We present Reduced Gaussian Blendshapes Avatar (RGBAvatar), a method for reconstructing photorealistic, animatable head avatars at speeds sufficient for on-the-fly reconstruction. Unlike prior approaches that utilize linear bases from 3D morphable models (3DMM) to model Gaussian blendshapes, our method maps tracked 3DMM parameters into reduced blendshape weights with an MLP, leading to a compact set of blendshape bases. The learned compact base composition effectively captures essential facial details for specific individuals, and does not rely on the fixed base composition weights of 3DMM, leading to enhanced reconstruction quality and higher efficiency. To further expedite the reconstruction process, we develop a novel color initialization estimation method and a batch-parallel Gaussian rasterization process, achieving state-of-the-art quality with training throughput of about 630 images per second. Moreover, we propose a local-global sampling strategy that enables direct on-the-fly reconstruction, immediately reconstructing the model as video streams in real time while achieving quality comparable to offline settings.