When Synthetic Speech Is All You Have: Better Call GRPO

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LLM-based ASR adapted to regulated domains such as banking is bottlenecked by privacy: real speech is costly and legally constrained to collect, making synthetic text-to-speech (TTS) an attractive substitute. Yet synthetic speech stays acoustically mismatched with real recordings, and work on this gap has stayed within supervised fine-tuning (SFT). We instead turn to reinforcement learning, and show that Group Relative Policy Optimization (GRPO) extracts far more from the same synthetic speech than SFT. Synthetic-only adaptation of the model with GRPO, a critic-free method rewarding low-WER hypotheses, reduces WER by 40\% relative to SFT (36.71\%$\to$22.09\%), and an SFT-then-GRPO combination pushes this further to 45\%. We trace the gain to behavior rather than representation: GRPO reduces insertion errors by improving stopping calibration and speech-to-text alignment by better anchoring attention to audio, leaving early-layer representations intact. When synthetic speech is the main resource, reinforcement learning should be preferred over supervised fine-tuning.