In this paper, we propose CUDA-L2, a system that combines large language models (LLMs) and reinforcement learning (RL) to automatically optimize Half-precision General Matrix Multiply (HGEMM) CUDA kernels. Using CUDA execution speed as the RL reward, CUDA-L2 automatically optimizes HGEMM kernels across 1,000 configurations. CUDA-L2 systematically outperforms major matmul baselines to date, from the widely-used this http URL to state-of-the-art Nvidia's closed-source libraries, i.e., cuBLAS, cuBLASLt. In offline mode, where kernels are executed consecutively without time intervals, CUDA-L2 yields +22.0% over this http URL on average; +19.2% over cuBLAS using the optimal layout configuration (normal-normal NN and transposed-normal TN); +16.8% over cuBLASLt-heuristic, which queries cuBLASLt library and selects the algorithm based on the heuristic's suggestion; and +11.4% over the most competitive cuBLASLt-AutoTuning model, which selects the fastest algorithm from up to 100 candidates from cuBLASLt's suggestions. In server mode, where kernels are executed at random intervals simulating real-time inference, the speedups further increase to +28.7%, +26.0%, +22.4%, and +15.9% for this http URL, cuBLAS, cuBLASLt-heuristic, and cuBLASLt-AutoTuning respectively. CUDA-L2 shows that even the most performance-critical, heavily-optimized kernels like HGEMM can be improved through LLM-guided RL automation by systematically exploring configuration spaces at scales impractical for humans.