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declearn.optimizer.modules.RMSPropModule

Bases: OptiModule

Root Mean Square Propagation (RMSProp) module.

This module implements the following algorithm:

Init(beta, eps):
    state = 0
Step(grads, step):
    state = beta*state + (1-beta)*(grads**2)
    grads /= (sqrt(state) + eps)

In other words, gradients (i.e. indirectly the learning rate) are scaled down by the square-root of the momentum-corrected sum of the past squared gradients. See reference [1].

References

[1] Tieleman and Hinton, 2012. Lecture 6.5-rmsprop: Divide the Gradient by a Running Average of its Recent Magnitude.

Source code in declearn/optimizer/modules/_adaptive.py 
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class RMSPropModule(OptiModule):
    """Root Mean Square Propagation (RMSProp) module.

    This module implements the following algorithm:

        Init(beta, eps):
            state = 0
        Step(grads, step):
            state = beta*state + (1-beta)*(grads**2)
            grads /= (sqrt(state) + eps)

    In other words, gradients (i.e. indirectly the learning rate)
    are scaled down by the square-root of the momentum-corrected
    sum of the past squared gradients. See reference [1].

    References
    ----------
    [1] Tieleman and Hinton, 2012.
        Lecture 6.5-rmsprop: Divide the Gradient by a Running
        Average of its Recent Magnitude.
    """

    name: ClassVar[str] = "rmsprop"

    def __init__(
        self,
        beta: float = 0.9,
        eps: float = 1e-7,
    ) -> None:
        """Instantiate the RMSProp gradients-adaptation module.

        Parameters
        ----------
        beta: float
            Beta parameter for the momentum correction
            applied to the adaptive scaling term.
        eps: float, default=1e-7
            Numerical-stability improvement term, added
            to the (divisor) adapative scaling term.
        """
        self.ewma = EWMAModule(beta=beta)
        self.eps = eps

    def get_config(
        self,
    ) -> Dict[str, Any]:
        return {"beta": self.ewma.beta, "eps": self.eps}

    def run(
        self,
        gradients: Vector,
    ) -> Vector:
        v_t = self.ewma.run(gradients**2)
        scaling = (v_t**0.5) + self.eps
        return gradients / scaling

    def get_state(
        self,
    ) -> Dict[str, Any]:
        return self.ewma.get_state()

    def set_state(
        self,
        state: Dict[str, Any],
    ) -> None:
        self.ewma.set_state(state)

__init__(beta=0.9, eps=1e-07)

Instantiate the RMSProp gradients-adaptation module.

Parameters:

Name Type Description Default
beta float

Beta parameter for the momentum correction applied to the adaptive scaling term.

 0.9
eps float

Numerical-stability improvement term, added to the (divisor) adapative scaling term.

 1e-07
Source code in declearn/optimizer/modules/_adaptive.py 
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def __init__(
    self,
    beta: float = 0.9,
    eps: float = 1e-7,
) -> None:
    """Instantiate the RMSProp gradients-adaptation module.

    Parameters
    ----------
    beta: float
        Beta parameter for the momentum correction
        applied to the adaptive scaling term.
    eps: float, default=1e-7
        Numerical-stability improvement term, added
        to the (divisor) adapative scaling term.
    """
    self.ewma = EWMAModule(beta=beta)
    self.eps = eps