Quasars are luminous objects in the universe that exhibit stochastic brightness variations encoding information about the supermassive black holes powering them, and modeling these variations from ground-based survey data time series, known as light curves, is a statistical challenge.
This paper reviews how stochastic differential equations (SDEs) have been adapted with neural network parameterizations to overcome this challenge in history.
We create the Continuous-Delayed-Memory Stochastic Gradient Descent which depend on the past state of the discrete iteration process.
We performed the simulation on some 2-dimensional landscape and observed some wider-exploration and more precise convergent behavior compared to Vanilla SGD by adjusting hyperparameters.
Besides, we proposed a reinforcement learning structure with continuous time policy gradients for exploratory policies without solving HJB PDE, and we show that its optimality conditions recover the Gibbs policy of previous works.