LostTech.TensorFlow : API Documentation

Construct a new Adam optimizer.

Initialization:

$$m_0 := 0 \text{(Initialize initial 1st moment vector)}$$ $$v_0 := 0 \text{(Initialize initial 2nd moment vector)}$$ $$t := 0 \text{(Initialize timestep)}$$

The update rule for `variable` with gradient `g` uses an optimization described at the end of section 2 of the paper:

$$t := t + 1$$ $$lr_t := \text{learning\_rate} * \sqrt{1 - beta_2^t} / (1 - beta_1^t)$$

$$m_t := beta_1 * m_{t-1} + (1 - beta_1) * g$$ $$v_t := beta_2 * v_{t-1} + (1 - beta_2) * g * g$$ $$variable := variable - lr_t * m_t / (\sqrt{v_t} + \epsilon)$$

The default value of 1e-8 for epsilon might not be a good default in general. For example, when training an Inception network on ImageNet a current good choice is 1.0 or 0.1. Note that since AdamOptimizer uses the formulation just before Section 2.1 of the Kingma and Ba paper rather than the formulation in Algorithm 1, the "epsilon" referred to here is "epsilon hat" in the paper.

The sparse implementation of this algorithm (used when the gradient is an IndexedSlices object, typically because of tf.gather or an embedding lookup in the forward pass) does apply momentum to variable slices even if they were not used in the forward pass (meaning they have a gradient equal to zero). Momentum decay (beta1) is also applied to the entire momentum accumulator. This means that the sparse behavior is equivalent to the dense behavior (in contrast to some momentum implementations which ignore momentum unless a variable slice was actually used).