The Price of Ignorance: Information-Free Quotation for Data Retention in Machine Unlearning

Bin Han; Di Feng; Zexin Fang; Jie Wang; Hans D. Schotten

cs.GTApr 13, 2026

The Price of Ignorance: Information-Free Quotation for Data Retention in Machine Unlearning

Authors: Bin Han, Di Feng, Zexin Fang, Jie Wang, Hans D. Schotten

Organizations: RPTU University Kaiserslautern-Landau, Germany · Dongbei University of Finance and Economics, China · Tongji University, China · German Research Center for Artificial Intelligence (DFKI), Germany

Abstract

When users exercise data deletion rights under the General Data Protection Regulation (GDPR) and similar regulations, mobile network operators face a tradeoff: excessive machine unlearning degrades model accuracy and incurs retraining costs, yet existing pricing mechanisms for data retention require the server to know every user's private privacy and accuracy preferences, which is infeasible under the very regulations that motivate unlearning. We ask: what is the welfare cost of operating without this private information? We design an information-free ascending quotation mechanism where the server broadcasts progressively higher prices and users self-select their data supply, requiring no knowledge of users' parameters. Under complete information, the protocol admits a unique subgame-perfect Nash equilibrium characterized by single-period selling. We formalize the Price of Ignorance -- the welfare gap between optimal personalized pricing (which knows everything) and our information-free quotation (which knows nothing) -- and prove a three-regime efficiency ordering. Numerical evaluation across seven mechanisms and 5000 Monte Carlo runs shows that this price is near zero: the information-free mechanism achieves >=99% of the welfare of its information-intensive benchmarks, while providing noise-robust guarantees and comparable fairness.

Figures & tables

Fig. 1 : Different cases of the server’s cost function.

Parameter	Value	Remark
$I$	$10$	Number of users
$d_{i},\forall i\in\mathcal{I}$	6000	Data amount per user
$\lambda_{i},\forall i\in\mathcal{I}$	$\sim\mathcal{U}(0.5,30)$	Privacy valuation
$\theta_{i},\forall i\in\mathcal{I}$	$\sim\mathcal{U}(0,5)$	Accuracy sensitivity
$k_{i},\forall i\in\mathcal{I}$	$1.0$	Privacy elasticity
$\Delta d$	$1$	Unit data amount

TABLE I : Simulation Setup

	Major-first	Minor-first	Prop.	Rand.
Server’s payoff	684.8	683.6	684.1	684.9
Users’ payoff	1133.5	1158.2	1150.2	1134.0
Social welfare	1818.4	1841.8	1834.3	1818.9

TABLE II : Comparing the oversupply-handling strategies

Fig. 2 : Privacy-only welfare comparison across mechanisms

Fig. 3 : Accuracy-aware welfare comparison (

\theta_{i}\sim\mathcal{U}(0,5)

). The accuracy externality reduces welfare across all mechanisms.

Regime	OPP	CIQ	IIQ	IIQ/OPP
Under-supply (fill $\approx 66\%$ )	1968	1981	1977	1.00
Over-supply (fill $\approx 89\%$ )	7581	7619	4604	0.61

TABLE III : Social welfare across supply regimes (accuracy-aware).

Fig. 4 : Robustness: OPP welfare degrades with estimation noise

\sigma

, while IIQ remains constant (green dashed line, with

\pm 1\sigma

band).

Fig. 5 : Sensitivity of social welfare to key parameters. Each panel sweeps one parameter while holding others at defaults.

Fig. 6 : Left: Fairness-efficiency tradeoff across mechanisms. Right: Free-rider characterization—mean supply fraction by accuracy sensitivity level.

Fig. 7 : Convergence analysis. (a) Price increments to termination vs.

\Delta B

(log-log; dashed:

O(1/\Delta B)

reference). (b) Price increments vs. number of users

I

Property	OPP	CIQ	IIQ
Private params. required by server	Yes	No	No
Strategic reasoning required by users	No	Yes	No
Implementable in practice	No	No	Yes
Welfare at $\rho=1$ (acc.-aware)	1968	1981	1977
Robust to estimation noise	No	N/A	Yes
Ex post individually rational	Yes	Yes	Yes

TABLE IV : Practical comparison of the three regimes.

Mechanism Design

Mechanism design studies rules for allocating resources and shaping incentives when participants hold private information or act strategically.

See all 142 papers

Efficient Unlearning with Privacy Guarantees
Jul 7, 2025Josep Domingo-Ferrer, Najeeb Jebreel, David SánchezPrivacy-Preserving ML Machine Unlearning
1CYBERCAT (Center for Cybersecurity Research of2026 Catalonia), ComSCIAM-Center for Computational Science and Applied Mathematics, Department of Computer EngineeringJun and Mathematics, Universitat Rovira i Virgili, Av. Pa¨ısos26 Catalans 26, E-43007 Tarragona, Catalonia
Efficient machine unlearning with minimax optimality
Apr 7, 2026Jingyi Xie, Linjun Zhang, Sai LiMachine Unlearning Statistical Learning Theory
Institute of Statistics and Big Data, Renmin University of China, Beijing 100872, China · Department of Statistics, Rutgers University, Piscataway, NJ 08854, USA · Department of Statistics and Data Science, Tsinghua University, Beijing 100084, China
Unlearning Offline Stochastic Multi-Armed Bandits
May 1, 2026Zichun Ye, Runqi Wang, Xuchuang Wang +3Multi-Armed Bandits Robust Multi-Armed Bandits
Shanghai Jiao Tong University, Shanghai, China · University of Massachusetts Amherst, Massachusetts, United States · University of Washington, Tacoma, United States

Jul 7, 2025J/K move · Enter open · S save

Efficient Unlearning with Privacy Guarantees

Josep Domingo-Ferrer, Najeeb Jebreel, David Sánchez

1CYBERCAT (Center for Cybersecurity Research of2026 Catalonia), ComSCIAM-Center for Computational Science and Applied Mathematics, Department of Computer EngineeringJun and Mathematics, Universitat Rovira i Virgili, Av. Pa¨ısos26 Catalans 26, E-43007 Tarragona, Catalonia

Privacy-Preserving ML Machine Unlearning

Open paper AskPDF arXiv

Privacy protection laws, such as the GDPR, grant individuals the right to request the forgetting of their personal data not only from databases but also from machine learning (ML) models trained on them. Machine unlearning has emerged as a practical means to facilitate model forgetting of data instances seen during training. Although some existing machine unlearning methods guarantee exact forgetting, they are typically costly in computational terms. On the other hand, more affordable methods do not offer forgetting guarantees and are applicable only to specific ML models. In this paper, we present efficient unlearning with privacy guarantees (EUPG), a novel machine unlearning framework that offers formal privacy guarantees to individuals whose data are being unlearned. EUPG involves pre-training ML models on data protected using privacy models, and it enables {\em efficient unlearning with the privacy guarantees offered by the privacy models in use}. Through empirical evaluation on four heterogeneous data sets protected with

k

-anonymity and

ε

-differential privacy as privacy models, our approach demonstrates utility and forgetting effectiveness comparable to those of exact unlearning methods, while significantly reducing computational and storage costs. Our code is available at https://github.com/najeebjebreel/EUPG.

Abstract

Mechanism Design

Explore similar work

Efficient Unlearning with Privacy Guarantees

Efficient machine unlearning with minimax optimality

Unlearning Offline Stochastic Multi-Armed Bandits