AMoPO: Adaptive Multi-objective Preference Optimization without Reward Models and Reference Models

Desheng Wang; Haodong Zhao; Hao Li; Jiansong Chen; Jingqing Ruan; Qi Liu; Tong Xu; Wan Guanglu; Xunliang Cai; Zhi Zheng

REVIEW 6 major objections 6 minor 45 references

AMoPO: Adaptive Multi-objective Preference Optimization without Reward Models and Reference Models

T0 review · 6 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A single LLM can balance multiple preference dimensions without any reward model.

desk verdict A useful weight-sampling idea buried in a paper whose headline gains are inflated and whose central evaluation ignores its training distribution. read the letter →

arxiv 2506.07165 v1 pith:JJPCWYRH submitted 2025-06-08 cs.LG cs.AI

Qi Liu , Jingqing Ruan , Hao Li , Haodong Zhao , Desheng Wang , Jiansong Chen , Wan Guanglu , Xunliang Cai

show 2 more authors

Zhi Zheng Tong Xu

This is my paper

classification cs.LGcs.AI

keywords multi-objectivepreferenceoptimizationreference-freealignmentreward-model-freeimplicitrewardsadaptiveweightassignmentGaussiansamplingdimension-conditionedpromptsLLM

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes that a single language model can learn to balance several quality dimensions — helpfulness, correctness, and instruction following — in one training run, without a reward model or a reference model. The training signal is the model's own average token log-likelihood on dimension-conditioned prompts, combined through a weighted sum of SimPO-style losses. An adaptive mechanism samples per-dimension weights from a Gaussian distribution fit to the model's token probabilities, so the model prioritizes the dimensions it is most confident about. The authors report an average 28.5% improvement over the single- and multi-objective baselines they compare, and show that the gains grow from 7B to 14B to 32B parameters. If the claim holds, multi-objective alignment becomes cheaper and can be steered by the model's learned confidence rather than by fixed user-chosen weights.

What carries the argument

The load-bearing object is the Multi-Objective Bradley-Terry (MOBT) model: a product over dimensions of sigmoid comparisons, $\pi(y_w \succ y_l \mid x; \alpha; d) = \log \prod_{k=1}^K \sigma^{\alpha_k}\big(r_k(x^*_k, y_w) - r_k(x^*_k, y_l)\big)$, where each per-dimension reward $r_k$ is the policy's own length-normalized log-likelihood. The second half of the machinery is the adaptive weight sampler: for each dimension, the mean $\mu_k$ and variance $\sigma^2_k$ of the token probabilities over the chosen and rejected responses are computed, a weight $\alpha_k \sim \mathcal{N}(\mu_k, \sigma^2_k)$ is sampled, and the weights are softmax-normalized. This sampler decides how much each dimension contributes to the final loss at every update, and the paper argues it lets the model adaptively prioritize the dimensions it is most confident about.

What would settle it

Train AMoPO on Qwen2.5-14B with the published setup but decode on the original, unconditioned prompts, and compare with a control trained on the identical weighted loss using plain prompts instead of $x^*_k = f(x, d_k)$. If the dimension-conditioned training does not beat the plain-prompt control by the reported margin, or if the template must be present at inference to recover the gains, the central transfer claim is falsified.

Watch

Extended reading notes

Core claim

The central claim is that one policy LLM can be aligned with multiple preference dimensions at once using only its own generation probabilities as rewards. AMoPO replaces the traditional Bradley-Terry reward with a Multi-Objective Bradley-Terry objective in which each dimension $k$ contributes a length-normalized log-likelihood comparison $\sigma\left(\frac{\beta}{|y_w|}\log \pi_\theta(y_w|x^*_k) - \frac{\beta}{|y_l|}\log \pi_\theta(y_l|x^*_k)\right)$, with $x^*_k = f(x, d_k)$ the prompt rewritten to focus on that dimension. The dimension weights $\alpha_k$ are not fixed; they are sampled from a Gaussian whose mean and variance are computed from the model's token-level probabilities on that dimension, then softmax-normalized. The authors report that this outperforms previous single- and multi-objective baselines by an average 28.5% across AlpacaEval 2, Arena-Hard, and MT-bench, and that the advantage over fixed equal weights widens from 7B to 14B to 32B.

