  Pairwise learning, an important domain within machine learning, addresses
loss functions defined on pairs of training examples, including those in metric
learning and AUC maximization. Acknowledging the quadratic growth in
computation complexity accompanying pairwise loss as the sample size grows,
researchers have turned to online gradient descent (OGD) methods for enhanced
scalability. Recently, an OGD algorithm emerged, employing gradient computation
involving prior and most recent examples, a step that effectively reduces
algorithmic complexity to $O(T)$, with $T$ being the number of received
examples. This approach, however, confines itself to linear models while
assuming the independence of example arrivals. We introduce a lightweight OGD
algorithm that does not require the independence of examples and generalizes to
kernel pairwise learning. Our algorithm builds the gradient based on a random
example and a moving average representing the past data, which results in a
sub-linear regret bound with a complexity of $O(T)$. Furthermore, through the
integration of $O(\sqrt{T}{\log{T}})$ random Fourier features, the complexity
of kernel calculations is effectively minimized. Several experiments with
real-world datasets show that the proposed technique outperforms kernel and
linear algorithms in offline and online scenarios.
