3 papers
math.OC2024
Stochastic Gradient Descent Revisited
Azar Louzi
Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong…
q-fin.RM2024
Adaptive Multilevel Stochastic Approximation of the Value-at-Risk
Stéphane Crépey, Noufel Frikha, Azar Louzi +1
Crépey, Frikha, and Louzi (2025) introduced a multilevel stochastic approximation scheme to compute the value-at-risk of a financial loss that is only simulatable by Monte Carlo. T…
q-fin.RM2023
Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall
Stéphane Crépey, Noufel Frikha, Azar Louzi +1
Crépey, Frikha, and Louzi (2025) introduced a nested stochastic approximation algorithm and its multilevel acceleration to compute the value-at-risk and expected shortfall of a ran…