Online Conformal Prediction with Corrupted Feedback

Bowen Wang; Matteo Zecchin; Osvaldo Simeone

arxiv: 2605.20515 · v1 · pith:T34QWJ76new · submitted 2026-05-19 · 💻 cs.LG · eess.SP

Online Conformal Prediction with Corrupted Feedback

Bowen Wang , Matteo Zecchin , Osvaldo Simeone This is my paper

Pith reviewed 2026-05-21 07:08 UTC · model grok-4.3

classification 💻 cs.LG eess.SP

keywords online conformal predictioncorrupted feedbackrobust calibrationmiscoverage guaranteesprediction setssequential learningbinary flip model

0 comments

The pith

Online conformal prediction can keep its calibration guarantees when feedback about past accuracy is corrupted by noise or flips.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how to extend online conformal prediction so that its long-run coverage guarantees survive when the observed success or failure of each past prediction set is sometimes inverted or lost. It first models any such corruption as an arbitrary sequence of binary flips and proves that ordinary online conformal prediction then loses its deterministic bounds. To recover control, the authors introduce two explicit fixes: one filters the observed indicators by exploiting how the prediction threshold is constructed, and the other adds an active compensation term that offsets likely errors. Both fixes come with new, explicit upper bounds on the overall miscoverage rate that hold for independent random flips and for any error sequence whose memory is bounded.

Core claim

We model feedback corruption as an arbitrary binary flip sequence and analyze how it degrades the miscoverage performance of standard online conformal prediction. We then propose two robust schemes: robust OCP via filtering, which leverages the structural properties of the predicted threshold to filter corrupted feedback, and robust OCP via active compensation, which incorporates an active compensation mechanism to mitigate the effect of corrupted feedback. For both methods, we establish explicit miscoverage guarantees, which are further specialized for an independent stochastic flip model and for an arbitrary error model with memory bounds.

What carries the argument

The binary flip sequence model of feedback corruption, which supports both the degradation analysis of standard online conformal prediction and the derivation of restored miscoverage bounds for the filtering and active-compensation schemes.

If this is right

Standard online conformal prediction loses its deterministic long-run miscoverage guarantee as soon as any positive fraction of feedback signals is flipped.
Filtering observed coverage indicators according to the internal structure of the prediction threshold restores an explicit bound on miscoverage.
An active compensation term added to the threshold update cancels the cumulative effect of flips and produces smaller prediction sets on average.
The same bounds continue to hold when flips occur independently at random or when the error process has finite memory.
Real-data experiments confirm that both schemes achieve markedly lower empirical miscoverage and smaller average set sizes than unmodified online conformal prediction.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same flip-sequence analysis could be used to quantify robustness in other online set-valued predictors that rely on observed coverage signals.
Systems that experience only temporary feedback outages would fall inside the bounded-memory error model and therefore inherit the paper's guarantees without extra tuning.
One could test whether the compensation mechanism can be made fully adaptive by estimating the current flip rate from the stream itself.

Load-bearing premise

That every instance of corrupted feedback can be represented as a binary flip that simply inverts the true coverage indicator.

What would settle it

Generate a sequence of binary flips with a known rate or memory bound, apply one of the robust schemes to a streaming dataset, and measure whether the long-run fraction of uncovered outcomes stays strictly below the explicit bound derived in the paper.

Figures

Figures reproduced from arXiv: 2605.20515 by Bowen Wang, Matteo Zecchin, Osvaldo Simeone.

**Figure 2.** Figure 2: Average coverage and average set size performance of OCP under [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Illustration of F-ROCP: When the threshold [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Illustration of AC-ROCP: When the threshold [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Illustration of the independent stochastic feedback error model shown [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Illustration of the deterministic feedback error model with memory [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Effect of the corruption probability p on the performance of the different methods with T = 10,000 and α = 0.1. Results are averaged over 104 independent trials, with the shaded region denoting a two-sided interval with half-width equal to one standard deviation. (a) Coverage versus p. (b) Average set size versus p. set size, but it remains more conservative than the ideal feedback benchmark. The proposed … view at source ↗

**Figure 8.** Figure 8: Effect of the inter-training interval on the performance of the different [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

read the original abstract

Modern artificial intelligence systems require calibrated uncertainty estimates that remain reliable in sequential and non-stationary environments. Online conformal prediction (OCP) addresses this challenge through adaptively updated prediction sets that provide deterministic long-run miscoverage guarantees. These guarantees, however, hinge on the assumption of perfect feedback about the coverage of past prediction sets. In practice, the observed miscoverage indicator may be corrupted by noise, communication failures, or adversarial manipulation, which can severely degrade OCP's calibration guarantees. In this paper, we study OCP under corrupted feedback. We first model feedback corruption as an arbitrary binary flip sequence, and analyze how feedback corruption affects and degrades the miscoverage performance of standard OCP. We then propose two robust schemes: robust OCP via filtering, which leverages the structural properties of the predicted threshold to filter corrupted feedback, and robust OCP via active compensation, which incorporates an active compensation mechanism to mitigate the effect of corrupted feedback. For both methods, we establish explicit miscoverage guarantees, which are further specialized for an independent stochastic flip model and for an arbitrary error model with memory bounds. Experiments on real-world datasets validate the proposed approach, showing markedly improved calibration and significantly smaller prediction sets compared with baseline OCP methods under corrupted feedback.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper fixes online conformal prediction for corrupted feedback using filtering and active compensation with explicit bounds, but the compensation guarantees look conditional on a known memory bound.

