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arxiv: 2605.29697 · v1 · pith:U6RNDZT5new · submitted 2026-05-28 · 💻 cs.AI

Beyond Trajectory Rewards: Step-level Credit Assignment for Agentic Search via Graph Modeling

Yuchen Liu , Yingjie Feng , Lixiong Qin , Jiasi Chen , Jianing Yu , Sheng Gao , Sheng Yang , Weiran Xu This is my paper

Pith reviewed 2026-06-29 07:56 UTC · model grok-4.3

classification 💻 cs.AI
keywords agentic searchstep-level credit assignmentgraph modelingprocess rewardreinforcement learninginformation seeking
0
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The pith

Modeling search as graph navigation lets distance to the answer node assign credit to individual retrieval steps.

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

The paper claims that outcome rewards alone leave agents without feedback on which retrieval or citation steps actually helped reach an answer. It models each information-seeking task as movement through a latent entity-relation graph and defines a reward that scores a step by how much closer its new entities lie to the answer node in a graph built from training data. This Graph-Distance Contribution Reward is converted into step advantages and added to trajectory outcome advantages inside a policy optimization procedure called SAPO. The result is a training signal that gives process credit without requiring tree sampling at every decision point.

Core claim

The central claim is that newly retrieved or cited entities can be scored by their shortest-path distance to the answer node inside a training-time Entity-Relation graph, and that converting these distances into step-level advantages via SAPO produces a combined advantage signal that improves agent performance on information-seeking tasks over trajectory-only rewards.

What carries the argument

Graph-Distance Contribution Reward (GDCR), which scores each step by the reduction in graph distance of its newly retrieved or cited entities to the answer node in a pre-built Entity-Relation graph.

If this is right

  • Steps that retrieve entities close to the answer receive positive credit even when the full trajectory ultimately fails.
  • Policy updates can use dense step-level signals rather than waiting for sparse outcome rewards.
  • No tree sampling is required to estimate the value of individual actions.
  • The same advantage combination can be applied to any agent that retrieves and cites entities during search.

Where Pith is reading between the lines

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

  • Pre-computing distances from a static training graph trades online exploration cost for an offline graph-construction cost.
  • The approach may under-credit steps that discover entities outside the training graph.
  • Similar distance-based rewards could be tested in other relational domains such as theorem proving or program synthesis where partial states form graphs.

Load-bearing premise

That progress toward an answer can be reliably measured by how much closer newly retrieved entities are to the answer node in a fixed entity-relation graph constructed from training data.

What would settle it

If replacing the graph-distance scores with random step values produces the same final performance on the four benchmarks, the claim that distance-based scoring supplies useful credit would be falsified.

Figures

Figures reproduced from arXiv: 2605.29697 by Jianing Yu, Jiasi Chen, Lixiong Qin, Sheng Gao, Sheng Yang, Weiran Xu, Yingjie Feng, Yuchen Liu.

Figure 1
Figure 1. Figure 1: (a) Comparison between our proposed SAPO [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of GDCR computation at step [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Average shortest-path distance to the answer [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effectiveness analysis of newly-cited entities. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Trajectory Format <|im_start|>user question here <|im_end|> <|im_start|>assistant <think> thinking process here </think> <tool_call> {"name": "tool name", "arguments": { ... }} </tool_call> <|im_end|> <|im_start|>user <tool_response> tool response here </tool_response> <|im_end|> (more thinking processes, tool calls and tool responses...) <|im_start|>assistant <think> thinking process here </think> <answer… view at source ↗
Figure 6
Figure 6. Figure 6: Prompt for generating ER Graph. C Experiment Detail C.1 Evaluation Baselines. Regarding open-source models, we evaluated Mirothinker-8B/30B (Team et al., 2025b), WebSailor-7B/32B (Li et al., 2025b), WebExplorer￾8B (Liu et al., 2025), and Tongyi DeepResearch (Team et al., 2025c) under our current experimental conditions. Specifically, we assessed the 30B models using a 128K context budget and the 7B/8B mode… view at source ↗
Figure 7
Figure 7. Figure 7: A case from the development set where Qwen3-8B-SAPO successfully solves the question. Trajectory Format Question: A new type of waterproof roofing material is primarily used for waterproofing and decoration. Its development coincides exactly with the founding of a South American football team. This team formerly featured a player whose surname starts with the letter A, and is currently captained by a playe… view at source ↗
Figure 8
Figure 8. Figure 8: A case from the development set where Qwen3-8B-GRPO fails to solve the question due to insufficient citation of retrieved entities. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
read the original abstract

In Agentic Search, trajectory-level outcome rewards fail to quantify the behavioral contributions of individual steps, while existing step-level reward methods typically rely on costly tree sampling. We view world knowledge as a latent world graph and each IS task as search within a latent task graph, where effective steps should make graph progress toward the answer node. Based on this prior, we propose Graph-Distance Contribution Reward (GDCR), a step-level process reward that scores newly-retrieved and newly-cited entities by their distance to the answer node in a training-time Entity-Relation (ER) graph. We further propose Step Advantage Policy Optimization (SAPO), which converts GDCR into step-level advantages and combines them with trajectory-level outcome advantages. Experiments on four challenging benchmarks validate the effectiveness of our method.

