This is a fantastic post! Thank you so much for sharing it. Perhaps another post (which maybe you should write! Or I may (though I'm certainly nowhere as good)

This is a fantastic post! Thank you so much for sharing it. Perhaps another post (which maybe you should write! Or I may (though I'm certainly nowhere as good), or why not both!) might the unifying principle of finding solutions to fixed-point equations. In general, having a Bellman-style update equation, you can usually construct either (a) DP solutions to this problem or (b) contraction mappings whose fixed point solves this problem. Perhaps the most general form I know of the above principles is the Hamilton-Jacobi-Bellman equation [0], which is used absolutely everywhere in control theory and has deep connections to several fields (including the theory of PDEs, such as heat equations on manifolds along with several other cases). Many, many problems (including all of the ones mentioned above) reduce immediately to an appropriate instance of the HJB equation (either in the finite or the infinite case), which admits a simple DP solution that can be very quickly computed. Anyways, again, awesome post. I'll be following your blog quite closely :) --- [0] https://en.wikipedia.org/wiki/Hamilton–Jacobi–Bellman_equation https://en.wikipedia.org/wiki/Hamilton–Jacobi–Bellman_equati...