read the letter

The main thing to know is that standard online conformal prediction assumes clean feedback on whether each prediction set covered the label, and this paper shows how binary flip corruption breaks that and offers two fixes with some guarantees attached. They first model the corruption as an arbitrary sequence of flips and work out how it degrades the usual threshold update. Then they introduce robust OCP via filtering, which uses the structure of the running threshold to ignore bad signals, and robust OCP via active compensation, which adds a correction step to offset the flips. Both get explicit miscoverage bounds, tightened further for independent random flips and for arbitrary flips whose errors have bounded memory. The real-world dataset experiments show tighter sets and better calibration than plain OCP when feedback is noisy. The soft spot sits in the active compensation scheme for the arbitrary error model. The bound appears to need a known memory length on the corruption process to hold while the online update continues. If that length is not an input to the algorithm and cannot be estimated without biasing coverage, the guarantee applies to a version that is not quite what gets implemented. Filtering avoids this dependency. This work is for people building sequential predictors that must stay calibrated under imperfect observations, such as streaming classification or adaptive control with sensor dropouts. A reader already working on conformal methods or robust online learning would get concrete schemes and bounds to build on. It deserves a serious referee because the problem is practical and the proposals are specific enough to check, though the arbitrary case needs clearer handling of the memory bound.

Referee Report

1 major / 2 minor

Summary. The paper models feedback corruption in online conformal prediction (OCP) as an arbitrary binary flip sequence, analyzes degradation of standard OCP guarantees, and proposes two robust schemes: filtering that exploits threshold structure and active compensation. It derives explicit miscoverage guarantees for both, specialized to an independent stochastic flip model and an arbitrary error model with memory bounds, and reports experiments on real-world datasets showing improved calibration and smaller prediction sets relative to baselines under corruption.

Significance. If the guarantees are correctly derived without hidden assumptions on the corruption process, the work meaningfully extends OCP theory to noisy and potentially adversarial feedback settings common in deployed systems. The provision of explicit (non-asymptotic) bounds and their specialization to both stochastic and bounded-memory arbitrary models, together with empirical validation, strengthens the contribution for practical sequential uncertainty quantification.

major comments (1)

[Active compensation mechanism and Theorem for arbitrary error model] Active compensation section (around the description of the compensation mechanism and its guarantee for the arbitrary error model): the explicit miscoverage bound for the memory-bounded corruption case appears to require knowledge of the memory bound M to invert or bound the effect of the flip sequence while preserving the online threshold update. It is unclear whether M is an input to the algorithm or must be estimated from data; if the latter, the derived guarantee does not directly apply to the implemented procedure. This is load-bearing for the central claim of explicit guarantees under arbitrary corruption.

minor comments (2)

[Experimental results] Experiments lack reported error bars, standard deviations, or multiple-run statistics, making it difficult to assess the statistical significance of the reported improvements in calibration and set size.
[Problem formulation] The definition of the binary flip corruption sequence and its relation to the observed miscoverage indicator could be stated more explicitly with a short equation or pseudocode to aid readers.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying this important point of clarification regarding the active compensation mechanism. We address the comment below.

read point-by-point responses

Referee: Active compensation section (around the description of the compensation mechanism and its guarantee for the arbitrary error model): the explicit miscoverage bound for the memory-bounded corruption case appears to require knowledge of the memory bound M to invert or bound the effect of the flip sequence while preserving the online threshold update. It is unclear whether M is an input to the algorithm or must be estimated from data; if the latter, the derived guarantee does not directly apply to the implemented procedure. This is load-bearing for the central claim of explicit guarantees under arbitrary corruption.

Authors: We thank the referee for highlighting this point. In our development of the active compensation scheme, the memory bound M is a known parameter of the arbitrary error model with bounded memory and is provided as an explicit input to the algorithm. The compensation step uses knowledge of M to bound the worst-case propagation of any flip over the preceding M time steps when adjusting the online threshold. The explicit miscoverage guarantee in the corresponding theorem is derived under this modeling assumption that M is known; it does not rely on estimating M from observed data. This is consistent with the standard treatment of bounded-memory corruption models, where the bound is part of the model specification. We will revise the manuscript to state this assumption more explicitly in the algorithm description, the theorem statement, and the surrounding discussion to remove any ambiguity. revision: yes

Circularity Check

0 steps flagged

Guarantees derived from binary-flip model and threshold structure; no reduction to fitted inputs or self-referential definitions

full rationale

The derivation establishes miscoverage bounds by modeling corruption as an arbitrary binary flip sequence and exploiting structural properties of the online threshold update. These steps rely on the stated corruption model and standard OCP recursion rather than redefining quantities in terms of the target guarantee or fitting parameters to the same data used for validation. No load-bearing self-citation chain or ansatz smuggling is evident in the provided analysis; the central claims remain independent of the derived guarantees themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility into parameters or entities; corruption modeled as binary flips appears as a modeling choice rather than a fitted parameter.

axioms (1)

domain assumption Standard conformal prediction assumptions such as exchangeability or appropriate data conditions hold for the base method.
OCP guarantees rely on these background conditions before corruption is introduced.

pith-pipeline@v0.9.0 · 5741 in / 1091 out tokens · 85550 ms · 2026-05-21T07:08:14.631244+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

rt+1 = rt − η(α − et) ... MisCov(T) ≤ B + η/ηT + |GT0→1 − GT1→0|/T + max{α GT1→0,(1−α)GT0→1}/T
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

robust OCP via filtering ... active compensation ... memory bounds f(Δ)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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