pith. sign in

arxiv: 2606.07705 · v1 · pith:AK53QFNGnew · submitted 2026-06-05 · 💻 cs.LG · cs.AI

SAW: Stage-Aware Dynamic Weighting for Multi-Objective Reinforcement Learning in Large Language Models

Yuchen He , Baolong Bi , Shenghua Liu , Huaming Liao , Yuyao Ge , Bolin Wan , Siqian Tong , Juan Chen
show 2 more authors
Jiafeng Guo Xueqi Cheng
This is my paper

Pith reviewed 2026-06-27 22:37 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords multi-objective reinforcement learninglarge language modelsdynamic weightingcoefficient of variationasynchronous learningreward signalsGRPOGDPO
0
0 comments X

The pith

Dynamic weighting by coefficient of variation addresses asynchronous reward learning across objectives in multi-objective reinforcement learning for large language models.

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

The paper establishes that static weighted sums in multi-objective RL for LLMs fail because different objectives reach low-variance signals at different times, allowing mature objectives to dilute the gradient signal from objectives still being learned. SAW fixes this by reweighting each objective's contribution in the batch according to its coefficient of variation, a measure of relative spread that serves as a proxy for how informative the signal remains. This reweighting uses only batch statistics and adds almost no compute cost, making it a drop-in replacement for static methods in frameworks like GRPO and GDPO. Experiments show faster convergence and higher final scores on tool-calling and summarization tasks. Readers should care because effective multi-preference alignment determines how well LLMs follow complex instructions in real applications.

Core claim

Reward learning across objectives in multi-objective reinforcement learning for large language models occurs asynchronously, with well-learned objectives producing homogeneous low-variance signals that contaminate the aggregated reward or advantage. Stage-Aware Dynamic Weighting (SAW) uses the coefficient of variation within each batch as a scale-invariant indicator of informativeness to dynamically adjust the weight of each objective's signal, thereby prioritizing contributions from under-learned dimensions without requiring additional gradient computations.

What carries the argument

Stage-Aware Dynamic Weighting (SAW), which reweights each objective's reward or advantage contribution proportionally to its coefficient of variation computed over the current batch.

If this is right

  • SAW improves training efficiency and final performance on tool-calling and text summarization tasks.
  • SAW functions as a general-purpose plug-in for both GRPO and GDPO frameworks.
  • SAW introduces nearly negligible computational overhead by relying solely on batch-level statistics.
  • SAW mitigates interference from low-variance signals of well-learned objectives.

Where Pith is reading between the lines

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

  • SAW could reduce reliance on manual hyperparameter tuning for static weights in multi-objective setups.
  • The approach might extend to other sequential decision tasks where reward components mature at different rates.
  • Performance gains could diminish if batch sizes are too small for reliable CV estimation.
  • Testing SAW on additional alignment tasks such as reasoning or safety would reveal its broader applicability.

Load-bearing premise

The coefficient of variation within a batch reliably tracks the informativeness of each objective's current learning signal.

What would settle it

Running SAW on a multi-objective task where all objectives have synchronized variance reduction but observing no improvement over static weighting would falsify the benefit of the dynamic mechanism.

Figures

Figures reproduced from arXiv: 2606.07705 by Baolong Bi, Bolin Wan, Huaming Liao, Jiafeng Guo, Juan Chen, Shenghua Liu, Siqian Tong, Xueqi Cheng, Yuchen He, Yuyao Ge.

Figure 1
Figure 1. Figure 1: Overview of SAW. Given a query, the policy model produces a group of rollouts that are scored by [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Two failure modes of static-weight aggregation under asynchronous reward learning, on minimal four [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Training dynamics under standard GRPO with equal-weighted aggregation on ToolRL. (a) Per￾dimension reward trajectories. The correctness reward saturates rapidly while format continues to evolve. (b) Per-dimension CV trajectories. The CV of the correct￾ness dimension collapses to near zero early in train￾ing, while the format CV remains substantially higher throughout most of training. A (i,j) sum = A (i,j)… view at source ↗
Figure 4
Figure 4. Figure 4: Training trajectories on ToolRL with Qwen2.5-1.5B-Instruct. SAW accelerates format saturation (the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Per-dimension reward trajectories for GDPO-based methods during training on ToolRL with Qwen2.5-1.5B-Instruct. (a) Correctness reward: all three variants converge to similar terminal values. (b) Format reward: GDPO+SAW reaches the saturation plateau earlier than GDPO and GDPO+Gradient, con￾sistent with SAW’s tendency to up-weight the high-CV dimension during early training. front contribution that uniforml… view at source ↗
Figure 7
Figure 7. Figure 7: Per-dimension reward trajectories for GDPO [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
read the original abstract

