Title: PolarNet: Learning to Optimize Polar Keypoints for Keypoint Based Object Detection. Abstract: A variety of anchor-free object detectors have been actively proposed as possible alternatives to the mainstream anchor-based detectors that often rely on complicated design of anchor boxes. Despite achieving promising performance on par with anchor-based detectors, the existing anchor-free detectors such as FCOS or CenterNet predict objects based on standard Cartesian coordinates, which often yield poor quality keypoints. Further, the feature representation is also scale-sensitive. In this paper, we propose a new anchor-free keypoint based detector ``PolarNet", where keypoints are represented as a set of Polar coordinates instead of Cartesian coordinates. The ``PolarNet" detector learns offsets pointing to the corners of objects in order to learn high quality keypoints. Additionally, PolarNet uses features of corner points to localize objects, making the localization scale-insensitive. Finally in our experiments, we show that PolarNet, an anchor-free detector, outperforms the existing anchor-free detectors, and it is able to achieve highly competitive result on COCO test-dev benchmark ($47.8\%$ and $50.3\%$ AP under the single-model single-scale and multi-scale testing) which is on par with the state-of-the-art two-stage anchor-based object detectors. The code and the models are available at https://github.com/XiongweiWu/PolarNetV1