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# tf.compat.v1.train.sdca_optimizer

Distributed version of Stochastic Dual Coordinate Ascent (SDCA) optimizer for

linear models with L1 + L2 regularization. As global optimization objective is strongly-convex, the optimizer optimizes the dual objective at each step. The optimizer applies each update one example at a time. Examples are sampled uniformly, and the optimizer is learning rate free and enjoys linear convergence rate.

Proximal Stochastic Dual Coordinate Ascent.
Shai Shalev-Shwartz, Tong Zhang. 2012

$$Loss Objective = \sum f_{i} (wx_{i}) + (l2 / 2) * |w|^2 + l1 * |w|$$

Adding vs. Averaging in Distributed Primal-Dual Optimization.
Chenxin Ma, Virginia Smith, Martin Jaggi, Michael I. Jordan, Peter Richtarik, Martin Takac. 2015

Stochastic Dual Coordinate Ascent with Adaptive Probabilities.
Dominik Csiba, Zheng Qu, Peter Richtarik. 2015

sparse_example_indices A list of Tensor objects with type int64. a list of vectors which contain example indices.
sparse_feature_indices A list with the same length as sparse_example_indices of Tensor objects with type int64. a list of vectors which contain feature indices.
sparse_feature_values A list of Tensor objects with type float32. a list of vectors which contains feature value associated with each feature group.
dense_features A list of Tensor objects with type float32. a list of matrices which contains the dense feature values.
example_weights A Tensor of type float32. a vector which contains the weight associated with each example.
example_labels A Tensor of type float32. a vector which contains the label/target associated with each example.
sparse_indices A list with the same length as sparse_example_indices of Tensor objects with type int64. a list of vectors where each value is the indices which has corresponding weights in sparse_weights. This field maybe omitted for the dense approach.
sparse_weights A list with the same length as sparse_example_indices of Tensor objects with type float32. a list of vectors where each value is the weight associated with a sparse feature group.
dense_weights A list with the same length as dense_features of Tensor objects with type float32. a list of vectors where the values are the weights associated with a dense feature group.
example_state_data A Tensor of type float32. a list of vectors containing the example state data.
loss_type A string from: "logistic_loss", "squared_loss", "hinge_loss", "smooth_hinge_loss", "poisson_loss". Type of the primal loss. Currently SdcaSolver supports logistic, squared and hinge losses.
l1 A float. Symmetric l1 regularization strength.
l2 A float. Symmetric l2 regularization strength.
num_loss_partitions An int that is >= 1. Number of partitions of the global loss function.
num_inner_iterations An int that is >= 1. Number of iterations per mini-batch.
adaptative An optional bool. Defaults to True. Whether to use Adaptive SDCA for the inner loop.
name A name for the operation (optional).

A tuple of Tensor objects (out_example_state_data, out_delta_sparse_weights, out_delta_dense_weights).
out_example_state_data A Tensor of type float32.
out_delta_sparse_weights A list with the same length as sparse_example_indices of Tensor objects with type float32.
out_delta_dense_weights A list with the same length as dense_features of Tensor objects with type float32.

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