In recent years we have witnessed an increasing interest in applying Deep Neural Networks (DNNs) to improve the rate-distortion performance in image compression. However, the existing approaches either train a post-processing DNN on the decoder side, or propose learning for image compression in an end-to-end manner. This way, the trained DNNs are required in the decoder, leading to the incompatibility to the standard image decoders (e.g., JPEG) in personal computers and mobiles. Therefore, we propose learning to improve the encoding performance with the standard decoder. In this paper, We work on JPEG as an example. Specifically, a frequency-domain pre-editing method is proposed to optimize the distribution of DCT coefficients, aiming at facilitating the JPEG compression. Moreover, we propose learning the JPEG quantization table jointly with the pre-editing network. Most importantly, we do not modify the JPEG decoder and therefore our approach is applicable when viewing images with the widely used standard JPEG decoder. The experiments validate that our approach successfully improves the rate-distortion performance of JPEG in terms of various quality metrics, such as PSNR, MS-SSIM and LPIPS. Visually, this translates to better overall color retention especially when strong compression is applied. The codes are available at https://github.com/ YannickStruempler/LearnedJPEG.