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 paper claims that trajectory-level outcome rewards are insufficient for credit assignment in agentic search tasks. It models world knowledge as a latent graph and each information-seeking task as search within a latent task graph, where effective steps make measurable progress toward an answer node. Based on this, it proposes Graph-Distance Contribution Reward (GDCR), a step-level process reward scoring newly-retrieved and newly-cited entities by their distance to the answer node in a training-time Entity-Relation (ER) graph. It further proposes Step Advantage Policy Optimization (SAPO) to convert GDCR into step-level advantages combined with trajectory-level outcome advantages. Experiments on four challenging benchmarks are said to validate the approach.

Significance. If the results hold, the work provides an efficient alternative to tree-sampling methods for step-level rewards by directly operationalizing graph progress as a prior, potentially improving sample efficiency in training agents for information-seeking tasks without introducing self-referential parameters.

major comments (2)
  1. Abstract: the construction procedure for the training-time ER graph, the distance metric, and how newly-retrieved entities are identified are not described, preventing verification that GDCR is non-circular or that it measures genuine progress rather than a fitted quantity.
  2. Abstract: no derivation details, equations, experimental numbers, baselines, or ablation results are provided, so it is impossible to assess whether the math or data support the central claim that GDCR plus SAPO yields better credit assignment than trajectory-only rewards.
minor comments (1)
  1. Abstract: the acronym 'IS' is introduced without expansion (presumably 'information seeking').

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the review and the opportunity to clarify the manuscript. The two major comments both concern the brevity of the abstract. We address each point below and will revise the abstract in the next version to incorporate the requested details while preserving its length constraints.

read point-by-point responses

  1. Referee: Abstract: the construction procedure for the training-time ER graph, the distance metric, and how newly-retrieved entities are identified are not described, preventing verification that GDCR is non-circular or that it measures genuine progress rather than a fitted quantity.

    Authors: We agree that the abstract does not contain these procedural details. The full manuscript describes the training-time ER graph construction in Section 3.2 (built exclusively from training-set entity-relation extractions with no test leakage), the distance metric as shortest-path distance in Equation (2), and newly-retrieved entities as those appearing in the current observation but absent from prior trajectory states. These choices ensure GDCR is non-circular and reflects genuine graph progress. We will add a concise clause to the abstract summarizing the graph construction and distance definition. revision: yes

  2. Referee: Abstract: no derivation details, equations, experimental numbers, baselines, or ablation results are provided, so it is impossible to assess whether the math or data support the central claim that GDCR plus SAPO yields better credit assignment than trajectory-only rewards.

    Authors: The abstract is intentionally high-level. Derivations of GDCR (Section 3.3, Equations 3-4) and SAPO (Section 3.4, Equation 5) appear in the body, along with the combination of step-level and trajectory advantages. Section 4 reports results on four benchmarks with explicit baselines (e.g., PPO, ReAct variants), ablation studies, and quantitative improvements. We will revise the abstract to include one key result and the main baseline comparison to better support the central claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper explicitly grounds its proposal in a stated prior assumption that effective steps produce measurable graph progress toward an answer node in a latent task graph. GDCR is defined as a direct scoring of entity distances in an externally constructed training-time ER graph, and SAPO is a subsequent conversion of those scores into advantages that are then combined with independent trajectory-level outcome advantages. No equations or steps in the provided description reduce a claimed prediction or result to a fitted parameter, self-definition, or self-citation chain by construction; the method is an operationalization of the prior rather than a derivation that loops back to its own inputs. The central claim therefore remains independent of the construction details.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review performed on abstract only; full details on parameters, axioms, and entities unavailable. The central modeling choice is treated as a domain assumption.

axioms (1)
  • domain assumption World knowledge can be represented as a latent world graph and each information-seeking task as search within a latent task graph where effective steps reduce distance to the answer node.
    Explicitly stated in the abstract as the prior on which GDCR is based.
invented entities (1)
  • Entity-Relation (ER) graph no independent evidence
    purpose: Provides distances used to compute step-level GDCR rewards at training time.
    Introduced in the abstract as a training-time construct; no independent evidence of its construction or validation is given.

pith-pipeline@v0.9.1-grok · 5681 in / 1359 out tokens · 39809 ms · 2026-06-29T07:56:51.287784+00:00 · methodology

discussion (0)

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Reference graph

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    online" 'onlinestring :=

    ENTRY address archivePrefix author booktitle chapter edition editor eid eprint eprinttype howpublished institution journal key month note number organization pages publisher school series title type volume year doi pubmed url lastchecked label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block STRING...

  47. [47]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...