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arxiv: 2605.00638 · v1 · submitted 2026-05-01 · 💻 cs.LG · cs.DS

Unlearning Offline Stochastic Multi-Armed Bandits

Zichun Ye , Runqi Wang , Xuchuang Wang , Xutong Liu , Shuai Li , Mohammad Hajiesmaili This is my paper

Pith reviewed 2026-05-09 20:20 UTC · model grok-4.3

classification 💻 cs.LG cs.DS
keywords machine unlearningmulti-armed banditsoffline learningprivacystochastic banditsdata deletionregret bounds
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The pith

Unlearning in offline stochastic multi-armed bandits can be achieved with performance guarantees using adaptive combinations of Gaussian noise and rollback.

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

The paper initiates the first study of machine unlearning for offline stochastic multi-armed bandits, a core sequential decision-making setting. It formalizes privacy constraints around data deletion and judges success by the quality of decisions made after unlearning occurs. The work analyzes single-source and multi-source deletion scenarios under both fixed-sample and distributional data models. Algorithms adaptively combine the Gaussian mechanism for noise addition with rollback to prior states, backed by upper bounds on performance and matching lower bounds. Experiments confirm the predicted trade-offs between privacy and decision quality.

Core claim

We initiate the first study of unlearning for offline stochastic multi-armed bandits by formalizing the privacy constraint and measuring utility via post-unlearning decision quality. We design adaptive algorithms that switch between the Gaussian mechanism and rollback for single- and multi-source settings under fixed-sample and distribution models, supported by performance guarantees and lower bounds under both data models.

What carries the argument

The adaptive switching algorithm between the Gaussian mechanism and rollback procedure, which balances privacy requirements against post-unlearning decision quality depending on the data regime.

If this is right

  • Unlearning incurs only bounded additional cost to decision quality in both single- and multi-source scenarios.
  • The same algorithmic template yields guarantees under both fixed-sample and distributional data models.
  • Lower bounds match the upper bounds, establishing tightness for the two dataset models.
  • The mixing procedure explains when to prefer noise addition over rollback.

Where Pith is reading between the lines

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

  • The framework could extend to online bandit problems where new data arrives after initial training.
  • Similar adaptive mechanisms might address deletion requests in related sequential problems such as contextual bandits.
  • In practice, these methods could reduce the need for full retraining when handling user data erasure requests in recommendation systems.

Load-bearing premise

That utility for unlearning is fully captured by measuring only the quality of decisions made after data deletion.

What would settle it

An experiment or instance in the distribution model where an algorithm satisfying the privacy constraint produces post-unlearning regret that exceeds the stated upper bounds.

Figures

Figures reproduced from arXiv: 2605.00638 by Mohammad Hajiesmaili, Runqi Wang, Shuai Li, Xuchuang Wang, Xutong Liu, Zichun Ye.

Figure 1
Figure 1. Figure 1: Comparison of Algorithm 2 with baselines under Mf (uniform) and Md (C ∗ = 5). 4.2. Experiments of the Distribution Model When C ∗ ∈ [2, ∞), we generate 200 independent synthetic offline datasets using a stochastic behavior policy that se￾lects a ∗ with probability 1/C∗ , C∗ = 5 and distributes the remaining probability uniformly over suboptimal arms. Other configurations are the same as those in Section 4.… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of Algorithm 4 with baselines under Mf (uniform) and Md (C ∗ = 5) when fixing γ = 0.5 and k = 80, fixing γ = 0.5 and N = 3000, and fixing k = 80 and N = 3000. B.4. Experiments of Algorithm 7 The experimental setup follows the same protocol as described in Section B.1, except that we focus exclusively on the fixed-sample setting, in accordance with the theoretical analysis of the multi-source unl… view at source ↗
Figure 3
Figure 3. Figure 3: shows that Algorithm 7 consistently exhibits robust and competitive performance across all configurations. In the hard case, where deletions affect the top arms, Algorithm 7 remains consistently competitive and avoids the sharp degradation observed for the Gaussian mechanism under large γ or large k. Quantitatively, when N = 2000 and γ = 0.05, it achieves 8% (k = 40) and 9% (k = 80) reduction in sub-optima… view at source ↗
read the original abstract

Machine unlearning aims to unlearn data points from a learned model, offering a principled way to process data-deletion requests and mitigate privacy risks without full retraining. Prior work has mainly studied unsupervised / supervised machine unlearning, leaving unlearning for sequential decision-making systems far less understood. We initiate the first study of a foundational sequential decision-making problem: offline stochastic multi-armed bandits (MAB). We formalize the privacy constraint for offline MAB and measure utility by the post-unlearning decision quality. We conduct a systematic study of both single- and multi-source unlearning scenarios under two data-generation models, the fixed-sample model and the distribution model. For these settings, our algorithmic design is built on two canonical base algorithms: Gaussian mechanism and rollback, and we propose adaptive algorithms that switch between them according to the data regime and privacy constraint. We further introduce a mixing procedure that elucidates the rationale behind these baselines. We provide performance guarantees across the above settings and establish lower bounds under both dataset models. Experiments validate the predicted tradeoffs and demonstrate the effectiveness of the proposed methods.

