I often come across these four paradigms. The more I look into the literature, the more I notice they appear to have same goal (i.e. searching the algorithm space to find or improve on a solver). I think I am simplifying a bit too much. What do others people think?
I think machine learning is basically different from the other approaches, because it includes such promising methods as deep learning, which is suitable for many problems solving and at present it is just the beginning of deep learning methods used in machine learning
Yes there is much overlap between the above paradigms you mention. In general one constructs some parametric mathematical model and then converts this into a problem (by relating it to observations, ie the inference of machine learning). Such problems can generally be formalised as an optimisation problem of some kind or another.
There are many ways to formulate a model of a system, just as there are many ways to perform inference with respect to a given model. Thus I think many techniques can be shared across these domains especially with regards to how one approaches the task of optimising a given problem.
I think the most interesting thing is how one can often pick and choose models/algorithms from different areas which can be useful in areas where they were not originally intended. For example, I believe the Ising model, initially developed in Physics also has applications in neurology, another example might be how gravitational models can be used to describe crowd behaviour.
Perhaps machine learning is the best example of this...many of the models are pulled from interpretations of models in other areas of science. When discussing such things, I always find it helpful to focus on the specific problem/application, ie is the problem (pseudo)-convex, non-smooth, etc.
Even sub-fields of machine learning (ie "deep" learning) have become kind of rather large fields/buzzwords in their own right. Perhaps one might argue that the machine learning paradigm could encompass the others, but not the other way round??
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