# Cost-Aware Retrieval-Augmentation Reasoning Models with Adaptive Retrieval Depth

arXiv: https://arxiv.org/abs/2510.15719 · HTML: https://mlsanity.com/paper/2510.15719/

## Key facts

- Cited by 2 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 20 of its 44 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)
- Retrieval-augmented generation / [Agentic RAG, agents and memory](https://mlsanity.com/rag/agentic-rag-agents-and-memory/)

## Builds on (most cited first, 20 of 20)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Interleaving Retrieval with Chain-of-Thought Reasoning for Knowledge-Intensive Multi-Step Questions](https://mlsanity.com/paper/2212.10509/) (2022)
- [Search-o1: Agentic Search-Enhanced Large Reasoning Models](https://mlsanity.com/paper/2501.05366/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [ReSearch: Learning to Reason with Search for LLMs via Reinforcement Learning](https://mlsanity.com/paper/2503.19470/) (2025)
- [SimpleTIR: End-to-End Reinforcement Learning for Multi-Turn Tool-Integrated Reasoning](https://mlsanity.com/paper/2509.02479/) (2025)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [Inference Scaling for Long-Context Retrieval Augmented Generation](https://mlsanity.com/paper/2410.04343/) (2024)
- [Supervising the search process produces reliable and generalizable information-seeking agents](https://mlsanity.com/paper/2502.13957/) (2025)
- [Contextual Compression in Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2409.13385/) (2024)

## Built on by (most cited first, 2 of 2)

- [AdaTIR: Adaptive Tool-Integrated Reasoning via Difficulty-Aware Policy Optimization](https://mlsanity.com/paper/2601.14696/) (2026)
- [Rethinking the Necessity of Adaptive Retrieval-Augmented Generation through the Lens of Adaptive Listwise Ranking](https://mlsanity.com/paper/2604.15621/) (2026)

## Abstract (arXiv)

Reasoning models have gained significant attention due to their strong performance, particularly when enhanced with retrieval augmentation. However, these models often incur high computational costs, as both retrieval and reasoning tokens contribute substantially to the overall resource usage. In this work, we make the following contributions: (1) we propose a retrieval-augmented reasoning model that dynamically adjusts the length of the retrieved document list based on the query and retrieval results; (2) we develop a cost-aware advantage function for training of efficient retrieval-augmented reasoning models through reinforcement learning; and (3) we explore both memory- and latency-bound implementations of the proposed cost-aware framework for both proximal and group relative policy optimization algorithms. We evaluate our approach on seven public question answering datasets and demonstrate significant efficiency gains, without compromising effectiveness. In fact, we observed that the model latency decreases by ~16-20% across datasets, while its effectiveness increases by ~5% on average, in terms of exact match.