Updated repo README

README.md

@@ -1,5 +1,10 @@
 # `adawhatever`
-A collection of various stochastic gradient descent (SGD) solvers implemented in MATLAB.
+A collection of various stochastic gradient descent (SGD) solvers implemented in MATLAB:
+* Vanilla SGD
+* AdaGrad (vanilla / with decay)
+* Adadelta
+* Adam
+* Adamax
 
 ## Introduction
 Stochastic gradient descent is a state of the art optimisation method in machine learning. It suits the concept of learning on many data points very well and outperforms many _theoretically_ superior second-order methods.
@@ -12,5 +17,16 @@ Furthermore, 'classic' optimisation terms are used instead of machine learning l
 * hyperparameters ~ solver parameters
 
 ## How to use it
+All solvers require the stochastic gradient of the objective `sg`, initial value of the decision variables `x0`, number of iterations `nIter` and the indices of the stochastic gradient that should be used at each iteration `idxSG`. Furthermore, each solver requires its specific solver parameters. See MATLAB documentation and references for further details.
 
-TODO :warning:
+The solver function returns a matrix with the `i`-th guess of the decision variables in the `i+1`-th column (first column contains `x0`).
+
+A typical solver calling script would look like this:
+```matlab
+gs = @<stochastic gradient function>;
+x0 = [0; 0; 0; 0];
+nIter = 500;
+idxSG = randi(<number of stochastic gradients>, 1, nIter);
+
+xMat = <solver>(gs, x0, nIter, idxSG, <solver parameters>);
+```