CarbonGearRL: Precision-Elastic, Carbon-Aware Scheduling for Foundation-Model Training

The carbon footprint of training large language models now rivals that of entire data centres, yet most optimisation efforts treat accelerator count and numeric precision as static hyper\-parameters. We introduce \textbf{CarbonGearRL}, an end-to-end system that \emph{jointly} schedules cluster width and arithmetic precision against real-time grid carbon signals. A dual-driven soft Q-learning scheduler scales GPUs up to FP8 during low-carbon windows and down to BF16 when emissions peak, while a precision-adaptive AdamW provides provable stability under stochastic quantisation noise. We derive sublinear carbon regret relative to a clairvoyant oracle and match the $\mathcal{O}(1/\sqrt{B})$ convergence rate of fixed-precision baselines. On 13 B/70 B LLaMA-style models our prototype cuts CO$_2$-e by up to 52 \% without throughput loss.