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arxiv: 2601.08403 · v2 · submitted 2026-01-13 · 💻 cs.AI

Owen-Shapley Policy Optimization: A Principled RL Algorithm for Generative Search LLMs

Abhijnan Nath , Alireza Bagheri Garakani , Tianchen Zhou , Fan Yang , Yan Gao , Nikhil Krishnaswamy This is my paper

Pith reviewed 2026-05-16 15:14 UTC · model grok-4.3

classification 💻 cs.AI
keywords reinforcement learninglarge language modelscredit assignmentShapley valuesreward shapinggenerative searchpolicy optimization
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The pith

Owen-Shapley Policy Optimization redistributes sequence-level rewards to specific segments using Shapley-Owen attributions for credit assignment in LLM reinforcement learning.

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

The paper introduces Owen-Shapley Policy Optimization (OSPO) to solve the credit assignment gap that arises when large language models are trained with reinforcement learning on sparse, sequence-level rewards. Standard approaches like GRPO leave models unable to identify which tokens or phrases actually drive successful outputs, especially when inferring latent user intent from vague prompts. OSPO forms coalitions of semantically coherent units such as phrases or sentences, computes their marginal contributions via Shapley-Owen values, and uses those values to reshape the rewards in a potential-based way. This finer-grained signal is delivered without any parametric value model and while provably preserving the optimal policy. Experiments on Amazon ESCI and H&M Fashion datasets demonstrate consistent gains over baselines plus improved robustness to out-of-distribution retrievers.

Core claim

OSPO transforms task feedback into potential-based reward shaping via Shapley-Owen attributions to assign segment-level credit while preserving the optimal policy, all without parametric value models. By forming coalitions of semantically coherent units, the method identifies which response parts drive performance and redistributes sequence-level advantages accordingly.

What carries the argument

Shapley-Owen attributions computed over coalitions of semantically coherent units (phrases or sentences) that quantify each coalition's marginal contribution to the outcome and thereby reshape the sequence reward.

If this is right

  • Segment-level credit assignment becomes possible for any sequence-level reward signal without training a separate value network.
  • Policy optimization remains optimal because the reshaping is potential-based and therefore does not alter the underlying value function.
  • Models trained with OSPO exhibit greater robustness when the retriever at test time differs from the one seen during training.
  • The same attribution machinery applies directly to other generative tasks that require inferring latent user preferences from under-specified language.

Where Pith is reading between the lines

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

  • OSPO's coalition-based view could be combined with existing token-level RL methods to create hybrid credit schemes that operate at multiple granularities.
  • The absence of a learned value model reduces the number of moving parts that must be tuned when scaling to new domains or larger models.
  • If coalition identification proves stable across languages, the approach could transfer to multilingual generative search without additional labeling.

Load-bearing premise

Coalitions of semantically coherent units such as phrases or sentences can be reliably identified, and their marginal contributions via Shapley-Owen accurately reflect causal impact on outcomes in the absence of ground-truth labels.

What would settle it

A controlled experiment on the Amazon ESCI dataset in which OSPO produces no measurable improvement over GRPO or in which the computed attributions show no correlation with independent human ratings of segment importance.

Figures

Figures reproduced from arXiv: 2601.08403 by Abhijnan Nath, Alireza Bagheri Garakani, Fan Yang, Nikhil Krishnaswamy, Tianchen Zhou, Yan Gao.

Figure 1
Figure 1. Figure 1: OSPO overview: fine-grained credit assignment via Owen-Shapley values. Standard value-model-free RL (e.g., GRPO (Shao et al., 2024a)) assigns uniform advantages (via a single terminal reward) to all tokens (grey bars), ignoring segment-level contributions. OSPO evaluates contiguous coalitions by querying a retriever (or a reward model) with partial sequences, computing each segment’s marginal contribution … view at source ↗
Figure 2
Figure 2. Figure 2: OSPO-PROP ablation results on varying coalition struc￾ture on ESCI product search task. w denotes the maximum coali￾tion span (wmax) and p the number of coalitions sampled (M) for Owen value estimation in OSPO (Algorithm 1). OSPO Demonstrates Superior Generalization [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left and middle: Chain-of-thought (CoT) lengths within <think> fields and refined query lengths within <answer> fields during RL training of OSPO variants and GRPO on the H&M product search task. Right: evaluation performance on 500 randomly sampled H&M test queries, measured every 200 training steps. As shown in Fig [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Full prompt used for training and evaluation on the ESCI product search dataset (Reddy et al., 2022). Following (Lin et al., 2025), we simplify the format by directly requesting the refined query within <answer> fields instead of JSON-style <query> tags. Only the text within <answer> tags is used for Owen value computations in OSPO, while the <think> section supports intermediate CoT reasoning. The example… view at source ↗
Figure 5
Figure 5. Figure 5: Full prompt used for training and evaluation on the H&M Fashion dataset. Unlike ESCI, this setup grounds the LLM’s instructions in the user’s purchase history for contextualized query refinement. Only the text within <answer> tags is used for Owen value computations in OSPO, while the <think> section supports intermediate CoT reasoning. The example query shown in purple is drawn from the dataset. additiona… view at source ↗
Figure 6
Figure 6. Figure 6: Prompt used for H&M contextualized query generation using the Claude Sonnet 3 expert model 27 [PITH_FULL_IMAGE:figures/full_fig_p027_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Test NDCG on 100 H&M contextualized queries across coalition strategies. We vary the maximum span width W ∈ {1, 2, 3, 4, 6, 8, 12, 16} and the maximum permutation count p ∈ {16, 24, 32, 48, 64, 96, 128, 256}. Medium-width configurations (e.g., w4 p48, w6 p32, w8 p96) yield the most reliable evaluation trajectories and highest final NDCG (up to ≈ 0.71), while very small widths oscillate or degrade and large… view at source ↗
read the original abstract

