Do Not Trust The Auctioneer: Learning to Bid in Feedback-Manipulated Auctions

Luigi Foscari; Matilde Tullii; Vianney Perchet

arxiv: 2605.22438 · v1 · pith:A2M27E5Cnew · submitted 2026-05-21 · 📊 stat.ML · cs.GT· cs.LG

Do Not Trust The Auctioneer: Learning to Bid in Feedback-Manipulated Auctions

Luigi Foscari , Matilde Tullii , Vianney Perchet This is my paper

Pith reviewed 2026-05-22 03:30 UTC · model grok-4.3

classification 📊 stat.ML cs.GTcs.LG

keywords online learningfirst-price auctionsregret boundsshillingfeedback manipulationdynamic pricingbidding strategies

0 comments

The pith

In first-price auctions with shilling that only manipulates feedback, a learning algorithm achieves standard regret rates by robust elimination or debiasing.

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

Shilling in repeated first-price auctions inflates the observed competing bid after losses without affecting the auction outcome itself. This manipulation changes the information the learner receives and thus the difficulty of learning the optimal bid. The paper establishes that even under this feedback-only shilling, and with the shill distribution known, it is possible to design an algorithm that achieves the dynamic pricing regret rate of order T to the two-thirds or the faster first-price rate of order square root T. It does so by running a robust branch that ignores suspicious reports and an optimistic branch that corrects the biased observations when they can be trusted. A validation procedure allows the algorithm to select which branch to follow without knowing the feedback structure ahead of time. This shows that feedback manipulation alone can change the statistical properties of the bidding problem.

Core claim

The paper claims that in repeated first-price auctions where after a loss the learner observes the maximum of the true competing bid and an independent shill bid, assuming the shill-bid distribution is known, regret with respect to the best fixed bid can be bounded by combining a robust interval-elimination procedure achieving the tilde O of T to the 2/3 rate with an optimistic debiasing procedure achieving the tilde O of square root T rate, using a validation and racing procedure to choose between them without knowing the scale or geometry in advance, and that this is tight up to logs in the single-active-region case.

What carries the argument

A dual-branch algorithm with robust interval-elimination that discards shilled feedback to achieve the slower rate, paired with optimistic debiasing that exploits reliable low-shill observations for the faster rate, selected by a validation and racing procedure.

If this is right

Regret remains controlled even when most observations are masked by shilling and useful information arrives only intermittently.
The racing procedure allows the algorithm to adapt to the unknown feedback geometry and scale.
A matching lower bound holds in the single-active-region case up to logarithmic factors.
The approach separates the effects of shilling on allocation versus on feedback.

Where Pith is reading between the lines

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

Extending the debiasing technique to cases where the shill distribution must be learned simultaneously could lead to new regret bounds.
This framework may apply to other online decision problems where feedback is adversarially corrupted in a known distributional way.
Testing the algorithm in real auction data with estimated shill behaviors would validate practical performance.

Load-bearing premise

The distribution of the shill bids is known to the learner ahead of time.

What would settle it

A simulation or theoretical construction in the single-active-region case where any algorithm suffers regret larger than order T to the two-thirds would falsify the upper bounds, while an algorithm achieving better than order square root T would falsify the lower bound.

Figures

Figures reproduced from arXiv: 2605.22438 by Luigi Foscari, Matilde Tullii, Vianney Perchet.

