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Localized Adaptive Risk Control
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Proposes Localized Adaptive Risk Control (L-ARC), an online calibration method that updates an RKHS-valued threshold function so risk guarantees are localized in covariate space while retaining ARC's worst-case long-term control.
Problem
Adaptive risk control (ARC) guarantees long-term risk only marginally over inputs, so risk can be distributed unevenly across subpopulations; conditional or localized risk guarantees are needed in online settings.
Approach
Replace ARC's scalar threshold with a covariate-dependent threshold g(x)=f(x)+c, with f in an RKHS updated by online gradient descent with regularization; the kernel's length scale controls the localization of the risk guarantee, trading off against convergence speed.
Key results
- On tumor segmentation, ARC yields FNR ranging from 0.08 (CVC-300) to 0.32 (ETIS-LaribPolypDB), while L-ARC equalizes FNR across repositories and gets test FNR closer to the 0.1 target.
- Theory: the long-term risk deviation converges at rate O(T^{-1/2}) to a neighborhood of size kappa*B, which vanishes only in the constant-threshold (no localization) case.
- On electricity demand, L-ARC reduces weekend coverage error relative to ARC as the length scale decreases while all methods hit the 0.9 long-term coverage target.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Localized threshold function in RKHS (L-ARC) vs single scalar threshold (ARC) | tumor segmentation calibration of PraNet · Tumor segmentation (Kvasir, CVC, ETIS-LaribDB) | per-repository FNR spread and test FNR closeness to target | Helped |
| Localization of threshold via kernel length scale (smaller l) (ablation) | L-ARC on electricity demand (Elec2) · Elec2 weekend vs weekday coverage | weekend miscoverage error balance | Helped |
| Localized threshold (L-ARC) vs ARC and Mondrian ARC in beam selection | beam selection · Beam selection wireless network | average beam set size at target long-term SNR regret | Helped |
| Stronger localization (larger kernel scale kappa and rho) in L-ARC | L-ARC theory: statistical and long-term guarantees · theoretical | conditional risk gap and long-term risk bias C(G)=kappa B | Hurt |
Surprising findings
- Localization introduces a non-vanishing long-term bias term kappa*B, so localized guarantees trade off against convergence speed to the long-term target.
Limitations
- Effectiveness depends on choosing an appropriate kernel function.
- Memory requirements grow linearly with time because all past inputs and coefficients must be stored.
- Localized guarantee introduces a residual bias term kappa*B in long-term risk control.
Experimental setup
Datasets: Elec2 Kvasir CVC-300 CVC-ColonDB CVC-ClinicDB ETIS-LaribPolypDB fruit-360 Sionna ray-tracer simulated channels
Benchmarks: Elec2 tumor segmentation polyp datasets beam selection simulation fruit-360 image classification
Metrics: long-term miscoverage/FNR conditional miscoverage across subpopulations FNR across data sources average prediction set size SNR regret
Baselines: ARC Mondrian ARC
Builds on: Adaptive Risk Control Adaptive conformal prediction Mondrian conformal prediction
Closest papers by meaning
- Performative Risk Control: Calibrating Models for Reliable Deployment under Performativity (NeurIPS 2025 · similarity 0.82)
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