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The NovoGrad Optimizer was first proposed in [Stochastic Gradient

Methods with Layerwise Adaptvie Moments for training of Deep Networks](

NovoGrad is a first-order SGD-based algorithm, which computes second moments per layer instead of per weight as in Adam. Compared to Adam, NovoGrad takes less memory, and has been found to be more numerically stable. More specifically we compute (for more information on the computation please refer to this link:

Second order moment = exponential moving average of Layer-wise square of grads: v_t <-- beta2 * v{t-1} + (1-beta_2) * (g_t)^2 First order moment in one of four modes:

1. moment of grads normalized by v_t:
    m_t <- beta_1 * m_{t-1} + [ g_t / (sqrt(v_t)+epsilon)]
2. moment similar to Adam: exponential moving average of grads
normalized by v_t (set grad_averaging = True to use this):
    m_t <- beta_1 * m_{t-1} +
           [(1 - beta_1) * (g_t / (sqrt(v_t) + epsilon))]
3. weight decay adds a w_d term after grads are rescaled by
1/sqrt(v_t) (set weight_decay > 0 to use this0:
    m_t <- beta_1 * m_{t-1} +
           [(g_t / (sqrt(v_t) + epsilon)) + (w_d * w_{t-1})]
4. weight decay + exponential moving average from Adam:
    m_t <- beta_1 * m_{t-1} +
           [(1 - beta_1) * ((g_t / (sqrt(v_t + epsilon)) +
           (w_d * w_{t-1}))]

Weight update: wt <- w{t-1} - lr_t * m_t

Example of usage:

opt = tfa.optimizers.NovoGrad(


  • learning_rate: A Tensor or a floating point value. or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule The learning rate.
  • beta_1: A float value or a constant float tensor. The exponential decay rate for the 1st moment estimates.
  • beta_2: A float value or a constant float tensor. The exponential decay rate for the 2nd moment estimates.
  • epsilon: A small constant for numerical stability.
  • weight_decay: A floating point value. Weight decay for each param.
  • grad_averaging: determines whether to use Adam style exponential moving averaging for the first order moments.
  • **kwargs: keyword arguments. Allowed to be {clipnorm, clipvalue, lr, decay}. clipnorm is clip gradients by norm; clipvalue is clip gradients by value, decay is included for backward compatibility to allow time inverse decay of learning rate. lr is included for backward compatibility, recommended to use learning_rate instead.


  • iterations: Variable. The number of training steps this Optimizer has run.
  • weights: Returns variables of this Optimizer based on the order created.



Add a new slot variable for var.



Apply gradients to variables.

This is the second part of minimize(). It returns an Operation that applies gradients.


  • grads_and_vars: List of (gradient, variable) pairs.
  • name: Optional name for the returned operation. Default to the name passed to the Optimizer constructor.


An Operation that applies the specified gradients. The iterations will be automatically increased by 1.


  • TypeError: If grads_and_vars is malformed.
  • ValueError: If none of the variables have gradients.


Creates an optimizer from its config.

This method is the reverse of get_config, capable of instantiating the same optimizer from the config dictionary.


  • config: A Python dictionary, typically the output of get_config.
  • custom_objects: A Python dictionary mapping names to additional Python objects used to create this optimizer, such as a function used for a hyperparameter.


An optimizer instance.


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Returns the config of the optimimizer.

An optimizer config is a Python dictionary (serializable) containing the configuration of an optimizer. The same optimizer can be reinstantiated later (without any saved state) from this configuration.


Python dictionary.


Returns gradients of loss with respect to params.


  • loss: Loss tensor.
  • params: List of variables.


List of gradient tensors.


  • ValueError: In case any gradient cannot be computed (e.g. if gradient function not implemented).



A list of names for this optimizer's slots.




Minimize loss by updating var_list.

This method simply computes gradient using tf.GradientTape and calls apply_gradients(). If you want to process the gradient before applying then call tf.GradientTape and apply_gradients() explicitly instead of using this function.


  • loss: A callable taking no arguments which returns the value to minimize.
  • var_list: list or tuple of Variable objects to update to minimize loss, or a callable returning the list or tuple of Variable objects. Use callable when the variable list would otherwise be incomplete before minimize since the variables are created at the first time loss is called.
  • grad_loss: Optional. A Tensor holding the gradient computed for loss.
  • name: Optional name for the returned operation.


An Operation that updates the variables in var_list. The iterations will be automatically increased by 1.


  • ValueError: If some of the variables are not Variable objects.


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Returns variables of this Optimizer based on the order created.