decidability of artificial intelligence

Not sure whether this is the correct place to post the question. some of my terms might not accurate.

currently AI is used for classification, inference, and so forth, is AI problem decidable? for example, given a dataset, prior/constraints and neural network, whether it can recognize a pattern (properly accuracy greater than some lower bound) is decidable? I understood the decidable problem is searching in a finite space. In terms of Machine learning techniques, the parameter space is finite, can I say it is decidable?

Also, Many problem solved by machine learning is quite different with traditional problem which has an algorithm, but machine learning problem doesn't have an algorithm format. And therefore, it is undecidable

Finally, for many proved math theorem, let's say the bound in some constrained problems (ex: Shannon limit in communication). Can I say such problem (constrained problem exists bound) is decidable, since people could find an algorithm (or math formula) to define limits.

For a problem to be approachable using what we presently call "AI methods", it has to be, at least theoretically, also solvable using "regular" methods (writing a set of instructions that solves it, line by line). Thus, decidable.

AI systems may create effective algorithms whose operation no human can understand. Also, by using AI methods we may find solutions to new problems, by accident, or discover that problems are decidable. These things do not contradict the affirmative above.

An algorithm exists that solves the problem.

StackExchange Computer Science Q#63584, answer score: 2