# AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning

arXiv: https://arxiv.org/abs/2508.14313 · HTML: https://mlsanity.com/paper/2508.14313/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 75 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)
- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)
- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 30 of 34)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [Planning with Large Language Models for Code Generation](https://mlsanity.com/paper/2303.05510/) (2023)
- [A Connection between Generative Adversarial Networks, Inverse Reinforcement Learning, and Energy-Based Models](https://mlsanity.com/paper/1611.03852/) (2016)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning](https://mlsanity.com/paper/2410.02884/) (2024)
- [OVM, Outcome-supervised Value Models for Planning in Mathematical Reasoning](https://mlsanity.com/paper/2311.09724/) (2023)
- [Agent-R: Training Language Model Agents to Reflect via Iterative Self-Training](https://mlsanity.com/paper/2501.11425/) (2025)

## Built on by (most cited first, 14 of 14)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [M^3-Bench: Multi-Modal, Multi-Hop, Multi-Threaded Tool-Using MLLM Agent Benchmark](https://mlsanity.com/paper/2511.17729/) (2025)
- [Behavior Knowledge Merge in Reinforced Agentic Models](https://mlsanity.com/paper/2601.13572/) (2026)
- [A Survey of Inductive Reasoning for Large Language Models](https://mlsanity.com/paper/2510.10182/) (2025)
- [Weak Critics Make Strong Learners: On-Policy Critique Distillation for Scalable Oversight](https://mlsanity.com/paper/2606.00424/) (2026)
- [DTop-p MoE: Sparsity-Controlled Dynamic Top-p MoE for Foundation Model Pre-training](https://mlsanity.com/paper/2512.13996/) (2025)
- [Reasoning over Precedents Alongside Statutes: Case-Augmented Deliberative Alignment for LLM Safety](https://mlsanity.com/paper/2601.08000/) (2026)
- [Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals](https://mlsanity.com/paper/2602.03061/) (2026)
- [MARTI-MARS2: Scaling Multi-Agent Self-Search via Reinforcement Learning for Code Generation](https://mlsanity.com/paper/2602.07848/) (2026)
- [DARE: Difficulty-Adaptive Reinforcement Learning with Co-Evolved Difficulty Estimation](https://mlsanity.com/paper/2605.09188/) (2026)
- [Explainable reinforcement learning from human feedback to improve alignment](https://mlsanity.com/paper/2512.13837/) (2025)
- [Cumulative Path-Level Semantic Reasoning for Inductive Knowledge Graph Completion](https://mlsanity.com/paper/2601.05629/) (2026)
- [Latent Reward Steering: An Adaptive Inference-Time Framework that Implicitly Promotes Cognitive Behaviors in Reasoning LLMs](https://mlsanity.com/paper/2606.00726/) (2026)
- [When LLM Meets Tree Search: A Systematic View of Inference as Search in Large Language Models](https://mlsanity.com/paper/2608.30395/) (2026)

## Abstract (arXiv)

Test-time scaling strategies for Large Language Models predominantly rely on either reinforcement learning with sparse outcome rewards or search-based methods guided by static Process Reward Models. However, outcome-based RL often suffers from training instability and sample inefficiency, while static PRMs require expensive step-wise supervision and are susceptible to reward hacking due to distributional shifts. In this paper, we introduce AIRL-S, a unified framework that integrates Adversarial Inverse Reinforcement Learning with Group Relative Policy Optimization. By inferring a dense, step-wise reward model directly from reference trajectories, AIRL-S eliminates the dependency on labeled process data and uses the same learned PRM as both a training signal and a verifier for search-based TTS. Extensive evaluations across eight benchmarks in mathematics, science, and code generation demonstrate that our policy model improves average performance by 9% over the base model, matching GPT-4o. We further analyze how the AIRL and GRPO objectives complement each other and how the learned PRM transfers across generators and search algorithms, establishing a robust and cost-effective methodology for scaling test-time computation in complex reasoning tasks.