Large Language Models (LLMs) as agents often fail to improve in new environments. We identify and characterize a failure mode we call exploration collapse: under reinforcement learning (RL) in environments whose states are unfamiliar to the policy, Pass@k, the probability that at least one of k sampled trajectories succeeds, drops markedly over training even as Pass@1 edges up, revealing increasingly brittle exploration; environments closer to the pretraining distribution show no such decline. We trace this collapse to weak grounding in environment states and dynamics, and study a simple remedy: explicitly teaching the agent to estimate the current state and predict its transitions before optimizing for reward. We instantiate it as SPA, an explore-then-exploit recipe that cold-starts the policy with a Self-Experience supervised finetuning (SFT) stage, collecting the model's own interaction trajectories and supervising state and next-state prediction, and then runs standard RL. The resulting world model serves as a grounded initialization for RL rather than an inference-time planner. Across unseen environments, SPA consistently and substantially improves over vanilla RL: for example, it raises the Sokoban success rate from 25.6% to 59.8% on Qwen2.5-1.5B-Instruct, letting sub-3B models surpass a 20B baseline on these tasks. Controlled studies indicate that the gains track four factors: grounded state representations, explicit transition modeling, self-experience trajectories from a sufficiently strong exploration policy, and adequate coverage of transition data.

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