# Bayesian Stochastic Gradient Descent for Stochastic Optimization with Streaming Input Data

arXiv: https://arxiv.org/abs/2202.07581 · HTML: https://mlsanity.com/paper/2202.07581/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2022.

## Built on by (most cited first, 2 of 2)

- [Variational Stochastic Gradient Descent for Deep Neural Networks](https://mlsanity.com/paper/2404.06549/) (2024)
- [ONG: Orthogonal Natural Gradient Descent](https://mlsanity.com/paper/2508.17169/) (2025)

## Abstract (arXiv)

We consider stochastic optimization under distributional uncertainty, where the unknown distributional parameter is estimated from streaming data that arrive sequentially over time. Moreover, data may depend on the decision of the time when they are generated. For both decision-independent and decision-dependent uncertainties, we propose an approach to jointly estimate the distributional parameter via Bayesian posterior distribution and update the decision by applying stochastic gradient descent on the Bayesian average of the objective function. Our approach converges asymptotically over time and achieves the convergence rates of classical SGD in the decision-independent case. We demonstrate the empirical performance of our approach on both synthetic test problems and a classical newsvendor problem.