, which can adapt slowly when a shift occurs after a long stationary period. In this work, we introduce an approach that requires no hyperparameters and provably adapts quickly to shifts occurring at unknown times. Our key idea is to frame the penalized betting problem as portfolio selection in a three-asset market. Then, we use a restarting universal portfolio, with a heavy-tailed wealth allocation over time. We establish anytime false-alarm control and derive optimal finite-sample bounds on detection delay under detectable alternatives. We also develop an FFT-based implementation that computes the portfolio sequence over $T$ rounds in $\mathcal{O}(T^2\ln T)$ time, instead of $\mathcal{O}(T^3)$ of the naive implementation. Synthetic and real-world experiments suggest that the proposed approach adapts rapidly after long periods of null samples, with detection delays depending…