The Joule Thief is what kind of oscillator? Armstrong? Relaxation? or what? Thanks!
Yes, the Joule Thief, at least the classic 'Clive' Joule Thief, clearly isn't an Armstrong. 

An Armstrong oscillator uses very light coupling between two inductors (it's often called a 'tickler' for this very reason) with one of the inductors in parallel with a capacitor to define the frequency.

The 'Clive' Joule Thief uses two strongly coupled inductors (aka a transformer), and no capacitor. The frequency is defined by the relaxation behaviour between the supply voltage, the value of the primary inductor, and the threshhold currents of the transistor to come out of saturation.

Wikipedia has now been corrected. The publication used to support the assertion that the oscillator is Armstrong,  "Fun Examples for Teaching Linear and Nonlinear Circuits", Circuits and Systems (ISCAS), 2013 IEEE International Symposium on, 19–23 May 2013, p2557 - 2560 quoted the Wikipedia Joule Thief article as its authority. A circular reference like that is obviously not reliable.