# Verifiable Hidden Dynamics Play: Generating Agentic RL Environments from Solved Mechanisms

arXiv: https://arxiv.org/abs/2609.27321 · HTML: https://mlsanity.com/paper/2609.27321/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 45 of its 48 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 30 of 45)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [LLM+P: Empowering Large Language Models with Optimal Planning Proficiency](https://mlsanity.com/paper/2304.11477/) (2023)
- [Leveraging Procedural Generation to Benchmark Reinforcement Learning](https://mlsanity.com/paper/1912.01588/) (2019)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [TextWorld: A Learning Environment for Text-based Games](https://mlsanity.com/paper/1806.11532/) (2018)
- [Measuring AI Ability to Complete Long Software Tasks](https://mlsanity.com/paper/2503.14499/) (2025)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [MemoryArena: Benchmarking Agent Memory in Interdependent Multi-Session Agentic Tasks](https://mlsanity.com/paper/2602.16313/) (2026)
- [Vending-Bench: A Benchmark for Long-Term Coherence of Autonomous Agents](https://mlsanity.com/paper/2502.15840/) (2025)
- [Reinforcing Multi-Turn Reasoning in LLM Agents via Fine-Grained Reward Structure and Credit Assignment](https://mlsanity.com/paper/2505.11821/) (2025)
- [Agent World Model: Infinity Synthetic Environments for Agentic Reinforcement Learning](https://mlsanity.com/paper/2602.10090/) (2026)
- [Towards a Science of AI Agent Reliability](https://mlsanity.com/paper/2602.16666/) (2026)
- [The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://mlsanity.com/paper/2509.09677/) (2025)
- [EnvScaler: Scaling Tool-Interactive Environments for LLM Agent via Programmatic Synthesis](https://mlsanity.com/paper/2601.05808/) (2026)
- [OR-Gym: A Reinforcement Learning Library for Operations Research Problems](https://mlsanity.com/paper/2008.06319/) (2020)
- [RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environments](https://mlsanity.com/paper/2511.07317/) (2025)
- [Agentic Reinforcement Learning with Implicit Step Rewards](https://mlsanity.com/paper/2509.19199/) (2025)
- [PDDLGym: Gym Environments from PDDL Problems](https://mlsanity.com/paper/2002.06432/) (2020)
- [Web-Shepherd: Advancing PRMs for Reinforcing Web Agents](https://mlsanity.com/paper/2505.15277/) (2025)
- [ScaleEnv: Scaling Environment Synthesis from Scratch for Generalist Interactive Tool-Use Agent Training](https://mlsanity.com/paper/2602.06820/) (2026)

## Abstract (arXiv)

Language-model agents increasingly face long-horizon tasks with evolving state, interdependent decisions, and delayed outcomes. Scaling their training requires diverse agentic environments, dependable outcome signals, and low extension cost. Existing generation pipelines commonly construct an environment before defining its outcome rule or annotating its trajectories, leaving dynamics and evaluation to be aligned post hoc. VHD-Play reverses this dependency by sampling and solving a mathematical model before a corpus-grounded setter renders its decision process as stateful tools. The executable dynamics and trajectory-scoring reference are inherited from the same solved model. The pipeline produces 3,300 diverse agentic environments at a cost of a few cents each. Training Qwen3.6-35B-A3B on three families raises its mean agentic score from 0.204 to 0.815 in a five-family diagnostic. Gains also appear on held-out instances from all three training families and eight unseen mechanism families, then extend beyond the generated substrate to external benchmarks for general function calling, travel planning, and 365-day e-commerce. On E-Commerce Bench, the trained checkpoint completes every run without bankruptcy and exceeds Qwen3.7-Max. We compare written-out problems with stateful versions that reveal or hide their parameters. The comparison shows that most of the learnable gap lies in stateful interaction rather than underlying problem solving. A frozen 35B setter realizes larger environments, and scale-matched training retains gains as mechanism size and horizon grow, indicating the potential for an evolving training substrate.