We consider the following formulation of Lai, Robbins and Wei (1979), and Lai and Wei (1982). Consider the following regression problem,
for where are unobservable random errors and are unknown parameters.
Typically for a regression problem, it is assumed that inputs are given and errors are IID random variables. However, we now want to consider a setting where we sequentially choose inputs and then get observations , and errors are a martingale difference sequence with respect to the filtration generated by .