In a stochastic gradient$-$based meta$-$learning algorithm for optimizing the hyperparameters of a neural

network, consider a dynamic system where the loss function $L$($ltheta$)$$ is non$-$convex and defined as a

weighted sum of multiple sub$-$loss functions over time $$t$$$.$ Assume the weight decay parameter

$lalpha$($t$)$$ follows a cyclic schedule. The total loss over a period of $$T$$ iterations is given by the integral:

$[$L$\_\{|$text$\{$total$\}\}=\backslash$int$\_0^$T L$(|$theta$($t$))$ dt$,]$where$[$L$(\backslash$theta$($t$))=$ gamma $t$ delta $\frac{\frac{?}{?}}{?}$ cdot

$|$theta$($t$)^1\mathrm{.}5$