One-shot personalization of autoregressive (AR) text-to-speech (TTS) models remains challenging because supervised fine-tuning (SFT) on a single reference pair rapidly degrades generation quality. We identify fixed, off-policy supervision as a key cause of failure in one-shot SFT for AR TTS, leading to blank or near-empty outputs at inference. Diversifying the training data with zero-shot pseudo-pairs eliminates this failure but yields little improvement in speaker similarity and increases word error rate because the targets remain fixed and teacher-forced. We therefore propose two on-policy approaches for one-shot speaker personalization: Group Relative Policy Optimization (GRPO) with a speaker-similarity reward and On-Policy Self-Distillation (OPSD) with soft supervision from a reference-conditioned teacher. Both on-policy methods improve speaker similarity while preserving intelligibility, with different trade-offs: GRPO achieves the strongest overall performance, whereas OPSD enables substantially faster adaptation without external reward evaluation. Further analysis confirms that these gains stem from on-policy supervision rather than target diversity, establishing on-policy training as an effective framework for one-shot AR TTS personalization.

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