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I want to know if there is anything other than neural networks (or Deep NNs) that I can effectively use to perform function approximation? I am asking this w.r.t to the use of approximators in Q learning with large state space.

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  • $\begingroup$ Any parameterisable function does the trick. $\endgroup$
    – David
    Commented Nov 20, 2021 at 0:29
  • $\begingroup$ @DavidIreland Any examples? Actually, I am going to post my scenario specific question after 20 min (as I have to wait before posting another). I will give the link here. I request you to please also take a look on that, if possible. I have been asking small small questions and still stuck. So I decided to ask my scenario specific question finally. $\endgroup$ Commented Nov 20, 2021 at 0:33
  • $\begingroup$ @DavidIreland This is the link I said in the above comment. ai.stackexchange.com/questions/32472/… $\endgroup$ Commented Nov 20, 2021 at 0:59
  • $\begingroup$ It's a good idea to do a little bit of research before asking a question. Please, take a look at How do I ask a good question?. $\endgroup$
    – nbro
    Commented Nov 20, 2021 at 12:38
  • $\begingroup$ it looks like you’re using a graph as the state, in which case I’d recommend looking at graph neural networks. $\endgroup$
    – David
    Commented Nov 20, 2021 at 23:18

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Any series approximation technique will regress on training data. Taylor Series approximation is a popular technique. https://en.wikipedia.org/wiki/Taylor_series

Fourier series is also important in DSP and computing analog signals but can be used to approximate functions where a higher term count yields more accuracy. https://en.wikipedia.org/wiki/Fourier_series#:~:text=A%20Fourier%20series%20(%2F%CB%88f,be%20determined%20using%20harmonic%20analysis.

you can pick any degree of a polynomial and start regressing on data points for the coefficients but these term approximations show the calculus of choosing the degree of the approximator with respect to accuracy and other considerations such as if the data is even able to be modeled by a function (vertical line test) or if it needs to be transformed/mapped first.

To my understanding, Neural Networks have powerful generalization ability meaning they do well at modelling the function over a larger domain (including outside the trainning dataset as seen in cross-validation). To learn more on this I would suggest reading on the difference between neural networks and linear approximators.

I say this since any black box optimizer such as neural networks are equivalent to function approximators. Deep Learning is a subset of the study of function approximation but choosing what approximator is needed needs to be researched for each application.

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    $\begingroup$ One note of caution on the last paragraph: Deep Learning involves much more than function approximation. Topics like scalable system design, deployment, computational complexity and more don't fall cleanly into a "function approximator" perspective. This isn't a pedantic critique but a warning to anyone that might take that too seriously and then make reductive claims about the "nature of deep learning being nothing but function approximation." $\endgroup$
    – respectful
    Commented May 15, 2023 at 21:49

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