Learning Rate Schedules

# Cosine Annealing

Introduced by Loshchilov et al. in SGDR: Stochastic Gradient Descent with Warm Restarts

Cosine Annealing is a type of learning rate schedule that has the effect of starting with a large learning rate that is relatively rapidly decreased to a minimum value before being increased rapidly again. The resetting of the learning rate acts like a simulated restart of the learning process and the re-use of good weights as the starting point of the restart is referred to as a "warm restart" in contrast to a "cold restart" where a new set of small random numbers may be used as a starting point.

$$\eta_{t} = \eta_{min}^{i} + \frac{1}{2}\left(\eta_{max}^{i}-\eta_{min}^{i}\right)\left(1+\cos\left(\frac{T_{cur}}{T_{i}}\pi\right)\right)$$

Where where $\eta_{min}^{i}$ and $\eta_{max}^{i}$ are ranges for the learning rate, and $T_{cur}$ account for how many epochs have been performed since the last restart.

Text Source: Jason Brownlee

Image Source: Gao Huang

#### Papers

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