adam-one-step — Coinbase case

Coinbase-inspired fraud-model training service is validating an Adam optimizer implementation before running longer experiments. You need to perform the first Adam update (all moments start at zero) from the supplied parameters, gradient, learning rate and hyperparameters.

Perform the first Adam update, starting from zero moments ($m_0=v_0=0m\_0=v\_0=0$, step $t=1t=1$): $m=(1-{\beta }_1)gm=(1-\backslash beta\_1)g$, $v=(1-{\beta }_2)g^{2}v=(1-\backslash beta\_2)g^2$, bias-correct them, and return $\theta -\eta \widehat{m}\mathrm{/}(\sqrt{\widehat{v}}+\epsilon )\backslash theta-\backslash eta\backslash ,\backslash hat\; m/(\backslash sqrt\{\backslash hat\; v\}+\backslash varepsilon)$.

Implement solve(theta,g,lr,b1,b2,eps).

Returns. Return the updated parameters as a NumPy array.

Examples

Example 1

Input:

solve([1.0, 2.0], [0.5, -1.0], 0.1, 0.9, 0.999, 1e-8)

Output:

[0.9, 2.1]

Example 2

Input:

solve([1.0], [0.0], 0.1, 0.9, 0.999, 1e-8)

Output:

[1.0]