Load-bearing premise

The method works only if the model transfers dimension-conditioned training behavior to the original, unconditioned prompts used in evaluation, and only if the mean and variance of token probabilities are a trustworthy guide to per-dimension confidence; if either gives way, the reported gains could vanish.

Editorial extensions

If this is right

A $K$-dimension alignment run needs only the policy LLM and a scored preference dataset; no frozen reference model and no separately trained reward model need to be loaded, which reduces memory and compute.
The same weighted-loss machinery can be pointed at any set of scored dimensions, because each dimension enters only through a prompt template and a scalar score.
Larger models extract more value from the adaptive weights: on AlpacaEval 2 the Gaussian sampler beats fixed equal weights by +0.9 points at 7B but +4.0 points at 32B, so the method's advantage grows with scale.
The method improves helpfulness, correctness, and instruction following together, while several baselines lag on at least one of the three measured dimensions.
Because the weight sampler is modular, future work can replace the Gaussian with another confidence model without changing the overall AMoPO loss.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the train/eval transfer holds, AMoPO teaches implicit controllability: the model internalizes dimension emphasis from the training template and reproduces it on plain prompts, which would make it usable without control tokens at inference.
The Gaussian sampler is one instance of a confidence-driven weighting rule; entropy-based or calibration-based uncertainties could be substituted and compared, which would show whether token probabilities are informative for weighting or merely a stable proxy.
The paper trains on one static, three-dimension dataset, so a natural extension is online or multi-turn preference tracking where per-dimension confidence reweighting continues during dialogue; the authors themselves list multi-turn preferences as unaddressed.
Because the reported 28.5% is an average of per-benchmark improvement ratios, benchmark-by-benchmark margins such as win rates and MT-bench ratings should be read alongside the headline.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: AMoPO is a reasonable incremental contribution—SimPO-style loss with a weighted multi-objective sum and an adaptive Gaussian weight sampler—but the headline numbers shouldn't be taken at face value, and there's a train/eval mismatch that the paper never addresses.

What's genuinely new: the weight sampler. Using per-dimension token-probability moments (mean and variance) to sample weights for the multi-objective loss is not in the prior work I know. That's a real idea, and the comparison against fixed weights in Table 3 shows it does something—the 32B numbers especially look like more than noise. Credit also for keeping the framework reference-free and reward-model-free, which is a practical simplification, and for shipping code (if the repo ends up public as promised).

Where it gets soft. First, the 28.5% claim in the abstract is an average of relative improvements across benchmarks and baselines, and it's inflated by ORPO's terrible AlpacaEval baseline (163.5% relative improvement from 13.1). The MT-bench deltas are 0.03-0.1 rating. No seeds, no error bars. Second, and more load-bearing: training is done entirely on dimension-conditioned prompts x*=f(x,d), while all evaluations use the original prompt x. The paper provides no evidence that the conditioning transfers to plain prompts. It's plausible that the gains come from the data-augmentation effect of seeing HelpSteer2 examples in three templates, not from the MOBT model or the Gaussian weights. A control baseline trained on the same augmented data with a plain SimPO loss would answer this, and it's missing. Third, the 'Multi-Objective BT Model' in Eq (8) is not actually a BT model—it's a weighted sum of log-sigmoids, which is fine as a loss but is not a normalized preference probability. The derivation in Appendix A papers over that. Fourth, the Gaussian assumption for token-probability moments is heuristic; the authors don't provide evidence that these statistics encode per-dimension confidence. The ablations in D.7 are useful but don't cover the conditioning question.