**Figure 1.** Figure 1: Schematic lower-bound instance and information profile. On the left, the utility ua is flat on the hard interval J = [1/3, 1/2] apart from one hidden cell (in this case cell number a = 2 out of N = 5) which contains a bump of height ε. On the right, the order of the per-round KL envelope: direct local testing is based on the outcome of the auction and gives a strong signal of order ε 2 , but only on the hi… view at source ↗

**Figure 2.** Figure 2: Planted buyer CDF Fa and shilled CDF FO = FaFS with N = 5 and a = 2 in the interval J = [1/3, 1/2]. The baseline distribution is unchanged outside the hard interval J, while inside the planted cell Ia ⊂ J a localized bump raises the utility of bids in that cell. The perturbation vanishes at the endpoints of Ia, so the planted CDF matches the baseline on neighboring cells. After J, the CDF is flat, with the… view at source ↗

read the original abstract

Shilling is the use of artificial bids to make competition appear stronger and push prices upward. We study repeated first-price auctions in which shilling affects feedback but not allocation: the learner wins or loses against the real competing bid, but after a loss observes the maximum of the real bid and an independent shill bid. Thus the manipulation changes what the learner observes and hence how it learns to bid, without changing the outcome of the current auction. We analyze regret with respect to the best bid benchmark, assuming that the shill-bid distribution is known. Even then, shilling can mask the real bid, while useful side information appears only through intermittent low-shill events. Our algorithm combines a robust interval-elimination branch, which ignores the shilled report and achieves the dynamic-pricing rate $\tilde{\mathcal{O}}(T^{2/3})$, with an optimistic branch that debiases losing-side reports and exploits the resulting suffix information when it is reliable and achieves the first-price auctions rate $\tilde{\mathcal{O}}(\sqrt{T})$. A validation and racing procedure lets the algorithm use these optimistic updates without knowing the right scale or feedback geometry in advance. We complement the upper bounds with a matching lower bound, up to logarithmic factors, in the single-active-region case. Overall, the results show that even feedback-only shilling can sharply alter the statistical difficulty of repeated bidding.

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

The paper shows feedback-only shilling raises the statistical cost of learning in repeated first-price auctions, but a hybrid algorithm recovers the sqrt(T) rate when the shill distribution is known and falls back to T^{2/3} otherwise.

read the letter

The main thing to know is that this work isolates how shilling that only corrupts the observed losing bid (without changing who actually wins) makes repeated bidding harder to learn, and then gives a concrete algorithm plus rates for it. They model the setting where the learner sees max(real bid, shill) on losses, assume the shill distribution is known, and build a hybrid that runs a safe robust elimination branch for the dynamic-pricing-style O(T^{2/3}) guarantee alongside an optimistic debiasing branch that subtracts the known shill effect to extract more suffix information and hit the usual first-price O(sqrt(T)) rate. A racing/validation step lets it pick the right branch without prior knowledge of the geometry. They also supply a matching lower bound up to logs in the single-active-region case. That combination of model, algorithm, and bound is the actual novelty; it is not just a direct lift from prior first-price or pricing papers. The analysis uses standard regret tools plus the new debiasing step, which looks clean on the surface. The soft spot is the known-distribution assumption that powers the debiasing and the faster rate. The abstract is explicit that the O(sqrt(T)) result holds under that assumption, and the robust branch is the fallback precisely when debiasing is unreliable. If the distribution has to be learned on the fly, both the optimistic updates and the racing logic lose their guarantees, so the claimed rates would not carry over. The lower bound is also stated only for the single-active-region case, which narrows its scope relative to the upper bounds. The paper is aimed at people working on online learning in auctions and on feedback corruption more generally. A reader who already knows the dynamic-pricing and first-price regret literature will see the incremental modeling and algorithmic move clearly. It has enough new structure and explicit rates to merit sending to a serious referee rather than a desk reject, even though the known-distribution assumption will need discussion in review.

Referee Report

2 major / 2 minor

Summary. The paper studies repeated first-price auctions in which shilling manipulates feedback (the learner observes the maximum of the real competing bid and an independent shill bid after a loss) but does not affect allocation. Assuming the shill-bid distribution is known, the authors propose an algorithm that combines a robust interval-elimination branch achieving the dynamic-pricing rate Õ(T^{2/3}) with an optimistic debiasing branch that recovers suffix information to achieve the first-price rate Õ(√T); a validation/racing procedure selects between branches without prior knowledge of the scale. They also supply a matching lower bound (up to logs) in the single-active-region case.

