S3Gym: Can LLMs Turn Self-Testing and Self-Judging into Self-Improvement?

S3Gym evaluates self-testing, self-judging, and self-improvement in **seven text-based games** with executable verifiers. It compares **History ICL**, score-conditioned Summary Memory, and parameter Training.

Choose memory by task structure. Summaries fit reusable strategic rules; raw history can preserve precise state details; parameter updates may help when context-only adaptation is insufficient.

Improvement was inconsistent across model-game pairs. Training sometimes produced large gains but also instability and severe negative transfer, showing that recognizing good actions does not guarantee a transferable policy.