# Learning to Retrieve via Reinforcement Learning in Embedding Space

arXiv: https://arxiv.org/abs/2610.07731 · HTML: https://mlsanity.com/paper/2610.07731/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 55 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

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

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs](https://mlsanity.com/paper/2402.14740/) (2024)
- [ReasonIR: Training Retrievers for Reasoning Tasks](https://mlsanity.com/paper/2504.20595/) (2025)
- [Rank-R1: Enhancing Reasoning in LLM-based Document Rerankers via Reinforcement Learning](https://mlsanity.com/paper/2503.06034/) (2025)
- [ReasonRank: Empowering Passage Ranking with Strong Reasoning Ability](https://mlsanity.com/paper/2508.07050/) (2025)
- [NeuralNDCG: Direct Optimisation of a Ranking Metric via Differentiable Relaxation of Sorting](https://mlsanity.com/paper/2102.07831/) (2021)
- [DIVER: A Multi-Stage Approach for Reasoning-intensive Information Retrieval](https://mlsanity.com/paper/2508.07995/) (2025)
- [Embed-RL: Reinforcement Learning for Reasoning-Driven Multimodal Embeddings](https://mlsanity.com/paper/2602.13823/) (2026)
- [Learning To Retrieve: How to Train a Dense Retrieval Model Effectively and Efficiently](https://mlsanity.com/paper/2010.10469/) (2020)
- [Variance Reduction in Gradient Exploration for Online Learning to Rank](https://mlsanity.com/paper/1906.03766/) (2019)
- [Product-form estimators: exploiting independence to scale up Monte Carlo](https://mlsanity.com/paper/2102.11575/) (2021)
- [E2Rank: Unifying Text Embedding and Listwise Reranking for Effective and Efficient Search](https://mlsanity.com/paper/2510.22733/) (2025)
- [Retrieval-GRPO: A Multi-Objective Reinforcement Learning Framework for Dense Retrieval in Taobao Search](https://mlsanity.com/paper/2511.13885/) (2025)
- [Reinforcement Fine-Tuning for History-Aware Dense Retriever in RAG](https://mlsanity.com/paper/2602.03645/) (2026)

## Abstract (arXiv)

Dense retrieval models are typically trained with contrastive objectives that learn effective representations but do not directly optimize retrieval metrics or downstream task performance. To address this problem, we introduce RELER (REinforcement LEarning for Retrieval), a reinforcement learning framework that enables existing embedding models to learn to retrieve directly in embedding space and align to task-specific rewards. We train RELER by sampling unit-length query and document embedding actions from von Mises-Fisher (vMF) distributions centered on normalized encoder outputs, scoring the resulting retrieval or downstream outcomes as rewards, and updating the encoder with REINFORCE using a leave-one-out baseline (RLOO). As exploration in the high-dimensional embedding space is prone to sampling noise, we further propose conditional-mean projection (CMP), which projects each sampled embedding onto the low-dimensional subspace spanned by its encoder output and the candidate embeddings it is compared against, reducing noise in the policy gradient while preserving its expectation. We evaluate RELER on BRIGHT, a benchmark with reasoning-intensive queries that remain challenging for existing embedding models. RELER consistently outperforms InfoNCE and LambdaLoss in average nDCG@10 when post-training BGE-M3 and Qwen3-Embedding backbones. We further evaluate downstream utility through retrieval-augmented generation (RAG), where we adapt only the query encoder while keeping the document index and generator fixed. Across seven QA datasets, jointly optimizing retrieval and answer rewards improves both average retrieval performance and answer quality in RAG.