Significance. If the analysis holds, the work shows that feedback-only shilling can alter the statistical difficulty of repeated bidding while still permitting recovery of standard rates via adaptive debiasing when the distribution is known. The combination of robust and optimistic branches with an explicit racing procedure, together with the matching lower bound, constitutes a solid technical contribution to online learning in auctions with imperfect or manipulated feedback.

major comments (2)

[§4 (Optimistic branch analysis)] The O(√T) upper bound is obtained only in the optimistic debiasing branch that subtracts the known shill distribution from losing reports; the paper must supply the precise concentration argument (including any failure-probability union bounds) that guarantees the recovered suffix information is sufficiently accurate for the claimed rate to hold.
[§3.3 (Racing procedure)] The validation/racing procedure that decides when to trust the debiased updates is load-bearing for the adaptive claim; the analysis should explicitly bound the regret incurred during the racing phase and show that it does not degrade the overall Õ(√T) guarantee.

minor comments (2)

[Abstract and §2] The abstract and §2 should include a short paragraph clarifying that the known-distribution assumption is a modeling choice for the regret analysis and is not claimed to be learned on the fly.
[§2 (Model)] Notation for the shill distribution F_s and the real bid distribution should be introduced with an equation number in §2 to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment, and constructive suggestions. We address the two major comments below and will incorporate the requested clarifications via minor revisions to strengthen the presentation of the analysis.

read point-by-point responses

Referee: [§4 (Optimistic branch analysis)] The O(√T) upper bound is obtained only in the optimistic debiasing branch that subtracts the known shill distribution from losing reports; the paper must supply the precise concentration argument (including any failure-probability union bounds) that guarantees the recovered suffix information is sufficiently accurate for the claimed rate to hold.

Authors: We appreciate the referee highlighting the need for explicit concentration details. The manuscript derives the debiased estimates via subtraction of the known shill CDF from losing observations and applies Hoeffding inequalities to the resulting unbiased samples. A union bound is taken over the O(log T) active intervals and the T time steps, yielding a failure probability of O(1/T) that contributes only lower-order terms to the Õ(√T) regret. To address the comment, we will insert a new lemma in §4 that states the precise concentration bound, the union-bound calculation, and how the failure event is handled in the regret decomposition. revision: yes
Referee: [§3.3 (Racing procedure)] The validation/racing procedure that decides when to trust the debiased updates is load-bearing for the adaptive claim; the analysis should explicitly bound the regret incurred during the racing phase and show that it does not degrade the overall Õ(√T) guarantee.

Authors: We agree that an explicit regret bound for the racing phase is necessary for a complete proof. The racing/validation phase employs a doubling schedule and terminates after O(log T) rounds in expectation; each round incurs at most a constant (maximum bid value) regret. The resulting O(log T) total racing regret is absorbed into the Õ(√T) bound. We will expand §3.3 with a dedicated paragraph and lemma that computes this additive term and confirms it does not alter the leading √T rate. revision: yes

Circularity Check

0 steps flagged

No significant circularity; bounds derived from stated model assumptions

full rationale

The paper states upfront that the shill-bid distribution is known and performs regret analysis under this model. The O(T^{2/3}) rate follows from a robust interval-elimination procedure that ignores shilled reports, while the O(sqrt(T)) rate follows from a debiasing step that subtracts the known distribution from losing reports. Both are standard-style analyses of the resulting feedback model; neither reduces the claimed rates to fitted parameters or self-referential definitions by construction. The matching lower bound is derived separately within the same known-distribution setting. The derivation chain is therefore self-contained against external benchmarks for the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the shill-bid distribution is known and on standard concentration tools for interval elimination and debiasing; no free parameters or new invented entities are introduced in the abstract.

axioms (1)

domain assumption Shill-bid distribution is known to the learner
Explicitly stated as the setting that allows debiasing of losing-side reports.

pith-pipeline@v0.9.0 · 5789 in / 1288 out tokens · 50204 ms · 2026-05-22T03:30:37.773488+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.

