We address the problem of temporal action localization in videos. We pose action localization as a structured prediction over arbitrary-length temporal windows, where each window is scored as the sum of frame-wise classification scores. Additionally, our model classifies the start, middle, and end of each action as separate components, allowing our system to explicitly model each action's temporal evolution and take advantage of informative temporal dependencies present in this structure. In this framework, we localize actions by searching for the structured maximal sum, a problem for which we develop a novel, provablyefficient algorithmic solution. The frame-wise classification scores are computed using features from a deep Convolutional Neural Network (CNN), which are trained end-toend to directly optimize for a novel structured objective. We evaluate our system on the THUMOS '14 action detection benchmark and achieve competitive performance.