arxiv: 2603.28281 · v2 · submitted 2026-03-30 · 💻 cs.LG

Recognition: unknown

Corruption-robust Offline Multi-agent Reinforcement Learning From Human Feedback

Andi Nika , Debmalya Mandal , Parameswaran Kamalaruban , Adish Singla , Goran Radanovi\'c

Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:00 UTC · model grok-4.3

classification 💻 cs.LG

keywords offline multi-agent reinforcement learninghuman feedbackdata corruptionrobust estimationNash equilibriumcoarse correlated equilibriumlinear Markov games

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The pith

A robust algorithm for offline multi-agent RL from human feedback achieves an O(√ε) bound on the Nash gap when an ε-fraction of preference data is arbitrarily corrupted, under unilateral coverage of a Nash equilibrium and single-player devi

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

This paper develops corruption-robust methods for offline multi-agent reinforcement learning from human feedback in linear Markov games. Under a uniform coverage assumption on the clean data, a robust estimator bounds the gap to Nash equilibrium by O(ε to the power of nearly 1). Shifting to the weaker unilateral coverage regime, where only a Nash equilibrium and its single-player deviations are covered in the clean data, the algorithm attains an O(√ε) bound on the Nash gap. To address computational hardness, the paper relaxes the target to coarse correlated equilibria and derives a quasi-polynomial-time algorithm that preserves the O(√ε) scaling on the gap. This constitutes the first systematic analysis of adversarial corruption effects in offline multi-agent preference learning.

Core claim

In the linear Markov game model for offline MARLHF, the proposed robust estimator under unilateral coverage achieves an O(√ε) bound on the Nash equilibrium gap despite arbitrary corruption of an ε-fraction of trajectory-preference tuples; relaxing the solution concept to coarse correlated equilibria produces a quasi-polynomial-time algorithm with identical O(√ε) gap scaling.

What carries the argument

Robust estimator for corrupted trajectory-preference data in linear Markov games that identifies and bounds the effect of adversarial samples by exploiting unilateral coverage of a Nash equilibrium and its single-player deviations.

If this is right

Multi-agent policies can be learned from human preference data that contains arbitrary adversarial corruption while maintaining controlled equilibrium gaps.
The square-root dependence on the corruption fraction ε provides graceful degradation as data quality worsens.
Relaxing to coarse correlated equilibria makes the method computationally feasible without sacrificing the robustness scaling.
The framework supplies the first theoretical guarantees for corruption-robust offline MARLHF under linear function approximation.

Where Pith is reading between the lines

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

If unilateral coverage holds in practice, the method could support safer training of multi-agent systems from crowd-sourced or noisy human feedback.
The quasi-polynomial time for CCE suggests exploring further structural assumptions that might yield fully polynomial algorithms for the Nash case.
The coverage-based robust estimation technique may transfer to other multi-agent preference learning problems outside linear Markov games.

Load-bearing premise

The clean data must sufficiently cover at least one Nash equilibrium along with all single-player deviations from it.

What would settle it

A dataset where the clean portion covers a Nash equilibrium but omits its single-player deviations and the resulting Nash gap exceeds O(√ε) would show the bound does not hold.

read the original abstract

We consider robustness against data corruption in offline multi-agent reinforcement learning from human feedback (MARLHF) under a strong-contamination model: given a dataset $D$ of trajectory-preference tuples (each preference being an $n$-dimensional binary label vector representing each of the $n$ agents' preferences), an $\epsilon$-fraction of the samples may be arbitrarily corrupted. We model the problem using the framework of linear Markov games. First, under a uniform coverage assumption - where every policy of interest is sufficiently represented in the clean (prior to corruption) data - we introduce a robust estimator that guarantees an $O(\epsilon^{1 - o(1)})$ bound on the Nash equilibrium gap. Next, we move to the more challenging unilateral coverage setting, in which only a Nash equilibrium and its single-player deviations are covered. In this case, our proposed algorithm achieves an $O(\sqrt{\epsilon})$ bound on the Nash gap. Both of these procedures, however, suffer from intractable computation. To address this, we relax our solution concept to coarse correlated equilibria (CCE). Under the same unilateral coverage regime, we derive a quasi-polynomial-time algorithm whose CCE gap scales as $O(\sqrt{\epsilon})$. To the best of our knowledge, this is the first systematic treatment of adversarial data corruption in offline MARLHF.