Our algorithm combines a robust interval-elimination branch... with an optimistic branch that debiases losing-side reports... achieving the first-price auctions rate O(sqrt(T))
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

We prove a matching lower bound for the one-active-region case... min{T^{2/3}, sqrt(T) gamma^{-1/4}}

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

Works this paper leans on

15 extracted references · 15 canonical work pages · 4 internal anchors

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arXiv:2311.15203 [cs]. l. yang, M. Hajiesmaili, M. S. Talebi, J. C. S. Lui, and W. S. Wong. Adversarial Bandits with Corruptions: Regret Lower Bound and No-regret Algorithm. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin, editors,Advances in Neural Information Processing Systems, volume 33, pages 19943–19952. Curran Associates, Inc.,

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work page arXiv
[15]

Thus the deterministic noise bound is Rγ s = ( 1, s∈ S dir t , 4/γ, s∈ S suf t

For suffix measure- ments, admissibility givesFS(q)≥ γon every involved grid point, so 0≤Y(q)≤ 1 γ ,|Y suf s | ≤ 2 γ ,|ξ suf s | ≤ 4 γ . Thus the deterministic noise bound is Rγ s = ( 1, s∈ S dir t , 4/γ, s∈ S suf t . By the definition of the range certificate in equation (4), |X γ s,t| ≤B γ t (v)for everys≤t. Freedman’s inequality gives, for this fixedt,...

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[1] [1]

doi: 10.3982/ECTA15925

ISSN 0012-9682. doi: 10.3982/ECTA15925. URLhttps://www.econometricsociety.org /doi/10.3982/ECTA15925. N. Alon, N. Cesa-Bianchi, C. Gentile, and Y. Mansour. From Bandits to Experts: A Tale of Domination and Independence, July

work page doi:10.3982/ecta15925

[2] [2]

From Bandits to Experts: A Tale of Domination and Independence

URLhttp://arxiv.org/abs/1307.4564 . arXiv:1307.4564 [cs]. N. Alon, N. Cesa-Bianchi, O. Dekel, and T. Koren. Online Learning with Feedback Graphs: Beyond Bandits, Feb

work page internal anchor Pith review Pith/arXiv arXiv

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Online Learning with Feedback Graphs: Beyond Bandits

URLhttp://arxiv.org/abs/1502.07617. arXiv:1502.07617 [cs]. S. Balseiro, N. Golrezaei, M. Mahdian, V. Mirrokni, and J. Schneider. Contextual Bandits with Cross-learning, Nov

work page internal anchor Pith review Pith/arXiv arXiv

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arXiv:1809.09582 [cs]

URL http://arxiv.org/abs/1809.09582 . arXiv:1809.09582 [cs]. O. Besbes and A. Zeevi. Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms.Operations Research, 57(6):1407–1420, Dec

work page arXiv

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doi: 10.1287/opre.1080.0640

ISSN 0030-364X, 1526-5463. doi: 10.1287/opre.1080.0640. URLhttps://pubsonline.inf orms.org/doi/10.1287/opre.1080.0640. S. Boucheron, G. Lugosi, and O. Bousquet. Concentration inequalities. InSummer school on machine learning, pages 208–240. Springer,

work page doi:10.1287/opre.1080.0640

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URLhttps://proceedings.neurips.cc/paper_files/paper/2021/file/ef8 f94395be9fd78b7d0aeecf7864a03-Paper.pdf. J. Fan, Y. Guo, and M. Yu. Policy optimization using semiparametric models for dynamic pricing.Journal of the American Statistical Association, 119(545):552–564,

work page 2021

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Better Algorithms for Stochastic Bandits with Adversarial Corruptions