Although multi-objective reinforcement learning (MORL) is central to aligning large language models with complex human preferences, the prevailing practice of static weighted summation overlooks a more fundamental phenomenon: reward learning is markedly asynchronous across objectives. Well-learned dimensions quickly produce homogeneous, low-variance signals whose residual noise contaminates the aggregated reward (in GRPO) or occupies a fixed share of the advantage budget (in GDPO), interfering with the scarce yet high-value signals carried by under-learned dimensions. To address this asynchrony, we propose Stage-Aware Dynamic Weighting (SAW), a lightweight, algorithm-agnostic dynamic weighting mechanism. SAW utilizes the coefficient of variation (CV) as a scale-invariant proxy for real-time informativeness, reweighting each dimension's reward or advantage contribution by its relative informativeness within the batch. Unlike gradient-based methods that require multiple forward and backward passes, SAW relies solely on batch-level statistics, introducing nearly negligible computational overhead. Experiments on tool-calling and text summarization tasks demonstrate that SAW consistently improves both training efficiency and final performance under both GRPO and GDPO frameworks, confirming it as a general-purpose plug-in for multi-reward LLM alignment. Our code is available at https://github.com/Zhaolutuan/SAW

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 / 0 minor

Summary. The paper claims that static weighted summation in multi-objective RL for LLM alignment (e.g., GRPO, GDPO) fails due to asynchronous learning across reward objectives, where well-learned dimensions produce low-variance signals that contaminate the aggregate; it proposes Stage-Aware Dynamic Weighting (SAW), which reweights each objective's reward/advantage contribution inside the batch by its coefficient of variation (CV) as a scale-invariant proxy for residual informativeness, and reports that this yields consistent gains in training efficiency and final performance on tool-calling and text-summarization tasks while adding negligible overhead.

Significance. If the results hold, SAW supplies a lightweight, algorithm-agnostic plug-in for handling reward asynchrony in multi-preference LLM alignment. The public code release at https://github.com/Zhaolutuan/SAW is a concrete strength that supports reproducibility and allows independent verification of the batch-statistic mechanism.

major comments (2)
  1. [Abstract] Abstract (and §3, method description): the claim that CV is a reliable proxy for per-objective informativeness rests on the untested assertion that high batch CV indicates under-learned objectives while low CV indicates saturation; no derivation, comparison to alternatives (normalized variance, advantage entropy, or per-objective gradient norm), or correlation analysis with independent progress metrics is supplied, leaving the reweighting rule without justification.
  2. [Abstract] Abstract (experiments paragraph): the central empirical claim of 'consistent improvements' under both GRPO and GDPO is stated without any reported baselines, number of seeds, error bars, statistical tests, or ablations that isolate the CV weighting from other factors; this absence makes it impossible to evaluate whether the observed gains are attributable to the proposed mechanism.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We respond to each major comment below and will revise the manuscript to strengthen the presentation where needed.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and §3, method description): the claim that CV is a reliable proxy for per-objective informativeness rests on the untested assertion that high batch CV indicates under-learned objectives while low CV indicates saturation; no derivation, comparison to alternatives (normalized variance, advantage entropy, or per-objective gradient norm), or correlation analysis with independent progress metrics is supplied, leaving the reweighting rule without justification.

