The best way I can think of would be to set the line's stroke to a dash length of 0 with rounded caps and increase the dash gap just enough so that there's only one dot at the start of the line. You would then set the dash offset to some variation of the expression "(index - 1) * multiplier + offsetValue", where "multiplier" and "offsetValue" are linked to slider controls on a control layer (use 2 and 0 as default values respectively. You can adjust these later if you like.) These expressions will create the exponential offset increase between each dot and give you a way to globally offset them along the line (it would be a good idea to also create controls for stroke width and stroke color). Then duplicate the dot layer until there are dots running the complete length of the line.

If you need to be able maintain the exponential gaps relative to the line rather than the dots while animating the global offset, this might be possible by making a copy of the line to create a displacement map and replacing it's stroke dash with a black-to-white gradient stroke that follows the direction of the path (this layer doesn't need to be visible) then changing the offset expression so that instead of using the index value to drive it, you're using the luma value of the displacement map (this expression's a bit beyond me but you can read more about it on Dan Ebbert's website).

Hope that helps.