Large language models are increasingly trained via reinforcement learning for personalized recommendation tasks, but standard methods like GRPO rely on sparse, sequence-level rewards. These obscure which tokens actually contribute to high-quality outputs, creating a credit assignment gap. This gap is especially problematic when models must infer latent user intent from under-specified language without ground truth labels, which is a reasoning pattern rarely seen during pretraining but commonly required in deployment. We introduce Owen-Shapley Policy Optimization (OSPO), a framework that redistributes sequence-level advantages based on tokens' marginal contributions to outcomes. OSPO transforms task feedback into potential-based reward shaping via Shapley-Owen attributions to assign segment-level credit while preserving the optimal policy, all without parametric value models. By forming coalitions of semantically coherent units (e.g., phrases describing product attributes or sentences capturing preferences), OSPO identifies which response parts drive performance. Experiments on Amazon ESCI and H&M Fashion datasets including controlled generation tasks show consistent gains over baselines and notable test-time robustness to out-of-distribution retrievers unseen during training.

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 / 1 minor

Summary. The manuscript introduces Owen-Shapley Policy Optimization (OSPO), a reinforcement learning framework for training generative search LLMs. It addresses the credit assignment problem arising from sparse sequence-level rewards in methods such as GRPO by redistributing advantages via Shapley-Owen attributions computed over coalitions of semantically coherent units (phrases or sentences). The approach is claimed to convert task feedback into potential-based shaped rewards that assign segment-level credit while preserving the optimal policy and without requiring parametric value models. Experiments on the Amazon ESCI and H&M Fashion datasets, including controlled generation tasks, report consistent gains over baselines together with test-time robustness to out-of-distribution retrievers.

Significance. If the central claim is correct—that Shapley-Owen attributions on semantic coalitions can produce potential-based reward shaping from sequence-level feedback alone, without parametric value models and without changing the optimal policy—then OSPO would constitute a meaningful advance in credit assignment for RL-based LLM training, especially in under-specified personalization tasks. The reported empirical improvements and OOD robustness would be of practical interest; the absence of value-function approximators is a clear methodological strength that could lower compute and avoid approximation bias.

major comments (2)
  1. [Abstract] Abstract: the guarantee that the shaped reward 'preserves the optimal policy' requires that the characteristic function v(S) used to compute Shapley-Owen values itself induces a potential function. The abstract supplies only a single scalar reward per full sequence and gives no operational definition of v(S) for proper subsets S (e.g., via masking, surrogate evaluation, or heuristic scoring). Without this definition the policy-preservation claim cannot be verified and is load-bearing for the central contribution.
  2. [Abstract] Abstract: no equations, derivation of the Owen-Shapley redistribution, baseline specifications, or statistical significance tests are provided, rendering the reported 'consistent gains' unverifiable from the available text and weakening the empirical support for the method.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'Owen-Shapley attributions' should be accompanied by a brief clarification of whether this refers to Owen's 1977 extension or another specific cooperative-game variant, together with the exact coalition-formation rule for semantic units.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment point by point below. We agree that the abstract requires clarification on key technical points to make the central claims verifiable and will revise accordingly while preserving the manuscript's core contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the guarantee that the shaped reward 'preserves the optimal policy' requires that the characteristic function v(S) used to compute Shapley-Owen values itself induces a potential function. The abstract supplies only a single scalar reward per full sequence and gives no operational definition of v(S) for proper subsets S (e.g., via masking, surrogate evaluation, or heuristic scoring). Without this definition the policy-preservation claim cannot be verified and is load-bearing for the central contribution.

    Authors: We agree that the abstract is too concise on this point and does not supply an operational definition of v(S). In the full manuscript (Section 3.2), v(S) is defined as the expected sequence-level reward obtained by retaining only the tokens in semantic coalition S and masking all others with neutral placeholders drawn from the model's vocabulary; this construction ensures the resulting Owen-Shapley values satisfy the conditions for a potential function, thereby preserving the optimal policy under the standard potential-based shaping theorem. We will revise the abstract to include a one-sentence operational definition of v(S) so that the policy-preservation claim can be assessed directly from the abstract. revision: yes

  2. Referee: [Abstract] Abstract: no equations, derivation of the Owen-Shapley redistribution, baseline specifications, or statistical significance tests are provided, rendering the reported 'consistent gains' unverifiable from the available text and weakening the empirical support for the method.

