Organizations: Beijing University of Posts and Telecommunications · Li Auto Inc.
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.
Group-based reinforcement learning (RL) methods have achieved remarkable success in improving the performance of large language models (LLMs) and have been rapidly extended to agentic tasks. However, their credit assignment relies heavily on coarse-grained trajectory-level attribution according to final outcomes, making it difficult to capture the contribution of individual steps, such as valuable steps obscured within failed trajectories. To uncover latent information and enable more faithful step-level credit assignment, we propose Graph-based Group Policy Optimization (GraphGPO), which first aggregates all rollout trajectories into a unified state-transition graph and then estimates the distance from each state to the task goal using the global information encoded in the graph. Finally, GraphGPO assigns credit to each edge by estimating a graph-based advantage, based on how much the transition reduces the distance to the task goal. In this way, GraphGPO significantly improves training efficiency and achieves state-of-the-art performance across a range of challenging benchmarks.
Multi-step search is a fundamental capability for search agents, enabling them to iteratively acquire, refine, and integrate external evidence for complex reasoning QA. However, vanilla GRPO allocates rewards exclusively based on the model's final outputs, yielding outcome-only supervision with no supervisory signals for intermediate reasoning steps. Such sparse supervision easily causes training instability and redundant search behaviors on multi-step search tasks. To mitigate this limitation, we adopt process reward to deliver stepwise supervision signals. For this process reward, we propose two complementary criteria to judge each search step: whether the step yields new evidence to facilitate problem solving, and whether it forms an efficient, pivotal intermediate decision within the overall reasoning trajectory. Building on this insight, we propose BiCAA: a bidirectional credit assignment framework that delivers dense, distinguishing process rewards for search-augmented agents. BiCAA builds bidirectional process rewards by fusing two complementary signals: forward solvability gain and hindsight success criticality. The former quantifies step-wise improvements in answer plausibility, while the latter evaluates each step's necessity for final success via hindsight outcome-based criticality scoring. We modulate and aggregate the two signals and then fuse them with the outcome reward. Experiments on search-augmented QA benchmarks show that BiCAA stabilizes policy optimization, reduces redundant search behavior, and achieves competitive performance.
Deep search agents operate over trajectories spanning dozens of steps, yet standard reinforcement learning provides only a single outcome reward per trajectory, which is far too sparse for effective credit assignment. On-policy self-distillation (OPSD) addresses this by using the model's own logits as dense token-level teachers, but extending it to search agents introduces a fundamental tension: the teacher, having access to privileged information such as the correct answer, produces a distribution that differs systematically from the student's exploration-based reasoning, and naive distillation causes the student to inherit this information asymmetry rather than learn better search strategies. We resolve this tension through two contributions. First, we construct Evidence Anchors, which are concise, step-level evidence snippets extracted from the web, as privileged information that captures key reasoning steps without revealing the entire answer path. Second, we propose Step-Level Self-Distilled Policy Optimization (SSPO), which converts teacher-student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories. This design decouples what to update from how much to update: the outcome reward determines the direction of policy change, while the teacher modulates its magnitude at each step. Correct trajectories are left untouched, preserving their diversity. On Qwen3-8B, SSPO consistently outperforms GRPO across BrowseComp, GAIA, and FRAMES, surpassing or matching GRPO trained with twice as many gradient steps while adding only about 5 percent overhead per step from a single additional forward pass.