code: def adagrad(loss_or_grads, params, learning_rate=1.0, epsilon=1e-6):
      """Adagrad updates
  
      Scale learning rates by dividing with the square root of accumulated
      squared gradients. See [1]_ for further description.
  
      Parameters
      ----------
      loss_or_grads : symbolic expression or list of expressions
          A scalar loss expression, or a list of gradient expressions
      params : list of shared variables
          The variables to generate update expressions for
      learning_rate : float or symbolic scalar
          The learning rate controlling the size of update steps
      epsilon : float or symbolic scalar
          Small value added for numerical stability
  
      Returns
      -------
      OrderedDict
          A dictionary mapping each parameter to its update expression
  
      Notes
      -----
      Using step size eta Adagrad calculates the learning rate for feature i at
      time step t as:
  
      .. math:: \\eta_{t,i} = \\frac{\\eta}
         {\\sqrt{\\sum^t_{t^\\prime} g^2_{t^\\prime,i}+\\epsilon}} g_{t,i}
  
      as such the learning rate is monotonically decreasing.
  
      Epsilon is not included in the typical formula, see [2]_.
  
      References
      ----------
      .. [1] Duchi, J., Hazan, E., & Singer, Y. (2011):
             Adaptive subgradient methods for online learning and stochastic
             optimization. JMLR, 12:2121-2159.
  
      .. [2] Chris Dyer:
             Notes on AdaGrad. http://www.ark.cs.cmu.edu/cdyer/adagrad.pdf
      """
  
      grads = get_or_compute_grads(loss_or_grads, params)
      updates = OrderedDict()
  
      for param, grad in zip(params, grads):
          value = param.get_value(borrow=True)
          accu = theano.shared(
              np.zeros(value.shape, dtype=value.dtype),
              broadcastable=param.broadcastable,
          )
          accu_new = accu + grad**2
          updates[accu] = accu_new
          updates[param] = param - (
              learning_rate * grad / T.sqrt(accu_new + epsilon)
          )
  
      return updates
  
file_path: Lasagne/lasagne/updates.py
imports: from collections import OrderedDict
  import numpy
  import theano
  import theano.tensor
  from .None import utils
label_desc: Use image node_id 7 for calling a global function with example usage: adagrad(loss_or_grads, params, learning_rate, epsilon) and returns: updates