Efficient Online Conformal Selection with Limited Feedback

TL;DR

This paper develops an efficient online conformal selection method that guarantees success probability and minimizes resource use under limited feedback, using adaptive updates and Lyapunov-based analysis.

Contribution

It introduces a unifying algorithmic framework for online conformal selection with minimal feedback, ensuring validity and efficiency in adversarial and stochastic settings.

Findings

Guarantees success probability under adversarial sequences.

Achieves sublinear efficiency regret in i.i.d. settings.

Handles complex feedback models with less information than prior work.

Abstract

We address the problem of conformal selection, where an agent must select a minimal subset of options to ensure that at least one ``success'' is identified with a pre-specified target probability $\phi$. While traditional online conformal prediction focuses on maintaining validity for the observed sequence, minimizing the resource cost (efficiency) of such selections, especially under limited feedback, remains a significant challenge. In this work, we consider settings with the most limited ``bandit'' feedback, and demonstrate that the simple Adaptive Conformal Inference (ACI) update rule, when applied to the appropriate control parameter or dual variable, is both adversarially valid, ensuring the success target is met on average for any input sequence (and hence under distribution shifts), and stochastically efficient, achieving sublinear efficiency regret for $i.i.d.$ inputs against an appropriate stochastic benchmark. We show such guarantees under canonical models capturing bandit and semi-bandit feedback to the agent via a unifying algorithmic technique, and analytic framework involving Lyapunov functions. Our approach handles more complex settings than prior work, while requiring significantly less feedback, and our results provide a new theoretical bridge between efficient online learning with limited feedback and distribution-free uncertainty quantification.