Uncertainty and non-determinism

What is the difference between uncertainty and non-determinism? I am beginning to find that many graduate students, and even many researchers, I come across do not really distinguish between the two very much. In fact, even within the first class, what is the difference between probabilistic uncertainty and, say, set-membership description of uncertainty?

Now, if I ask the question properly, it becomes clear that there are differences and it is not that hard to guess what they are from the words used. However, these things have important influences on what they mean for various techniques, e.g., design of control strategies. If what you are dealing with is probabilistic uncertainty that can be modeled and statistically estimated then one could design control strategies in a way that is not all that different from the procedure for deterministic noise-free systems. The “right” procedure might be a lot harder for set-membership uncertainty. For more general forms of non-determinism, the concerns and design procedures tend to be even more different from the case of “noisy systems”.

So what? Well, for one thing, we have very little work in the robot learning or control learning areas which is able to do anything beyond the data-driven equivalent of stochastic control in the presence of “small noise”. Currently, non-determinism is really only handled by “re-planning” but we don’t have very efficient methods for that either, and even then this is built as a hierarchy of non-interacting black boxes. So, this area needs more work – which begins with more awareness of the underlying issue!

PS: I recently came across this interesting paper that is loosely related to what I say above but has a different focus and motivation: Ken Binmore, Rational Decisions in Large Worlds, Annales d’Économie et de Statistique, No. 86, pp. 25-41, 2007 (from the looks of it, this is a short version of a book).

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