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I have two questions that I think are closely related:

  • Why is it useful to introduce behaviors, e.g., goal-to-goal + obstacle avoidance? (The alternative would have been to just use a single behavior with the more complex cost function that rewards getting to the goal without hitting stuff)?
  • Why is it useful to analyze hybrid systems (instead of purely continuous systems that approximate switches and resets as continuous phenomena)?

I think know a naive answer: this makes system design & analysis more tractable, by splitting a very complex problem into smaller pieces that can be, to some extent, studied separately. But is there a more in-depth intuition behind these choices?

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The answer you have found out yourself is not naive but rather at the core of science and technology. In fact, when we are not good at tackling the problem as a whole, because it is way difficult or even intractable for us, or when we do not want to put too much effort into dealing with lots of details we are not interested in (think of your example of approximating continuous phenomena with discrete events), then we split it into pieces we are able to better manipulate, in the hope (sometimes we can get stronger guarantees though) that this new arrangement will help us solve the original problem.

A secondary reason underlying this methodology is to implement the composition of tools, which makes our lives much easier because allows us to reuse components that have been designed and realized for problems different from the one at hand. Therefore, by breaking down (analysis) a big goal into a list of smaller ingredients that can be combined together, we will be able later on to aggregate (synthesis) those units to solve other quests, maybe only loosely related to our starting point.

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  • $\begingroup$ Are there examples of systems built without such decompositio?. E.g., robots designed where there's only behavior with a cost function that covers all aspects of interst. $\endgroup$ – max Oct 4 '18 at 5:50
  • $\begingroup$ None worth mentioning that comes to my mind. The theory is too complex when dealing with high-level behaviors and the practice is even more complicated. Even a PID controller is a composition of simpler blocks. $\endgroup$ – Ugo Pattacini Oct 4 '18 at 8:26
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As @Ugo suggested, in the traditional optimal control theory, most (all?) interesting problems become intractable without decomposition / layered architecture.

For completeness, I wanted to link some excellent discussion of this topic from the perspective of an ML researcher (Sergey Levine of UC Berkeley).

TLDR: Sergey points out that deep learning offers an option to replace the traditional layered architecture by learned black-box components. Of course, while human engineers will no longer need to think about it, a deep network may (and likely will) do something roughly equivalent internally.

That said, Sergey isn't necessarily advocating in favor of letting DL handle the decomposition. He suggests that a more valuable benefit of DL is to propagate errors end-to-end (from the controls back through all the components -- regardless of whether the components are human-designed or learned).

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  • $\begingroup$ DL, as other ML techniques, does represent a way to solve a problem which many researchers resort to nowadays, but this does not necessarily mean that we have only one cost function in this case. For high-level tasks such as grasping things, we do still use more than one single NN: one for analyzing the scene, one for controlling the robot arm. Thus, I wouldn't mix how the problem is posed with the techniques we may choose to solve it. $\endgroup$ – Ugo Pattacini Oct 7 '18 at 18:11
  • $\begingroup$ @Ugo well, with end to end learning, you would actually use one NN. That single NN could be designed in a way that reflects the decomposition you describe; but it could also be designed without such considerations. It's probably too early to tell which of these two approaches will prove successful, since the end to end learning is still very young. $\endgroup$ – max Oct 7 '18 at 21:51
  • $\begingroup$ To stick to the example I made, there is no NN able to learn the reaching task with results as accurate as those yielded by traditional approaches. Reaching is a solved problem that does not require designing an ad-hoc NN. Thus, composition wins here as well as in many similar contexts. You could still deal with NN for the sake of research in fields where they do not represent the state of the art yet. Hoping/expecting that single end-to-end NN's will outperform any other technique in the future is perfectly legitimate but does not reflect the current knowledge. $\endgroup$ – Ugo Pattacini Oct 8 '18 at 18:31
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The benefit of a hybrid system depends on the goal of an academic work. If the aim is to prove that the robotic system doesn't work, than a purely continuous systems is the way to go. Ordinary differential equations ensure that apart from simple obstacle avoidance the robot can't do complex tasks. Especially from the perspective of philosophical foundations of AI it is important to show, that robots are harmless and that science is not able to build such machines.

Why is somebody interested in building machines who doesn't work? Because this is equal to demotivate the audience. It is the best practice method to use the own influence to hold down technology. Instead of arguing on facts, the debate can be biased into a philosophical one about the limits of Artificial Intelligence.

If the aim is to develop advanced robotics, a hybrid control system is the way to go. With multi-modal-planning and agent architectures, It is possible to implement human-like behavior. From a technical point of view such, such a control system will work very efficient and is able to not only follow a light, but pick up objects, doing complex tasks and parse textual commands. The disadvantage is, that the education situation becomes complicated. Because there is no limit and students could become motivated to think ahead. They will develop systems which break up the curriculum of the teacher.

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