On balance, this is a paper with one promising mechanism and one big unaddressed gap. The authors' own limitations section is honest about dataset and dimension coverage, which I read in their favor.

Who it's for: people working on reference-free multi-objective alignment will want to know about the weight sampler. I'd send it to a serious referee, but the referee should push hard on the train/eval test and error bars. If those don't hold up, the paper is a modest heuristic addition, not a 28.5% breakthrough.

Referee Report

6 major / 6 minor

Summary. AMoPO is a preference-optimization method for LLMs that removes both reward models and reference models. The paper's core idea is to condition training on dimension-specific prompt templates x* = f(x, d_k) for helpfulness, correctness, and instruction following, then train with a weighted sum of SimPO-style losses, where the weights are sampled from a Gaussian distribution whose mean and variance come from the policy's own token probabilities. Experiments on Qwen2.5-7B/14B/32B and LLaMA3.1-8B are reported on AlpacaEval 2, Arena-Hard, and MT-bench, with the abstract claiming a 28.5% average improvement over state-of-the-art baselines and 'scaling ability' across model sizes.

Significance. If the central claims were sound, AMoPO would be a useful lightweight alternative to multi-objective alignment methods that require multiple reward or reference models. The paper explicitly provides code and data, includes human validation, and reports ablations on the weight-assignment mechanism, which are strengths. However, the headline empirical claim rests on a statistically questionable aggregation, the experimental design does not isolate the effect of the prompt-conditioning transformation, and the paper's 'adaptive' claim is never evaluated at inference time. These issues substantially limit the significance of the reported results in their current form.

major comments (6)

[§5.2, Table 6] The headline '28.5% overall improvements' is computed by averaging per-baseline relative improvements across three benchmarks with very different scales. For Qwen2.5-7B, ORPO has an AlpacaEval win rate of 13.1, so its relative improvement is 346% on that benchmark and 163.5% on average, while SimPO's average relative improvement is only 2.1%. Averaging such heterogeneous relative improvements is not a meaningful performance measure, and no error bars, confidence intervals, or multiple seeds are reported. This undermines the central empirical claim of the abstract.
[§4.1, Algorithm 1, §5.1] Training uses dimension-conditioned prompts x* = f(x, d_k) for each objective, but all evaluation is performed on the original prompt x. The paper provides no control experiment or analysis demonstrating that gains transfer from the templated prompt distribution to plain prompts. Without a baseline trained on the same x* data with a standard loss and evaluated on x, the improvements in Table 2 could be attributed to prompt/data augmentation rather than to the MOBT model or the Gaussian weighting mechanism.
[§4.2, Eq. (8)] The Multi-Objective BT model is defined as a weighted sum of log-sigmoids, π(y_w ≻ y_l | x; α; d) = Σ_k α_k log σ(r_k(x*_k, y_w) − r_k(x*_k, y_l)). This expression is not a probability distribution: it is generally negative and unbounded. The subsequent claim that Eq. (9) is a maximum-likelihood objective under a Bradley-Terry-style model is therefore not justified. The loss itself is a reasonable scalarized SimPO objective, but the theoretical derivation is incorrect.
[§4.3, Eq. (10)] The adaptive weight assignment computes the mean and variance of the policy's own token probabilities and samples weights α_k from the resulting Gaussian, which are then used to weight the same policy's loss. This self-referential loop is not analyzed, and no evidence is provided that token-probability statistics encode meaningful per-dimension confidence. The ablation in Table 3 compares Gaussian sampling with fixed weights but does not isolate this mechanism from the prompt-conditioning transformation, so the contribution of the weight assignment is not clearly demonstrated.
[§5.2, Table 3] The abstract claims that experiments on 7B, 14B, and 32B models reveal the scaling ability of AMoPO, but the 32B results in Table 3 only compare Gaussian sampling with fixed weights within AMoPO; no baseline methods are evaluated at 32B. The scaling claim is therefore not supported by any comparison against state-of-the-art baselines at that scale.
[§1, §5] The paper describes AMoPO as 'adaptive' and capable of 'dynamic balance' across preference dimensions. However, at inference the model receives only the original prompt x with no dimension indicator, so the trained policy cannot adapt its balance across dimensions when a user specifies a preference. None of the evaluations test adaptivity by conditioning the prompt on a dimension at inference time. The central claim of adaptivity is therefore untested.