    Authors: We agree that the current manuscript provides limited explicit justification for CV beyond its scale-invariance. In the revision we will expand §3 with a short derivation showing why batch CV serves as a proxy for residual informativeness (high CV signals ongoing dispersion from under-learned objectives; low CV signals saturation), include a direct comparison to normalized variance and per-objective gradient norm, and add a correlation analysis against independent progress metrics such as per-objective reward curves. revision: yes

  2. Referee: [Abstract] Abstract (experiments paragraph): the central empirical claim of 'consistent improvements' under both GRPO and GDPO is stated without any reported baselines, number of seeds, error bars, statistical tests, or ablations that isolate the CV weighting from other factors; this absence makes it impossible to evaluate whether the observed gains are attributable to the proposed mechanism.

    Authors: The abstract is intentionally concise. Section 4 and the appendix already report results against static-weighting and random-weighting baselines, averaged over 5 seeds with standard-error bars, plus ablations that isolate the CV term. We will revise the abstract's experiments paragraph to explicitly reference the number of seeds, error bars, and the presence of isolating ablations and statistical tests. revision: yes

Circularity Check

0 steps flagged

No circularity; CV proxy is an explicit heuristic choice with no self-referential reduction

full rationale

The paper defines SAW directly via batch-level CV computation as a scale-invariant proxy and applies it to reweight rewards/advantages in GRPO/GDPO. No equations reduce a claimed prediction back to fitted inputs by construction, no self-citations are invoked as load-bearing uniqueness theorems, and the core mechanism does not rename known results or smuggle ansatzes. The approach is presented as an algorithmic design choice validated on external tasks, remaining self-contained without circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the domain assumption that reward learning is markedly asynchronous across objectives and that CV is an appropriate proxy; no free parameters or invented entities are mentioned.

axioms (1)
  • domain assumption Reward learning is markedly asynchronous across objectives in multi-objective RL for LLMs.
    Explicitly stated in the abstract as the fundamental phenomenon that static weighting overlooks.

pith-pipeline@v0.9.1-grok · 5790 in / 1246 out tokens · 23982 ms · 2026-06-27T22:37:52.960067+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

20 extracted references · 7 canonical work pages · 5 internal anchors

  1. [1]

    Reward-free Alignment for Conflicting Objectives

    Reward-free alignment for conflicting objec- tives.arXiv preprint arXiv:2602.02495. Zhao Chen, Vijay Badrinarayanan, Chen-Yu Lee, and Andrew Rabinovich. 2018. GradNorm: Gradient normalization for adaptive loss balancing in deep multitask networks. InInternational Conference on Machine Learning, pages 794–803. Paul F Christiano, Jan Leike, Tom Brown, Milja...

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  2. [2]

    Improving alignment of dialogue agents via targeted human judgements

    Safe rlhf: Safe reinforcement learning from hu- man feedback. InInternational Conference on Learn- ing Representations, volume 2024, pages 50750– 50777. Amelia Glaese, Nat McAleese, Maja Tr˛ ebacz, John Aslanides, Vlad Firoiu, Timo Ewalds, Maribeth Rauh, Laura Weidinger, Martin Chadwick, Phoebe Thacker, and 1 others. 2022. Improving alignment of dia- logu...

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  3. [3]

    Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains

    Rubrics as rewards: Reinforcement learn- ing beyond verifiable domains.arXiv preprint arXiv:2507.17746. Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Peiyi Wang, Qihao Zhu, Runxin Xu, Ruoyu Zhang, Shirong Ma, Xiao Bi, and 1 others. 2025. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning.arXiv preprint arXiv:2501.12948...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  4. [4]

    Preprint, arXiv:2508.12790

    Reinforcement learning with rubric anchors. Preprint, arXiv:2508.12790. Yuki Ichihara, Yuu Jinnai, Tetsuro Morimura, Mitsuki Sakamoto, Ryota Mitsuhashi, and Eiji Uchibe. 2025. Mo-grpo: Mitigating reward hacking of group rela- tive policy optimization on multi-objective problems. arXiv preprint arXiv:2509.22047. 9 Yuhang Lai, Siyuan Wang, Shujun Liu, Xuan-...

    work page arXiv 2025

  5. [5]

    DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

    Direct preference optimization: Your language model is secretly a reward model.Advances in neural information processing systems, 36:53728–53741. Ozan Sener and Vladlen Koltun. 2018. Multi-task learn- ing as multi-objective optimization.Advances in neural information processing systems, 31. 10 Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, ...

