# SQL-ASTRA: Alleviating Sparse Feedback in Agentic SQL via Column-Set Matching and Trajectory Aggregation

arXiv: https://arxiv.org/abs/2603.16161 · HTML: https://mlsanity.com/paper/2603.16161/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 37 of its 52 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 30 of 37)

- [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)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Can LLM Already Serve as A Database Interface? A BIg Bench for Large-Scale Database Grounded Text-to-SQLs](https://mlsanity.com/paper/2305.03111/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Fine-Grained Human Feedback Gives Better Rewards for Language Model Training](https://mlsanity.com/paper/2306.01693/) (2023)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [WebAgent-R1: Training Web Agents via End-to-End Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2505.16421/) (2025)
- [OmniSQL: Synthesizing High-quality Text-to-SQL Data at Scale](https://mlsanity.com/paper/2503.02240/) (2025)
- [SQL-R1: Training Natural Language to SQL Reasoning Model By Reinforcement Learning](https://mlsanity.com/paper/2504.08600/) (2025)
- [ACT-SQL: In-Context Learning for Text-to-SQL with Automatically-Generated Chain-of-Thought](https://mlsanity.com/paper/2310.17342/) (2023)
- [Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers](https://mlsanity.com/paper/2510.00915/) (2025)
- [Arctic-Text2SQL-R1: Simple Rewards, Strong Reasoning in Text-to-SQL](https://mlsanity.com/paper/2505.20315/) (2025)
- [MedEyes: Learning Dynamic Visual Focus for Medical Progressive Diagnosis](https://mlsanity.com/paper/2511.22018/) (2025)
- [Look Inward to Explore Outward: Learning Temperature Policy from LLM Internal States via Hierarchical RL](https://mlsanity.com/paper/2602.13035/) (2026)
- [EvoTool: Self-Evolving Tool-Use Policy Optimization in LLM Agents via Blame-Aware Mutation and Diversity-Aware Selection](https://mlsanity.com/paper/2603.04900/) (2026)
- [Bottom-up Policy Optimization: Your Language Model Policy Secretly Contains Internal Policies](https://mlsanity.com/paper/2512.19673/) (2025)
- [BIRD-INTERACT: Re-imagining Text-to-SQL Evaluation for Large Language Models via Lens of Dynamic Interactions](https://mlsanity.com/paper/2510.05318/) (2025)
- [ToolTree: Efficient LLM Agent Tool Planning via Dual-Feedback Monte Carlo Tree Search and Bidirectional Pruning](https://mlsanity.com/paper/2603.12740/) (2026)
- [Reasoning-Table: Exploring Reinforcement Learning for Table Reasoning](https://mlsanity.com/paper/2506.01710/) (2025)
- [STaR-SQL: Self-Taught Reasoner for Text-to-SQL](https://mlsanity.com/paper/2502.13550/) (2025)
- [CoE-SQL: In-Context Learning for Multi-Turn Text-to-SQL with Chain-of-Editions](https://mlsanity.com/paper/2405.02712/) (2024)
- [Evaluating the Data Model Robustness of Text-to-SQL Systems Based on Real User Queries](https://mlsanity.com/paper/2402.08349/) (2024)
- [Lyapunov Functions for First-Order Methods: Tight Automated Convergence Guarantees](https://mlsanity.com/paper/1803.06073/) (2018)
- [How Do Humans Write Code? Large Models Do It the Same Way Too](https://mlsanity.com/paper/2402.15729/) (2024)
- [FLEX: Expert-level False-Less EXecution Metric for Reliable Text-to-SQL Benchmark](https://mlsanity.com/paper/2409.19014/) (2024)
- [TIC-GRPO: Provable and Efficient Optimization for Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2508.02833/) (2025)

## Built on by (most cited first, 3 of 3)

- [SPPO: Sequence-Level PPO for Long-Horizon Reasoning Tasks](https://mlsanity.com/paper/2604.08865/) (2026)
- [Recursive Self-Evolving Agents via Held-Out Selection](https://mlsanity.com/paper/2606.28374/) (2026)
- [SERL-SQL: Selective Hindsight Distillation for Text-to-SQL Reinforcement Agentic Learning](https://mlsanity.com/paper/2608.00485/) (2026)

## Abstract (arXiv)

Agentic Reinforcement Learning (RL) shows promise for complex tasks, but Text-to-SQL remains mostly restricted to single-turn paradigms. A primary bottleneck is the credit assignment problem. In traditional paradigms, rewards are determined solely by the final-turn feedback, which ignores the intermediate process and leads to ambiguous credit evaluation. To address this, we propose Agentic SQL, a framework featuring a universal two-tiered reward mechanism designed to provide effective trajectory-level evaluation and dense step-level signals. First, we introduce Aggregated Trajectory Reward (ATR) to resolve multi-turn credit assignment. Using an asymmetric transition matrix, ATR aggregates process-oriented scores to incentivize continuous improvement. Leveraging Lyapunov stability theory, we prove ATR acts as an energy dissipation operator, guaranteeing a cycle-free policy and monotonic convergence. Second, Column-Set Matching Reward (CSMR) provides immediate step-level rewards to mitigate sparsity. By executing queries at each turn, CSMR converts binary (0/1) feedback into dense [0, 1] signals based on partial correctness. Evaluations on BIRD show a 5% gain over binary-reward GRPO. Notably, our approach outperforms SOTA Arctic-Text2SQL-R1-7B on BIRD and Spider 2.0 using identical models, propelling Text-to-SQL toward a robust multi-turn agent paradigm.