Ilya Loshchilov

Ilya Loshchilov is a researcher in optimization and machine learning whose work with Frank Hutter includes SGDR and AdamW. His Freiburg institutional profile identifies the same author and lists the two papers; it is an alumni record, rather than evidence of a current appointment.^[ref]

Their 2017 SGDR paper introduced a learning rate schedule that decreases the rate along a cosine curve, then raises it at a warm restart while retaining the current parameters. In one cycle,Here $u$ is elapsed cycle progress and $T$ its length. With ${\eta }_{\min }=0$ and ${\eta }_{\max }=0.1$, the rates at $u=0,T/2,T$ are $0.1,0.05,0$. Raising the rate starts another exploration from the learned parameters; it does not reinitialize the model.^[ref]

Their 2019 AdamW work separates decoupled weight decay from the gradient-based update. For ordinary gradient descent, adding $\lambda \Vert \theta {\Vert }^2/2$ gives ${\theta }^{\prime }=(1-\eta \lambda )\theta -\eta g$. Coordinate-dependent scaling can act differently on the penalty contribution, so that equivalence does not extend unchanged to an adaptive gradient method.^[ref] Writing the equation makes the contribution clearer than comparing optimizer names alone.