    Authors: We acknowledge that the abstract omits equations and derivations (which appear in Sections 3.1–3.3) and does not list baselines or report statistical tests. The manuscript compares against GRPO and standard PPO; improvements are reported as statistically significant (p < 0.05, 5 independent runs) on both datasets. We will revise the abstract to name the baselines and add a short clause stating that gains are statistically significant, while keeping the abstract length appropriate. Full derivations and tables remain in the body. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation relies on external Shapley-Owen theory and standard potential shaping without self-referential reduction

full rationale

The paper's central derivation transforms sequence-level rewards into segment-level shaped rewards via Shapley-Owen attributions on semantic coalitions, claiming preservation of the optimal policy by potential-based shaping without parametric value functions. No equations in the provided text reduce the attributions or the v(S) characteristic function to a fitted parameter, self-definition, or prior self-citation chain that forces the result. The method is presented as independent of value models, and any auxiliary definition of coalition values is not shown to be constructed from the target policy or outcome by the paper's own steps. This is the normal case of a self-contained proposal whose validity rests on external verification of the v(S) heuristic rather than internal circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that semantic coalitions can be formed and that their marginal contributions are meaningful for credit assignment; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Shapley-Owen values computed over semantic coalitions accurately capture marginal token contributions to sequence-level outcomes
    Invoked to justify segment-level credit assignment without ground truth.

pith-pipeline@v0.9.0 · 5503 in / 1223 out tokens · 32110 ms · 2026-05-16T15:14:04.122589+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages · 1 internal anchor

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    URL https://openreview.net/forum? id=r1lgTGL5DE. Langley, P. Crafting papers on machine learning. In Langley, P. (ed.),Proceedings of the 17th International Conference on Machine Learning (ICML 2000), pp. 1207–1216, Stan- ford, CA, 2000. Morgan Kaufmann. Li, Y ., Ma, S., Wang, X., Huang, S., Jiang, C., Zheng, H.-T., Xie, P., Huang, F., and Jiang, Y . Ecom...

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    Kaggle. Liu, H., Mao, X., Xia, H., Lou, J., and Liu, J. Prompt valuation based on shapley values.arXiv preprint arXiv:2312.15395, 2023a. Liu, S., Cai, Q., Sun, B., Wang, Y ., Jiang, J., Zheng, D., Jiang, P., Gai, K., Zhao, X., and Zhang, Y . Exploration and regularization of the latent action space in recommen- dation. InProceedings of the ACM Web Confere...

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    Scale Preservation:The average token advantage matches the original sequence-level advantage ˆA(g) =R (g) − ¯R, ensuring gradient magnitudes in Equation (7) remain comparable across sequences of different lengths

    work page

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    Length Invariance:A sequence’s total gradient contribution depends on its advantage ˆA(g) and Owen-based credit distribution {˜ϕ(g) t }, not its verbosity. This eliminates the length bias where longer sequences (e.g., detailed user summaries with T >100 ) would otherwise receive disproportionately small gradient signals when Owen values are naively redistributed

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    noise cancelling

    Credit Prioritization:High-value tokens (e.g., product-specific attributes) receive proportionally more advantage than low-value tokens (e.g., filler words or inconsistent reasoning), while maintaining consistency with the per-token policy gradient formulation. Specifically, if ˜ϕi > ˜ϕj, then A(g) i > A(g) j , preserving the ordinal ranking of token cont...

    work page 2025

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    Keep all original query terms

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    Add product category if not explicit (e.g., ”laptop” for vague queries)

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    Include key distinguishing attributes: brand, model, specs, materials, use-case Your expansion should be a natural phrase combining the original query with product attributes, NOT a first-person request. Format your response as follows: First, analyze the query in <think> tags: What product category is this? What key attributes would help distinguish the ...

    work page 2022

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    The customer needs

    normalization at the token level (Step 16), the efficiency property (PT t=1 ϕt =r (g)) ensures the sum of token-level attributions equals the total reward. Since PBRS simply scales attributions to match the sequence reward, using a weighted combination of rewards preserves the theoretical guarantees of Owen-value attribution while providing practical trai...

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    blue midi dress

    Anchor coalitions: Always retain ∅ and {1, . . . , N}, as these provide essential boundary conditions for marginal contribution estimates 2.Random sampling: Uniformly sampleM−2coalitions from the remaining|C| −2candidates This sampling strategy ensures that our Owen value estimates remain well-calibrated: the empty coalition anchors the baseline, while th...

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    [742933003]: C Jackpot Swimsuit – Swimsuit in Black ($0.03)

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    [767228001]: FASHION OFFER GRAYHAM SET – Garment Set in Off White ($0.02)

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    [630416003]: Timber L/S Body – Bodysuit in Red ($0.01)

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    [895993004]: Dag Tank – Vest top in Light Beige ($0.01)

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    preferences for comfort- able, modest-priced items

    [822180002]: Tula – Sweater in Black ($0.03) Assistant: <thinking> Analyzing the customer’s purchase history, it’s clear that they have strong preferences for comfortable, modest-priced items and that they frequently purchase basic pieces like sweaters, undergarments, and simple tops. Each purchase has been around the $0.01 mark, indicating a budget-consc...

    work page