Demon Adam is a stochastic optimizer where the Demon momentum rule is applied to the Adam optimizer.

$\beta\_{t} = \beta\_{init}\cdot\frac{\left(1-\frac{t}{T}\right)}{\left(1-\beta\_{init}\right) + \beta\_{init}\left(1-\frac{t}{T}\right)}$

$m\_{t, i} = g\_{t, i} + \beta\_{t}m\_{t-1, i}$

$v\_{t+1} = \beta\_{2}v\_{t} + \left(1-\beta\_{2}\right)g^{2}\_{t}$

$\theta_{t} = \theta_{t-1} - \eta\frac{\hat{m}\_{t}}{\sqrt{\hat{v}\_{t}} + \epsilon}$