Cosine LR Schedule

Compute the cosine-annealed learning rate at step t of T: ${\eta }_{\min }+\frac{1}{2}({\eta }_0-{\eta }_{\min })(1+\cos (\pi t\mathrm{/}T))\backslash eta\_\{\backslash min\}+\backslash tfrac12(\backslash eta\_0-\backslash eta\_\{\backslash min\})\backslash big(1+\backslash cos(\backslash pi\; t/T)\backslash big)$. t is clamped to $[0,T][0,T]$; if T <= 0 the rate is min_lr.

Implement solve(lr0, min_lr, t, T).

Returns. Return the learning rate as a float, starting at lr0 for $t=0t=0$ and ending at min_lr for $t=Tt=T$.

Examples

Example 1

Input:

solve(5.0, 1.0, 0, 10)

Output:

5.0

Example 2

Input:

solve(5.0, 1.0, 5, 10)

Output:

3.0

Example 3

Input:

solve(5.0, 1.0, 10, 10)

Output:

1.0