Source code for pennylane.optimize.rms_prop

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[docs]class RMSPropOptimizer(AdagradOptimizer): r"""Root mean squared propagation optimizer. The root mean square progation optimizer is a modified :class:Adagrad optimizer <pennylane.optmimize.AdagradOptimizer>, with a decay of learning rate adaptation. Extensions of the Adagrad optimization method generally start the sum :math:a over past gradients in the denominator of the learning rate at a finite :math:t' with :math:0 < t' < t, or decay past gradients to avoid an ever-decreasing learning rate. Root Mean Square propagation is such an adaptation, where .. math:: a_i^{(t+1)} = \gamma a_i^{(t)} + (1-\gamma) (\partial_{x_i} f(x^{(t)}))^2. Args: stepsize (float): the user-defined hyperparameter :math:\eta used in the Adagrad optmization decay (float): the learning rate decay :math:\gamma eps (float): offset :math:\epsilon added for numerical stability (see :class:Adagrad <pennylane.optmimize.AdagradOptimizer>) """ def __init__(self, stepsize=0.01, decay=0.9, eps=1e-8): super().__init__(stepsize) self.decay = decay self.eps = eps
[docs] def apply_grad(self, grad, x): r"""Update the variables x to take a single optimization step. Flattens and unflattens the inputs to maintain nested iterables as the parameters of the optimization. Args: grad (array): The gradient of the objective function at point :math:x^{(t)}: :math:\nabla f(x^{(t)}) x (array): the current value of the variables :math:x^{(t)} Returns: array: the new values :math:x^{(t+1)} """ grad_flat = list(_flatten(grad)) x_flat = _flatten(x) if self.accumulation is None: self.accumulation = [(1 - self.decay) * g*g for g in grad_flat] else: self.accumulation = [self.decay*a + (1-self.decay)*g*g for a, g in zip(self.accumulation, grad_flat)] x_new_flat = [e - (self._stepsize / np.sqrt(a + self.eps)) * g for a, g, e in zip(self.accumulation, grad_flat, x_flat)] return unflatten(x_new_flat, x)