1 : Bellman-Ford
2 : Currency Arbitrage
3 : Directional Shortest-Path
4 : Q-Learning
5 : Handling Randomness in Shortest-Path Algorithms
6 : Modern Q-Learning
7 : Physically-Based Rendering
8 : Summary and Questions
9 : Acknowledgements
"a basic tool [that should be] taught to all algorithms students together with divide-and-conquer, dynamic programming, and random sampling.” - sanjeev-arora
“so hard to believe that it has been discovered five times and forgotten.” - christos-papadimitrou [https://www.youtube.com/watch?v=KP0WFbdHhJM]
it has formed basis of algorithms in fields as diverse as machine-learning, optimization from e.g. tcp ^^), game-theory, economics, biology etc. etc.
The usage of text color on this image caption is brilliant.
It never occurred to me that you can do this technique to explain a diagram. Definitely love it. Will steal this technique for my own purpose.
There might be an article about this specific technique.
If you hover any diagram, there are options for a colorblind-friendly version.
This is very distracting.
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 , 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 :)
Say hello to Kwabena for me if you get the chance ;)
A crude variation on this is often used in games, known as "light probes". You precompute the light transport simulation on a subset of points in the scene (manually placed by artists), and lighting for dynamic objects simply lerps between the nearest light probes.
Any resources (i.e. textbooks) recommended for learning more about graph theory as well as currency arbitrage?
And of-fucking-course OP is at Google Brain.