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.

Referee Report

2 major / 2 minor

Summary. The paper initiates the first study of machine unlearning for offline stochastic multi-armed bandits. It formalizes a privacy constraint for this setting and defines utility solely via post-unlearning decision quality. The work examines single- and multi-source unlearning under fixed-sample and distribution data models, proposes adaptive algorithms that switch between the Gaussian mechanism and rollback, introduces a mixing procedure to explain the baselines, derives performance guarantees and lower bounds for the settings, and validates the tradeoffs via experiments.

Significance. If the formalization and guarantees hold under the stated definitions, the work is significant for opening a new direction in machine unlearning applied to sequential decision-making. It provides both algorithmic constructions with explicit performance bounds and matching lower bounds under two dataset models, plus a mixing procedure that clarifies design choices; these elements together establish a reproducible foundation for privacy-aware unlearning in bandits, which has direct relevance to recommendation and advertising systems that must honor deletion requests.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (formalization): the decision to measure utility exclusively by post-unlearning decision quality (final arm selection or policy quality) is load-bearing for all claimed guarantees and lower bounds, yet the manuscript provides no argument or robustness check showing that this definition remains sufficient when real deletion requests impose additional constraints such as trajectory-wide indistinguishability or bounds on intermediate regret.
  2. [§5] §5 (adaptive algorithms and mixing procedure): the adaptive switching rule between Gaussian noise and rollback, together with the mixing procedure, is asserted to satisfy the privacy definition while preserving the stated utility bounds, but no explicit derivation is given that the composition does not introduce unaccounted privacy leakage or extra utility loss; this directly affects whether the performance guarantees transfer to the multi-source and distribution-model cases.
minor comments (2)
  1. [Experiments] The experimental section should report the number of independent runs, confidence intervals, and the precise data-exclusion rules used when measuring post-unlearning decision quality, so that the claimed validation of tradeoffs can be reproduced.
  2. [Notation] Notation for the two data-generation models (fixed-sample vs. distribution) and the precise privacy parameter (ε, δ) should be introduced with a single table or definition block before the algorithmic sections to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and the positive assessment of the work's significance in opening a new direction for unlearning in sequential decision-making. We address the two major comments below, clarifying our design choices while agreeing to strengthen the manuscript with additional discussion and derivations where needed.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (formalization): the decision to measure utility exclusively by post-unlearning decision quality (final arm selection or policy quality) is load-bearing for all claimed guarantees and lower bounds, yet the manuscript provides no argument or robustness check showing that this definition remains sufficient when real deletion requests impose additional constraints such as trajectory-wide indistinguishability or bounds on intermediate regret.

    Authors: Our utility definition centers on post-unlearning decision quality because the offline stochastic MAB setting is fundamentally about identifying the best arm from a fixed dataset, with no ongoing online interactions or regret accumulation during deployment. This choice enables precise performance guarantees and matching lower bounds under the formalized privacy constraint. Real-world deletion requests may indeed involve stronger requirements such as trajectory-wide indistinguishability or intermediate regret bounds; however, these represent distinct privacy models outside the scope of this foundational study. We will add a dedicated discussion paragraph in the revised §3 (and abstract if space permits) explicitly acknowledging this limitation and outlining it as an avenue for future work. revision: yes

  2. Referee: [§5] §5 (adaptive algorithms and mixing procedure): the adaptive switching rule between Gaussian noise and rollback, together with the mixing procedure, is asserted to satisfy the privacy definition while preserving the stated utility bounds, but no explicit derivation is given that the composition does not introduce unaccounted privacy leakage or extra utility loss; this directly affects whether the performance guarantees transfer to the multi-source and distribution-model cases.

    Authors: The adaptive switching rule selects between mechanisms based on data statistics that are already part of the observable input, and the mixing procedure unifies the baselines to clarify when each is preferable. Privacy holds by construction for each base mechanism, with utility bounds derived separately before combination. To make this fully explicit, we will expand the analysis in the revised §5 and appendix with a dedicated composition argument (including a short theorem) confirming no additional privacy leakage occurs and that the utility bounds carry over unchanged to the multi-source and distribution-model settings. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper initiates a new formalization of privacy constraints and utility (post-unlearning decision quality) for offline stochastic MAB, then builds adaptive algorithms from standard base mechanisms (Gaussian and rollback) plus a mixing procedure. It derives performance guarantees and lower bounds under fixed-sample and distribution models. No equations or steps are shown that reduce claimed results to self-defined quantities, fitted parameters renamed as predictions, or load-bearing self-citation chains. The work is self-contained with independent content; any self-citations are not required for the core claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available, so ledger is necessarily incomplete; the central claims rest on an unstated formalization of privacy and utility that is treated as given.

axioms (1)
  • domain assumption Privacy constraint for offline MAB can be formalized such that post-unlearning decision quality is a meaningful utility measure.
    Invoked when defining the problem and measuring success; no justification supplied in abstract.

pith-pipeline@v0.9.0 · 5503 in / 1355 out tokens · 26676 ms · 2026-05-09T20:20:50.499654+00:00 · methodology

discussion (0)

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Reference graph

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