minor comments (6)

[§4.3, Eq. (10)] The variable T in Eq. (10) is not defined; it should be stated that T is the number of tokens in the response (or that the mean and variance are computed over the token positions).
[Appendix B, Table 4] Table 4 lists γ = 2.0 for AMoPO, but γ does not appear in Eq. (9) or Algorithm 1. Please clarify whether γ is used in the loss or remove it from the hyperparameter table.
[Figure 2] Figure 2 is referenced in the text (Section 4.1 and 4.4) but is not present in the manuscript; the pipeline figure should be included.
[References] There are duplicate references: Ramé et al. 2023a and 2023b are the same paper, and Wang et al. 2024b and 2024c appear to be the same work. These should be consolidated.
[§4.4] The sentence 'AMoPO transfers an original quadruple < x, y_w, y_l, d> into a set of quadruples {< x, y_w, y_l, d >}_{d∈d}' is confusing because d is used both as a variable ranging over the set of dimensions and as the set itself; please clarify the notation.
[Limitations] The Limitations section acknowledges that the Gaussian assumption may not generalize, but it does not mention the train/eval distribution shift or the statistical aggregation issue raised above. These are important limitations and should be discussed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: AMoPO's loss and adaptive weights are self-referential heuristics, but no prediction reduces to a fitted input or self-citation chain.

full rationale

We find no circular reasoning in AMoPO. The training objective (Eq. 9) is a weighted sum of SimPO-style per-dimension losses on dimension-conditioned prompts x*_k = f(x, d_k); the weights alpha_k are sampled from a Gaussian parameterized by the policy's own token probabilities (Eq. 10, Algorithm 1). This is a self-referential heuristic - the model weights dimensions by its own confidence - but it is not a fitted parameter renamed as a prediction, and no benchmark quantity is equal by construction to the loss. The derivation from the per-dimension BT model to the MOBT loss is algebraic (Appendix A), and the cited generation metric comes from external work (SimPO, Meng et al. 2024). The only self-citation (Xu et al. 2025, which shares two authors) is a passing reference to multi-dimensional preferences and is not load-bearing. The most serious validity threats - training on x* while evaluating on plain x, and the Gaussian assumption - are empirical or modeling concerns, not circularity. We therefore score 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 2 invented entities

The central claim rests on a chain of assumptions: the BT preference model, a questionable multi-objective generalization, a Gaussian modeling choice with no empirical support, and an implicit train/inference distribution shift. The only fitted hyperparameters are β and γ, but the adaptive weighting introduces a flexible, ad hoc mechanism that is not grounded in any theory.

free parameters (2)

beta (β) = 0.8
Scaling factor for the implicit reward difference in the loss (Eq. 9, Section 4.2; hyperparameter search in Table 4). Results are sensitive to it, but no sensitivity analysis is reported.
gamma (γ) = 2.0
Target reward margin reported in Table 4 for AMoPO, although the AMoPO loss in Eq. 9 does not contain γ; inconsistent with the method description.

