IG-Search: Step-Level Information Gain Rewards for Search-Augmented Reasoning

Reinforcement learning has emerged as an effective paradigm for training large language models to perform search-augmented reasoning. However, existing approaches rely on trajectory-level rewards that cannot distinguish precise search queries from vague or redundant ones within a rollout group, and collapse to a near-zero gradient signal whenever every sampled trajectory fails. In this paper, we propose IG-Search, a reinforcement learning framework that introduces a step-level reward based on Information Gain (IG). For each search step, IG measures how much the retrieved documents improve the model's confidence in the gold answer relative to a counterfactual baseline of random documents, thereby reflecting the effectiveness of the underlying search query. This signal is fed back to the corresponding search-query tokens via per-token advantage modulation in GRPO, enabling fine-grained, step-level credit assignment within a rollout. Unlike prior step-level methods that require either externally annotated intermediate supervision or shared environment states across trajectories, IG-Search derives its signals from the policy's own generation probabilities, requiring no intermediate annotations beyond standard question-answer pairs. Experiments on seven single-hop and multi-hop QA benchmarks demonstrate that IG-Search achieves an average EM of 0.430 with Qwen2.5-3B, outperforming the strongest trajectory-level baseline (MR-Search) by 1.6 points and the step-level method GiGPO by 0.9 points on average across benchmarks, with particularly pronounced gains on multi-hop reasoning tasks. Despite introducing a dense step-level signal, IG-Search adds only ~6.4% to per-step training wall-clock time over the trajectory-level baseline and leaves inference latency unchanged, while still providing a meaningful gradient signal even when every sampled trajectory answers incorrectly.