# Optimizing Agentic Reasoning with Retrieval via Synthetic Semantic Information Gain Reward

arXiv: https://arxiv.org/abs/2602.00845 · HTML: https://mlsanity.com/paper/2602.00845/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)
- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 9 of 9)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Search-o1: Agentic Search-Enhanced Large Reasoning Models](https://mlsanity.com/paper/2501.05366/) (2025)
- [Towards Agentic RAG with Deep Reasoning: A Survey of RAG-Reasoning Systems in LLMs](https://mlsanity.com/paper/2507.09477/) (2025)
- [Search and Refine During Think: Facilitating Knowledge Refinement for Improved Retrieval-Augmented Reasoning](https://mlsanity.com/paper/2505.11277/) (2025)
- [Supervising the search process produces reliable and generalizable information-seeking agents](https://mlsanity.com/paper/2502.13957/) (2025)
- [RAG-R1: Incentivizing the Search and Reasoning Capabilities of LLMs through Multi-query Parallelism](https://mlsanity.com/paper/2507.02962/) (2025)
- [Credible Plan-Driven RAG Method for Multi-Hop Question Answering](https://mlsanity.com/paper/2504.16787/) (2025)

## Built on by (most cited first, 6 of 6)

- [Inference-Time Budget Control for LLM Search Agents](https://mlsanity.com/paper/2605.05701/) (2026)
- [OASES: Outcome-Aligned Search-Evaluation Co-Training for Agentic Search](https://mlsanity.com/paper/2604.03675/) (2026)
- [LOTAPO: Leave-One-Turn Attribution for Self-Generated Process Rewards in Multi-Turn Search Reasoning](https://mlsanity.com/paper/2607.13501/) (2026)
- [Self-Induced Outcome Potential: Turn-Level Credit Assignment for Agents without Verifiers](https://mlsanity.com/paper/2605.04984/) (2026)
- [Unified Context Evolution for LLM Agents](https://mlsanity.com/paper/2606.02304/) (2026)
- [Beyond Dyadic Memory: Interaction-Aware Multimodal Memory with Adaptive Agentic Retrieval for Multi-Party Spoken Conversations](https://mlsanity.com/paper/2609.32522/) (2026)

## Abstract (arXiv)

Agentic reasoning enables large reasoning models (LRMs) to dynamically acquire external knowledge, but yet optimizing the retrieval process remains challenging due to the lack of dense, principled reward signals. In this paper, we introduce InfoReasoner, a unified framework that incentivizes effective information seeking via a synthetic semantic information gain reward. Theoretically, we redefine information gain as uncertainty reduction over the model's belief states, establishing guarantees, including non-negativity, telescoping additivity, and channel monotonicity. Practically, to enable scalable optimization without manual retrieval annotations, we propose an output-aware intrinsic estimator that computes information gain directly from the model's output distributions using semantic clustering via bidirectional textual entailment. This intrinsic reward guides the policy to maximize epistemic progress, enabling efficient training via Group Relative Policy Optimization (GRPO). Experiments across seven question-answering benchmarks demonstrate that InfoReasoner consistently outperforms strong retrieval-augmented baselines, achieving up to 5.4% average accuracy improvement. Our work provides a theoretically grounded and scalable path toward agentic reasoning with retrieval. The code is available at https://github.com/dl-m9/InfoReasoner