Bayesian Stochastic Gradient Descent for Stochastic Optimization with Streaming Input Data
针对分布参数未知且数据流式到达的随机优化问题，提出联合贝叶斯后验估计与随机梯度下降的方法，在决策独立和决策依赖两种不确定性下均能渐近收敛，并在合成问题和报童问题中验证了效果。
.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.KeywordsBayesian estimationstreaming input datastochastic gradient descentendogenous uncertaintyMSC codes90C15