URLhttp://arxiv.org/abs/1902.08647. arXiv:1902.08647 [cs]. Y. Han, Z. Zhou, and T. Weissman. Optimal no-regret learning in repeated first-price auctions. arXiv preprint arXiv:2003.09795,

work page internal anchor Pith review Pith/arXiv arXiv 1902

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IEEE Computer. Soc. ISBN 978-0-7695-2040-7. doi: 10.1109/SFCS.2003.1238232. URL http: //ieeexplore.ieee.org/document/1238232/. 13 R. D. Kleinberg. Nearly tight bounds for the continuum-armed bandit problem. InNeural information processing systems,

work page doi:10.1109/sfcs.2003.1238232 2040

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arXiv:2404.00475 [econ]

URL http://arxiv.org/abs/2404.00475. arXiv:2404.00475 [econ]. S. Lu, G. Wang, and L. Zhang. Stochastic Graphical Bandits with Adversarial Corruptions. Proceedings of the AAAI Conference on Artificial Intelligence, 35(10):8749–8757, May

work page arXiv

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doi: 10.1609/aaai.v35i10.17060

ISSN 2374-3468, 2159-5399. doi: 10.1609/aaai.v35i10.17060. URLhttps://ojs.aaai.org/i ndex.php/AAAI/article/view/17060. T. Lykouris, V. Mirrokni, and R. P. Leme. Stochastic bandits robust to adversarial corruptions, Mar

work page doi:10.1609/aaai.v35i10.17060

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Stochastic bandits robust to adversarial corruptions

URLhttp://arxiv.org/abs/1803.09353. arXiv:1803.09353 [cs]. Q. Wang, X. Xia, Z. Yang, X. Deng, Y. Kong, Z. Zhang, L. Wang, C. Yu, J. Xu, and B. Zheng. Learning against Non-credible Auctions, Nov

work page internal anchor Pith review Pith/arXiv arXiv

[12] [12]

arXiv:2311.15203 [cs]. l. yang, M. Hajiesmaili, M. S. Talebi, J. C. S. Lui, and W. S. Wong. Adversarial Bandits with Corruptions: Regret Lower Bound and No-regret Algorithm. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin, editors,Advances in Neural Information Processing Systems, volume 33, pages 19943–19952. Curran Associates, Inc.,

work page arXiv

[13] [13]

W.Zhang, Y.Han, Z.Zhou, A.Flores, andT.Weissman

URLhttps://proc eedings.neurips.cc/paper_files/paper/2020/file/e655c7716a4b3ea67f48c6322fc42 ed6-Paper.pdf. W.Zhang, Y.Han, Z.Zhou, A.Flores, andT.Weissman. LeveragingtheHints: AdaptiveBidding in Repeated First-Price Auctions, Nov

work page 2020

[14] [14]

arXiv:2211.06358 [cs]

URLhttp://arxiv.org/abs/2211.06358 . arXiv:2211.06358 [cs]. 14 A. Proofs of Section 2 A.1. Proof of Lemma 1 Lemma 1.For all p∈ (0, 1)where the reverse hazard rates are well defined,rO(p) = rB(p) + rS(p). Proof.First, we can write the PDF ofOfor anyp∈[0,1]as fO(p) =P(O=p) =P(max{B, S}=p) =P(B=p∧S < p) +P(S=p∧B < p) =f B(p)FS(p) +f S(p)FB(p), then, becauseF...

work page arXiv

[15] [15]

Thus the deterministic noise bound is Rγ s = ( 1, s∈ S dir t , 4/γ, s∈ S suf t

For suffix measure- ments, admissibility givesFS(q)≥ γon every involved grid point, so 0≤Y(q)≤ 1 γ ,|Y suf s | ≤ 2 γ ,|ξ suf s | ≤ 4 γ . Thus the deterministic noise bound is Rγ s = ( 1, s∈ S dir t , 4/γ, s∈ S suf t . By the definition of the range certificate in equation (4), |X γ s,t| ≤B γ t (v)for everys≤t. Freedman’s inequality gives, for this fixedt,...

work page 2003