assumptions (4)

domain assumption Bradley-Terry model describes pairwise preferences as a logistic function of reward differences (Eq. 2, Section 3).
Standard assumption in preference optimization, inherited from DPO/SimPO.
ad hoc to paper A weighted sum (or product) of per-dimension BT probabilities yields a valid preference distribution (Eq. 8, Section 4.2).
This is not proven and is in fact false for K>1: the object does not normalize to a probability distribution, yet it is treated as the 'Multi-Objective BT Model' and used as the basis for the loss.
ad hoc to paper The generation space of the LLM can be modeled as a Gaussian distribution whose moments are estimated from token probabilities (Eq. 10, Section 4.3).
No justification is given for the Gaussian assumption; the authors themselves note in the limitations that 'the Gaussian distribution assumption... may not generalize well to all types of preference dimensions.'
domain assumption Training on dimension-conditioned prompts x*_k = f(x, d_k) transfers to unconditioned prompts at inference.
The loss (Eq. 9) is computed on prompts augmented with dimension focus and score criteria, but evaluation (Section 5) uses plain instructions; the paper does not discuss this distribution shift.

invented entities (2)

Multi-Objective BT (MOBT) model
purpose: To generalize the BT model to multiple preference dimensions and justify a weighted-sum loss.
The MOBT model is a mathematical construct defined in Eq. 8; it is not a valid probability distribution and there is no independent evidence for its correctness beyond the paper's own usage.
Adaptive Gaussian weight policy
purpose: To assign per-dimension importance weights dynamically during training.
A heuristic mechanism (Section 4.3) that samples weights from a Gaussian parameterized by token-probability moments; no external validation or formal property is provided.

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Cite this review

Pith. "Pith review of AMoPO: Adaptive Multi-objective Preference Optimization without Reward Models and Reference Models." pith.science (2026). https://pith.science/paper/JJPCWYRH

@misc{pith2026250607165,
  author       = {Pith},
  title        = {Pith review of: AMoPO: Adaptive Multi-objective Preference Optimization without Reward Models and Reference Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JJPCWYRH}},
  note         = {Machine review of arXiv:2506.07165}
}

read the original abstract

Existing multi-objective preference alignment methods for large language models (LLMs) face limitations: (1) the inability to effectively balance various preference dimensions, and (2) reliance on auxiliary reward/reference models introduces computational complexity. To address these challenges, we propose Adaptive Multi-objective Preference Optimization (AMoPO), a novel framework that achieves dynamic balance across preference dimensions. By introducing the multi-objective optimization paradigm to use the dimension-aware generation metrics as implicit rewards, AMoPO aligns LLMs with diverse preferences without additional reward models or reference models. We introduce an adaptive weight assignment mechanism that models the generation space as a Gaussian distribution, allowing dynamic prioritization of preference dimensions. Empirical results demonstrate that AMoPO outperforms state-of-the-art baselines by 28.5%, and the experiments on 7B, 14B, and 32B models reveal the scaling ability of AMoPO. Moreover, additional analysis of multiple dimensions verifies its adaptability and effectiveness. These findings validate AMoPO's capability to achieve dimension-aware preference alignment, highlighting its superiority. Our codes and datasets are available at https://github.com/Javkonline/AMoPO.

Figures

Figures reproduced from arXiv: 2506.07165 by the authors.

**Figure 1.** LLM1 prefers helpfulness while LLM2 prefers correctness, yet both struggle to adapt across various dimensions. advanced single-objective alignment, fundamental limitations persist when addressing the multidimensional nature of real-world human preferences (Wang et al., 2024d; Cui et al., 2024; Xu et al., 2025) [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

**Figure 2.** The pipeline of AMoPO comprises two key stages: (a) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Three-Dimensional Margin (helpfulness, cor [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: The three-dimensional scores of different methods on Qwen2.5-14B-Instruct. To validate the response capability across the three dimensions on tested datasets, e.g., AlpacaEval 2, we apply gpt4o-2024-05-13 to evaluate scores across different dimensions for the response…

**Figure 5.** Figure 5: The instruction following score prompt template. [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]

**Figure 6.** Figure 6: The helpfulness score prompt template [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]

**Figure 7.** Figure 7: The correctness score prompt template [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]

**Figure 8.** Figure 8: The harmlessness judgement prompt template. [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]

