# Critical-State RL: Diagnosing Trainable States for Multi-Turn Tool Use

arXiv: https://arxiv.org/abs/2609.24985 · HTML: https://mlsanity.com/paper/2609.24985/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 50 references that are in the map.
- First posted on arXiv 21 Sep 2026.

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

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
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- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [ArCHer: Training Language Model Agents via Hierarchical Multi-Turn RL](https://mlsanity.com/paper/2402.19446/) (2024)
- [APIGen: Automated Pipeline for Generating Verifiable and Diverse Function-Calling Datasets](https://mlsanity.com/paper/2406.18518/) (2024)
- [RUDDER: Return Decomposition for Delayed Rewards](https://mlsanity.com/paper/1806.07857/) (2018)
- [SWEET-RL: Training Multi-Turn LLM Agents on Collaborative Reasoning Tasks](https://mlsanity.com/paper/2503.15478/) (2025)
- [xLAM: A Family of Large Action Models to Empower AI Agent Systems](https://mlsanity.com/paper/2409.03215/) (2024)
- [Agent Lightning: Train ANY AI Agents with Reinforcement Learning](https://mlsanity.com/paper/2508.03680/) (2025)
- [Hindsight Credit Assignment](https://mlsanity.com/paper/1912.02503/) (2019)
- [Reinforcing Multi-Turn Reasoning in LLM Agents via Fine-Grained Reward Structure and Credit Assignment](https://mlsanity.com/paper/2505.11821/) (2025)
- [AgentPRM: Process Reward Models for LLM Agents via Step-Wise Promise and Progress](https://mlsanity.com/paper/2511.08325/) (2025)
- [Counterfactual Credit Assignment in Model-Free Reinforcement Learning](https://mlsanity.com/paper/2011.09464/) (2020)
- [The Mirage of Action-Dependent Baselines in Reinforcement Learning](https://mlsanity.com/paper/1802.10031/) (2018)
- [Nemotron 3 Super: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2604.12374/) (2026)
- [Learning Long-Term Reward Redistribution via Randomized Return Decomposition](https://mlsanity.com/paper/2111.13485/) (2021)
- [TRACE: Turn-level Reward Assignment via Credit Estimation for Long-Horizon Agents](https://mlsanity.com/paper/2607.13988/) (2026)
- [Verified Critical Step Optimization for LLM Agents](https://mlsanity.com/paper/2602.03412/) (2026)
- [PivotRL: High Accuracy Agentic Post-Training at Low Compute Cost](https://mlsanity.com/paper/2603.21383/) (2026)
- [Breaking Contextual Inertia: Reinforcement Learning with Single-Turn Anchors for Stable Multi-Turn Interaction](https://mlsanity.com/paper/2603.04783/) (2026)
- [Factored Policy Gradients: Leveraging Structure for Efficient Learning in MOMDPs](https://mlsanity.com/paper/2102.10362/) (2021)
- [Agent Lightning v1.0: Towards Harnessed Agentic RL](https://mlsanity.com/paper/2608.17528/) (2026)

## Abstract (arXiv)

Multi-turn tool-use failures can hinge on a single model call, yet reward variation alone does not reveal which call would benefit from training. When rewards depend on later interactions, their variation can reflect downstream randomness rather than differences between the current actions. We introduce Critical-State RL to identify trainable states in multi-turn interactions. Given task-defined candidate calls and local rewards, the method assesses whether each reward captures the action's effect on task success and whether improvement over a reference policy is possible. It then uses nested sampling to separate action-dependent reward variation from continuation noise and optimizes the policy at the selected states using contextual-bandit training. Experiments on the Berkeley Function Calling Leaderboard (BFCL) v4 compare training at diagnostic-selected states with training at alternative states. For missing-function tasks, the diagnostic selects the response after the tool becomes available; for missing-argument tasks, it selects the response before the missing argument is supplied. Training the selected responses improves performance, including about 14 percentage points on the missing-function task, while training the alternatives leaves performance flat or worse. We further apply the recipe across models and tasks, including logged repeat-call avoidance and memory management.