class_docstr: AdaDelta optimizer.
  
  Parameters
  ----------
  rho
  eps
  
  Attributes
  ----------
  g2 : collections.defaultdict
  s2 : collections.defaultdict
  
  Examples
  --------
  
  >>> from river import datasets
  >>> from river import evaluate
  >>> from river import linear_model
  >>> from river import metrics
  >>> from river import optim
  >>> from river import preprocessing
  
  >>> dataset = datasets.Phishing()
  >>> optimizer = optim.AdaDelta()
  >>> model = (
  ...     preprocessing.StandardScaler() |
  ...     linear_model.LogisticRegression(optimizer)
  ... )
  >>> metric = metrics.F1()
  
  >>> evaluate.progressive_val_score(dataset, model, metric)
  F1: 80.56%
  
  References
  ----------
  [^1]: [Zeiler, M.D., 2012. Adadelta: an adaptive learning rate method. arXiv preprint arXiv:1212.5701.](https://arxiv.org/pdf/1212.5701.pdf)
code: def _step_with_dict(self, w, g):
      for i, gi in g.items():
          # Accumulate the gradient
          self.g2[i] = self.rho * self.g2[i] + (1 - self.rho) * gi**2
  
          # Compute the update
          step = -self._rms(self.s2[i]) / self._rms(self.g2[i]) * gi
  
          # Accumulate the update
          self.s2[i] = (
              self.rho * self.s2[i] + (1 - self.rho) * step**2
          )
  
          # Apply the update
          w[i] += step
  
      return w
  
file_path: river/river/optim/ada_delta.py
imports: from __future__ import annotations
  import collections
  from river import optim
label_desc: Use image node_id 3 for calling the AdaDelta obj's underlying member method code with example usage: obj._step_with_dict(w, g) and returns: w