One term that would describe it is, "Automated navigation," but no one can easily guess what others might call it. The requirement is a little fuzzy, which doesn't help name it properly. We can go over a few of the more likely variants.
- The system learns a particular navigation path, in which the case is called, "Test Case Recording," because functional tests are constructed using Selenium, Watir, and other tools. That's not AI though.
- The AI system naively learns how a particular person or set of people navigate when performing a particular task. Then it could be called, "Goal oriented web browsing automation." The naive learning of a goal oriented browsing pattern is fairly easy to do.
- The AI system cognitively learns how a particular person or set of people navigate when performing a particular task. Some level of AI comprehension of choices would requires a self-constructing model and significant research, possibly years or decades of it.
- The AI system learns how a particular person or set of people navigate when they don't have a defined goal in mind. Then it could be called, "Stream of consciousness browsing automation," however I can't see any purpose in that.
- The AI system seeks particular documents, in which case it would be a, "Network node classifier."
It is unlikely that demonstrating 1 to 5 saves would be sufficient unless it is the first item in the above list, which isn't AI. It's recording and putting a loop around like streams. Now if the AI is not involved in the recording at all but is to intelligently create the loop from two or three like sequences and know what to put before, inside, and after the loop to navigate in, iterate, and then finalize the task, perhaps by logging out, that is an offline task. That could be called, "Loop Configuration Automation," or, "Automated Iteration Programming."
Dealing with connection errors by waiting and trying again is not necessarily AI either, unless the wait period is driven by the probability distribution of success after waits based on past experience.
Screenshots are a bad idea. Look into Selenium, Katalon, and Watir. You want to be able to record and play back, even if the play back is generated by the AI instead of simply playing the recorded sequence.
These high level requirements will not be helpful in finding algorithms. To get into the algorithms, one would first have to clarify the high level requirements. Whether an MLP, LSTM, RBM, DQN, CNN, MDP, or whatever is appropriate can be determined when a clear understanding of exactly what it is that drives the search as an objective is known. If it is not know, no value or loss functions can be constructed intelligently and no solution is likely to arise.
Addendum in Response to Question Author Comment
The AI component would be receiving all the pertinent information regarding the HTTP(S) transaction during the training. If using Selenium, Katalon, Watir, or some other functional browsing tool, the pertinent information would be the DOM model and the events trapped by the browser from the mouse and keyboard or touch screen.
After learning completes, the AI component would still take as input the HTTP(S) request or DOM (depending on which layer of abstraction was used for training) and then drive that same layer using the trained component.
Using the higher level DOM will improve reliability significantly (possibly by a factor of thousands or more) because the AI will deal with web documents, forms, and events at the actual user interface, but DOM interaction is slower than dealing directly with the HTTP(S) request and response. Training and using the training using the DOM will require what is called a headless browser, but both Chrome and FireFox can operate that way in UNIX or LINUX with Xvfb.
The largest task in the project is to do thorough enough example log ins to learn. It may take many, and the It has to find the right link (navigation), recognize the form and fill it.
Finding the website names of all your tabs in chrome is not an AI task. There are plenty of browser plug-ins that can do that.