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 gives the first explicit corruption-robust bounds for offline MARLHF in linear Markov games, with O(sqrt(eps)) Nash gap under unilateral coverage, but the claims rest on untested assumptions and lack any validation.

read the letter

Hi, the main thing to know is that this is the first systematic treatment of adversarial corruption in offline multi-agent RL from human feedback. They model the setting as linear Markov games and derive explicit gap bounds under a strong contamination model where an epsilon fraction of the trajectory-preference data can be arbitrary. Under uniform coverage they recover a near-linear rate O(eps^{1-o(1)}) on the Nash gap. Under the weaker unilateral coverage, which only requires clean data on the equilibrium and single-player deviations, they still get O(sqrt(eps)) for the Nash gap, and they relax to coarse correlated equilibria to obtain a quasi-polynomial algorithm with the same scaling. The linear feature map is what lets them extrapolate from the covered directions, which is the key technical move. That part is cleanly stated and extends prior single-agent robust RL work in a natural way. The soft spots are that the abstract supplies the rates but no proof sketches or even high-level derivation steps, so it is impossible to check whether the linear extrapolation actually stays within sqrt(eps) when the features are imperfect or when corruption hits the covered directions. The unilateral coverage assumption is also load-bearing and not obviously easy to verify on real human feedback data. There is no mention of experiments, which leaves open whether the constants are usable or whether the rates degrade in practice. This work is aimed at researchers in robust multi-agent RL and preference-based learning. It has enough novelty and formal structure to deserve a serious referee, even though it will need the full proofs and some empirical checks before it can be relied on. I would send it to peer review.

Referee Report

3 major / 1 minor

Summary. The paper studies corruption-robust offline multi-agent RL from human feedback (MARLHF) in linear Markov games under an ε-strong contamination model on trajectory-preference tuples. It introduces a robust estimator that achieves an O(ε^{1-o(1)}) Nash gap under uniform coverage of all policies of interest, then an O(√ε) Nash gap under the weaker unilateral coverage (Nash equilibrium plus single-player deviations only). For computational tractability it relaxes to coarse correlated equilibria (CCE) and supplies a quasi-polynomial-time algorithm that retains the O(√ε) CCE gap under unilateral coverage. The abstract claims this is the first systematic treatment of adversarial corruption in offline MARLHF.

Significance. If the stated rates are rigorously proved, the work would be a meaningful extension of single-agent robust offline RL results to the multi-agent preference-learning setting, with the unilateral-to-CCE relaxation providing a pragmatic path to tractability. The explicit dependence on linear structure for extrapolation under partial coverage is a clear technical contribution, though its practical significance hinges on whether the coverage assumptions are realistic and verifiable.

major comments (3)

[Abstract] Abstract: the O(√ε) Nash-gap claim under unilateral coverage is stated without any derivation steps, proof sketch, or explicit use of the linear feature map. The skeptic correctly flags that this rate is load-bearing on the feature map permitting accurate extrapolation to non-covered joint policies despite ε-corruption; without that step shown, it is impossible to confirm that the gap does not inflate beyond √ε.
[Abstract] Abstract: the uniform-coverage result is stated as O(ε^{1-o(1)}), yet the abstract supplies neither the estimator construction nor the argument that reduces the final gap to this rate. Because the central claims rest entirely on these coverage assumptions and the linear model, the absence of even a high-level proof outline makes the support for either rate impossible to assess from the provided text.
[Abstract] Abstract: no discussion is given of how the unilateral coverage assumption (clean data covers only a Nash equilibrium and its single-player deviations) can be verified or is expected to hold in practice. This assumption is the weakest link; if it fails to enable the required extrapolation, the claimed degradation from uniform to unilateral coverage cannot be justified.

minor comments (1)

[Abstract] Abstract: the novelty claim (“to the best of our knowledge, this is the first systematic treatment”) should be accompanied by at least one or two citations to the closest prior robust offline RL or MARLHF works so that the precise advance is clear.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. We address each major comment below and have revised the manuscript to improve clarity on the abstract claims, proof outlines, and assumption discussion.

read point-by-point responses

Referee: [Abstract] Abstract: the O(√ε) Nash-gap claim under unilateral coverage is stated without any derivation steps, proof sketch, or explicit use of the linear feature map. The skeptic correctly flags that this rate is load-bearing on the feature map permitting accurate extrapolation to non-covered joint policies despite ε-corruption; without that step shown, it is impossible to confirm that the gap does not inflate beyond √ε.

Authors: We agree the abstract is too concise and omits key steps. The full derivation is in Section 4.2: under unilateral coverage the linear feature map permits extrapolation of value functions to the Nash equilibrium and single-player deviations via a robust least-squares estimator; corruption is controlled by a median-of-means procedure whose error scales as O(√ε) after applying the coverage condition to bound the extrapolation bias. We have added a one-sentence proof sketch and explicit reference to the linear feature map in the revised abstract. revision: yes
Referee: [Abstract] Abstract: the uniform-coverage result is stated as O(ε^{1-o(1)}), yet the abstract supplies neither the estimator construction nor the argument that reduces the final gap to this rate. Because the central claims rest entirely on these coverage assumptions and the linear model, the absence of even a high-level proof outline makes the support for either rate impossible to assess from the provided text.

