[Submitted on 19 Aug 2026]
[View PDF](/pdf/2608.19197)
[HTML (experimental)](https://arxiv.org/html/2608.19197v1)
Abstract:Continuous self-improvement requires an ever-expanding pool of self-generated, diverse, adaptive goals. For language agents, existing training environment pools (hand-curated, statically synthesized, or frozen-verifier) keep the goal distribution fixed as the learner scales. We introduce SPADE (Self-Play in Adaptive Synthetic Executable Environments), a self-play RL framework in which a single LLM plays two roles: an Environment Designer that writes complete, long-horizon training environments as executable code with an OpenAI Gym-style reset()/step() interface, and a Reasoning Agent that learns to act in them. Each is a stateful, multi-turn environment (state transitions, reward functions, and verification code), so one interface spans reasoning problems and multi-step agentic tool use. The Reasoning Agent's regret is estimated using the gap between its reward with and without privileged hints; in optimizing this regret signal the Environment Designer learns to target environments at the edge of the agent's capabilities while keeping them feasible. Through extensive experimentation, we find several components critical to success: grounding the Environment Designer on documents sampled from a large pretraining corpus, and giving it an accumulated environment memory. Scaling to 30B-parameter models, SPADE improves over the strongest fixed-environment baseline by +5.3 on average across eight held-out math, science, code, and reasoning benchmarks, and lifts the tool-use setting by +5.7 on BFCL-v4 multi-turn and +13.9 on ACEBench-Agent; on the games setting, the margin over the strongest baseline grows with model scale. By making environment design itself a learnable component, SPADE takes a concrete step toward open-ended self-improvement.
References & Citations
...
Bibliographic Explorer
(What is the Explorer?) Connected Papers
(What is Connected Papers?) Litmaps
(What is Litmaps?) scite Smart Citations
(What are Smart Citations?)# Code, Data and Media Associated with this Article alphaXiv
(What is alphaXiv?) CatalyzeX Code Finder for Papers
(What is CatalyzeX?) DagsHub
(What is DagsHub?) Gotit.pub
(What is GotitPub?) Hugging Face
(What is Huggingface?) ScienceCast
(What is ScienceCast?)# Demos Influence Flower
(What are Influence Flowers?) CORE Recommender
(What is CORE?)# arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.