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Adaptive Conformal Inference by Betting
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Proposes adaptive conformal inference via coin-betting parameter-free online convex optimization (KT and ONS bettors) to update prediction-interval radii without learning-rate tuning, with long-run miscoverage guarantees under bounded scores.
Problem
Online conformal inference without exchangeability assumptions requires adapting prediction interval radii, but existing OGD-based methods are highly sensitive to learning rates that are hard to tune, especially when scores scale is unknown.
Approach
Frame radius updates as coin-betting over the negated pinball-loss subgradients, using parameter-free betting strategies (KT estimator, ONS) so no learning rate must be specified; this yields provable long-term coverage under bounded nonconformity scores and sublinear regret.
Key results
- On the synthetic changepoint setting, KT-based conformal predictor achieves about 88% coverage at 90% nominal, with widths close to tuned OGD/SF-OGD across learning rates.
- On 5-step electricity demand forecasting, KT coverage is 88.9-89.1% versus OGD 89.8-89.9% and SF-OGD 89.2-90.1%, with KT yielding shorter sets in four of five horizons.
- On stock forecasting, KT coverage averages about 84-86% versus OGD 85-87%, while the native Prophet intervals reach only 53-69%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use KT betting instead of OGD | Adaptive conformal inference · Electricity demand, 5-step forecast (k=5) | width (×100): 36.3 -> 35.3 | Helped |
| Use KT betting instead of OGD | Adaptive conformal inference · Stock prices, 5-step forecast (k=5; five-stock aggregate) | coverage (%): 85.4 -> 84.6 | Hurt |
| Use SF-OGD instead of KT betting | Adaptive conformal inference · Stock prices, 5-step forecast (k=5; five-stock aggregate) | coverage (%): 84.6 -> 76.3 | Hurt |
| Use Prophet native intervals instead of KT conformal intervals | Stock price forecasting · Stock prices, 5-step forecast (k=5; five-stock aggregate) | coverage (%): 84.6 -> 58.8 | Hurt |
| Increase OGD learning rate to η=4 | Adaptive conformal inference · Changepoint setting | average interval width | Hurt |
| Use a too-small learning rate | OGD-based adaptive conformal inference · Changepoint setting | coverage | Hurt |
| Use OGD with η=0.1 instead of KT betting | Adaptive conformal inference · Electricity demand, one-step ahead | average interval width: almost 70% larger | Hurt |
| Use SF-OGD with η=0.1 instead of KT betting | Adaptive conformal inference · Electricity demand, one-step ahead | average interval width: 3% | Hurt |
| Use SF-OGD instead of KT betting | Adaptive conformal inference · Electricity demand, 5-step forecast (k=5) | localized coverage | Hurt |
| Use KT betting instead of OGD | Adaptive conformal inference · Changepoint setting | local width deviation | Helped |
Surprising findings
- Native Prophet intervals undercover heavily, with coverage dropping to around 53-60% at longer horizons.
- SF-OGD's decaying effective learning rate hurts recovery after distribution shifts, leading to poor coverage in stock forecasting.
Limitations
- Coverage guarantee is asymptotic; finite-sample coverage can fall somewhat below nominal (e.g., about 88% vs 90%).
- Requires bounded nonconformity scores for the coverage guarantee, and the bound is necessary.
- KT regret is sub-optimal by logarithmic factors relative to tuned OGD; ONS-based version lacks theoretical analysis.
Experimental setup
Datasets: synthetic changepoint linear model data New South Wales electricity demand daily closing prices of AAPL, META, MSFT, NFLX, WMT (2019-2024)
Benchmarks: synthetic changepoint setting New South Wales electricity demand stock price forecasting (5 stocks)
Metrics: empirical coverage average interval width localized coverage local width deviation regret
Baselines: OGD-based adaptive conformal inference SF-OGD adaptive conformal inference Prophet native prediction intervals
Builds on: online gradient descent adaptive conformal inference scale-free online gradient descent KT betting online Newton step
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