Authors: The abstract summarizes; the estimator and analysis appear in Section 3. Under uniform coverage we construct a robust estimator by combining truncated least-squares with a multi-agent median-of-means step that removes the ε-corruption bias up to a (1-o(1)) factor, yielding the stated rate. We have inserted a brief description of the estimator and the reduction argument into the revised abstract. revision: yes
Referee: [Abstract] Abstract: no discussion is given of how the unilateral coverage assumption (clean data covers only a Nash equilibrium and its single-player deviations) can be verified or is expected to hold in practice. This assumption is the weakest link; if it fails to enable the required extrapolation, the claimed degradation from uniform to unilateral coverage cannot be justified.

Authors: We accept that the abstract lacked any practical discussion. The revised version adds a short paragraph in the introduction and a dedicated paragraph in the discussion section explaining that unilateral coverage is expected when data are collected around stable equilibrium play (common in human-feedback settings) and can be verified empirically by checking feature coverage on the support of the equilibrium policy and its unilateral deviations. We also note the assumption's limitations if it is violated. revision: yes

Circularity Check

0 steps flagged

No circularity: bounds derived from explicit coverage assumptions and linear model

full rationale

The paper states its results as consequences of uniform coverage (every policy represented) and unilateral coverage (Nash + single-player deviations) in linear Markov games, using robust estimators to obtain O(ε^{1-o(1)}) or O(√ε) Nash/CCE gaps. These are direct theoretical derivations from the stated model and contamination model; no fitted parameter is renamed as a prediction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled. The derivation chain remains self-contained against the external assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; full paper details on parameters and axioms unavailable. The central claims rest on two domain assumptions about data coverage and the linear structure of the Markov game.

axioms (2)

domain assumption Uniform coverage: every policy of interest is sufficiently represented in the clean data
Invoked to obtain the O(ε^{1-o(1)}) Nash gap bound
domain assumption Unilateral coverage: only a Nash equilibrium and its single-player deviations are covered
Used for the O(√ε) Nash and CCE gap bounds

pith-pipeline@v0.9.0 · 5557 in / 1390 out tokens · 41846 ms · 2026-05-14T21:00:16.010348+00:00 · methodology

discussion (0)

Forward citations

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Reference graph

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Lemma A.1.[Lemma A.1 of Mandal et al

Nika, Mandal, Kamalaruban, Singla, and Radanovi´c Corruption-robust Offline Multi-agent Reinforcement Learning from Human Feedback Appendix Table of Contents A Proof of Theorem 3.1 13 B Proof of Theorem 4.1 18 C Proof of Theorem 5.1 28 D Technical Results 30 E Additional Algorithm Pseudocodes 32 A Proof of Theorem 3.1 In this section, we provide the full ...

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This is an immediate application of Lemma 4.2 of [Mandal et al., 2025] by applying the union bound for all agents

Proof. This is an immediate application of Lemma 4.2 of [Mandal et al., 2025] by applying the union bound for all agents. Note that the above bounds characterize the confidence set that we used throughout Section

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As a robust estimation technique, we again make use of RobEst based on the second part of Theorem A.1, which does not require uniform coverage. Lemma A.2 and Theorem A.1 give us the following guarantee for the output of the robust estimate eω, where, without loss of generality, we use the behavior policyµ: Eµ ϕ(s,a) ⊤(ω∗ −eω) 2 ≤c 2(δ)· s (H √ d+γ) 2poly(...

work page 2022
[21]

Set ΘUnil(·) as in Equation (5) and Γ(s,a) = E(d, m, δ, ϵ)· ∥ϕ(s,a)∥ Λ−1 h

Theorem B.1.Let ϵ∈[0,1/2) , λ≥Ω(dHlog(m/δ)/m) , and δ >0 . Set ΘUnil(·) as in Equation (5) and Γ(s,a) = E(d, m, δ, ϵ)· ∥ϕ(s,a)∥ Λ−1 h . Suppose Assumption 2 is satisfied and PGA is run for T1 steps with learning rate η= O(1/√T1). Then, there exist robust subroutines RobEst, TrimmedMLE, and RobMean such that, with probability at least 1−δ , the outputeπ of...

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Next, we provide an upper bound on the error of the estimate returned by theRobMeanalgorithm

The convexity of ΘUnil(θ′) is observed in [Mandal et al., 2025]. Next, we provide an upper bound on the error of the estimate returned by theRobMeanalgorithm. Theorem D.1(Proposition 1.5 of [Diakonikolas et al., 2020]).Let T be an ϵ-corrupted set of m samples from a distribution in Rd with mean ρ and covariance Σ. Let ϵ′ be in the order of (log(1/δ)/m+ϵ)≤...

work page 2025