**Figure 9.** Figure 9: The verbosity score prompt template [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]

**Figure 10.** Figure 10: The correctness score prompt template. As shown in [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]

**Figure 11.** Figure 11: The evaluation of win rate prompt template. [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]

**Figure 12.** Figure 12: The evaluation of rating prompt template of math category. [PITH_FULL_IMAGE:figures/full_fig_p024_12.png]

**Figure 13.** Figure 13: The evaluation of rating prompt template of none-math category. [PITH_FULL_IMAGE:figures/full_fig_p024_13.png]

**Figure 14.** Figure 14: The three-dimensional scores of different methods on Qwen2.5-7B-Instruct. As shown in Figure.14, although MODPO introduces a multi-dimensional reward model and CPO introduces the special tokens to incorporate multi-objective information, its effectiveness has not impr…

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Reference graph

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[2023]

Seongyun Lee, Sue Hyun Park, Seungone Kim, and Minjoon Seo

Personalized soups: Personalized large lan- guage model alignment via post-hoc parameter merg- ing.CoRR, abs/2310.11564. Seongyun Lee, Sue Hyun Park, Seungone Kim, and Minjoon Seo. 2024. Aligning to thousands of pref- erences via system message generalization.CoRR, abs/2405.17...

2024 arXiv
[2024]

Mohammad Gheshlaghi Azar, Zhaohan Daniel Guo, Bi- lal Piot, Rémi Munos, Mark Rowland, Michal Valko, and Daniele Calandriello

Introducing meta llama 3: The most capable openly available llm to date. Mohammad Gheshlaghi Azar, Zhaohan Daniel Guo, Bi- lal Piot, Rémi Munos, Mark Rowland, Michal Valko, and Daniele Calandriello. 2024. A general theoret- ical paradigm to understand learning from human prefe...

2024
[4455]

Anirudhan Badrinath, Prabhat Agarwal, and Jiajing Xu

PMLR. Anirudhan Badrinath, Prabhat Agarwal, and Jiajing Xu

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

**Partial Focus**: Addresses one aspect poorly

[2] [2]

- (2) Acknowledges both but slight deviations

**Partial Compliance**: - (1) Meets goals or restrictions, neglecting others. - (2) Acknowledges both but slight deviations

[3] [3]

Hybrid preference optimization: Augmenting direct preference optimization with auxiliary objec- tives.CoRR, abs/2405.17956. Lalit R. Bahl, Frederick Jelinek, and Robert L. Mercer

work page Pith review arXiv

[4] [4]

Based the instruction following rule and given my answer to an instruction, your role is to provide specific and constructive score for me

**Comprehensive Compliance**: Fully aligns, meets all requirements. Based the instruction following rule and given my answer to an instruction, your role is to provide specific and constructive score for me. You should find the best way for me to learn from your instruction following score and improve my performance. You should consider the all Instructio...

work page 2024

[5] [5]

Cal vary Ceme tery and Mor tu ary will be on your right. For the most ac cu rate and up -to -date di rec tions, it is rec om mended to use a GPS de vice or a map ping ser vice like Google Maps, Ap ple Maps, or Waze, as road con di tions and con struc tion can change. MODPO To travel from Rowan Av enue El emen tary School to Cal vary Ceme tery and Mor tu a...

work page

[6] [6]

Multi-objective alignment of large language models through hypervolume maximization.arXiv preprint arXiv:2412.05469. OpenAI. 2023. GPT-4 technical report.CoRR, abs/2303.08774. Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al

arXiv 2023

[7] [7]

Turn right onto S San Pe dro St

work page

[8] [8]

Direct preference optimization: Your language model is secretly a reward model. InAdvances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Sys- tems 2023, NeurIPS 2023, New Orleans, LA, USA, December 10 - 16, 2023. Alexandre Ramé, Guillaume Couairon, Corentin Dancette, Jean-Baptiste Gaya, Mustafa Shukor, Lau...

work page 2023