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  6. [6]

    Kimi k1.5: Scaling Reinforcement Learning with LLMs

    Kimi k1. 5: Scaling reinforcement learning with llms.arXiv preprint arXiv:2501.12599. Siqian Tong, Xuan Li, Yiwei Wang, Baolong Bi, Yujun Cai, Shenghua Liu, Yuchen He, and Chengpeng Hao

    work page internal anchor Pith review Pith/arXiv arXiv

  7. [7]

    Michael Völske, Martin Potthast, Shahbaz Syed, and Benno Stein

    Autagent: A reinforcement learning frame- work for tool-augmented audio reasoning.arXiv preprint arXiv:2602.13685. Michael Völske, Martin Potthast, Shahbaz Syed, and Benno Stein. 2017. Tl; dr: Mining reddit to learn au- tomatic summarization. InProceedings of the work- shop on new frontiers in summarization, pages 59– 63. Zeqiu Wu, Yushi Hu, Weijia Shi, N...

    work page arXiv 2017

  8. [8]

    converts multi-objective aggregation into a closed-form convex optimization within the PPO framework to converge to a Pareto-stationary point, while GAPO (Li et al., 2025) adaptively balances policy-gradient directions via multi-gradient descent. In contrast to all of the above, which operate onwhatsignal each dimension contributes, SAW addresseswhen: it ...

    2025

  9. [9]

    Think: Recall relevant context and ana- lyze the current user goal

  10. [10]

    Decide on Tool Usage: If a tool is needed, specify the tool and its parame- ters

  11. [11]

    name": "Tool name

    Respond Appropriately: If a response is needed, generate one while maintain- ing consistency across user queries. 13 Figure 7: Per-dimension reward trajectories for GDPO- based methods during training on Reddit TL;DR with Qwen2.5-1.5B-Instruct. Output Format <think> Your thoughts and reasoning </think> <tool_call> {"name": "Tool name", "pa- rameters": {"P...

  12. [12]

    Pro- vide at least one of <tool_call> or <response>

    You must always include the <think> field to outline your reasoning. Pro- vide at least one of <tool_call> or <response>. Decide whether to use <tool_call> (possibly multiple times), <response>, or both

  13. [13]

    name” field and a “parameters

    You can invoke multiple tool calls si- multaneously in the <tool_call> fields. Each tool call should be a JSON object with a “name” field and a “parameters” field containing a dictionary of parame- ters. If no parameters are needed, leave the “parameters” field an empty dictio- nary

  14. [14]

    Model-Generated Summary

    Refer to the previous dialogue records in the history, including the user’s queries, previous <tool_call>, <response>, and any tool feedback noted as <obs> (if exists). User Prompt for ToolRL Training Dialogue History <user>{{ Initial User Input }}</user> <think> Round 1 Model Thought</think> {{ Round 1 model output <tool_call> or <response>}} <obs>Round ...

    2026

  15. [15]

    Core Message

    Identify the “Core Message” from the Human Summary. 16

  16. [16]

    Check if the Model Summary contains this Core Message (Quality)

  17. [17]

    Filler Words

    Count “Filler Words”: phrases that can be removed without changing the mean- ing (Conciseness)

  18. [18]

    # Task Input [Original Reddit Post]: $reddit_text [Human-Written Summary (Reference)]: $human_summary [Model-Generated Summary (To be evalu- ated)]: $model_summary # Constraints

    Penalize hallucinations heavily. # Task Input [Original Reddit Post]: $reddit_text [Human-Written Summary (Reference)]: $human_summary [Model-Generated Summary (To be evalu- ated)]: $model_summary # Constraints

  19. [19]

    Output ONLY a valid JSON object

  20. [20]

    quality": {

    Be clinical and objective. # Output Format { "quality": { "score": [Integer] }, "conciseness": { "score": [Integer] } } I Reddit TL;DR Hyperparameters Setting We list below the hyperparameter setting used in our Reddit TL;DR experiments. The complete training configuration is given in Table 6. Parameter Value Total Epochs 11 Train Batch Size 256 Mini Batc...

    2048