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arXiv · 2609.20906

Continuous Delayed-Memory Stochastic Gradient Descent and Continuous-Time Reinforcement Learning from History of Astrophysical Time Series Studies

Debartha Paul·Juncheng Yi
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Abstract

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.

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Debartha Paul, Juncheng Yi. 2026-09-17. Continuous Delayed-Memory Stochastic Gradient Descent and Continuous-Time Reinforcement Learning from History of Astrophysical Time Series Studies. https://arxiv.org/abs/2609.20906

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