随机梯度下降算法
数学
随机优化
贝叶斯概率
数学优化
下降(航空)
梯度下降
贝叶斯优化
计算机科学
人工智能
统计
人工神经网络
工程类
航空航天工程
作者
Tianyi Liu,Yifan Lin,Enlu Zhou
出处
期刊:Siam Journal on Optimization
[Society for Industrial and Applied Mathematics]
日期:2024-01-25
卷期号:34 (1): 389-418
摘要
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 at 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 (SGD) 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.
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