  Recent research has shown that quasar-convexity can be found in applications
such as identification of linear dynamical systems and generalized linear
models. Such observations have in turn spurred exciting developments in design
and analysis algorithms that exploit quasar-convexity. In this work, we study
the online stochastic quasar-convex optimization problems in a dynamic
environment. We establish regret bounds of online gradient descent in terms of
cumulative path variation and cumulative gradient variance for losses
satisfying quasar-convexity and strong quasar-convexity. We then apply the
results to generalized linear models (GLM) when the underlying parameter is
time-varying. We establish regret bounds of online gradient descent when
applying to GLMs with leaky ReLU activation function, logistic activation
function, and ReLU activation function. Numerical results are presented to
corroborate our findings.
