Large Batch Optimization

# LAMB

Introduced by You et al. in Large Batch Optimization for Deep Learning: Training BERT in 76 minutes

LAMB is a a layerwise adaptive large batch optimization technique. It provides a strategy for adapting the learning rate in large batch settings. LAMB uses Adam as the base algorithm and then forms an update as:

$$r_{t} = \frac{m_{t}}{\sqrt{v_{t}} + \epsilon}$$ $$x_{t+1}^{\left(i\right)} = x_{t}^{\left(i\right)} - \eta_{t}\frac{\phi\left(|| x_{t}^{\left(i\right)} ||\right)}{|| m_{t}^{\left(i\right)} || }\left(r_{t}^{\left(i\right)}+\lambda{x_{t}^{\left(i\right)}}\right)$$

Unlike LARS, the adaptivity of LAMB is two-fold: (i) per dimension normalization with respect to the square root of the second moment used in Adam and (ii) layerwise normalization obtained due to layerwise adaptivity.

#### Papers

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