In order to render a nice looking scene (where light is concerned) we need to take into consideration that an object is lit by a combination of indirect and direct light, where each reflected light ray (indirect light) represents a new light source (small but not unimportant). With that in mind, the number of light sources in a scene expands rapidly and requires a program to traverse the lights optimally when estimating their significance and impact for each scene point. As such, the many-light problem is introduced when calculating global illumination.
There are different algorithms to compute the global illumination, but each of those algorithms needs to sample all the lights of the scene first, and then do the computations. Optimizing the light sampling algorithm leads to faster and more efficient use of rendering time with the same degree of image realism, which are the exact same reasons why improvement of many-light sampling in Appleseed is required.
Within the proposal I've given an overview of the implementation approach of the new many-light sampling algorithm, split the overall problem into smaller pieces and tried to propose a realistic implementation timeline.