title: Effect of --oaa 2 and --loss_function=logistic in Vowpal Wabbit
body: <p>What parameters should I use in VW for a binary classification task? For example, let's use <a href="https://github.com/JohnLangford/vowpal_wabbit/blob/master/test/train-sets/rcv1_small.dat" rel="nofollow">rcv1_small.dat</a>. I <a href="https://github.com/JohnLangford/vowpal_wabbit/wiki/Loss-functions#which-loss-function-should-i-use" rel="nofollow">thought</a> it is better to use the logistic loss function (or hinge) and it makes no sense to use <code>--oaa 2</code>. However, the empirical results (with progressive validation 0/1 loss reported in all 4 experiments) show that best combination is <code>--oaa 2</code> without logistic loss (i.e. with the default squared loss):</p>
  
  <pre><code>cd vowpal_wabbit/test/train-sets
  
  cat rcv1_small.dat | vw --binary
  # average loss = 0.0861
  
  cat rcv1_small.dat | vw --binary --loss_function=logistic
  # average loss = 0.0909
  
  cat rcv1_small.dat | sed 's/^-1/2/' | vw --oaa 2
  # average loss = 0.0857
  
  cat rcv1_small.dat | sed 's/^-1/2/' | vw --oaa 2 --loss_function=logistic
  # average loss = 0.0934
  </code></pre>
  
  <p>My primary question is: <strong>Why <code>--oaa 2</code> does not give exactly the same results as <code>--binary</code></strong> (in the above setting)<strong>?</strong></p>
  
  <p>My secondary questions are: Why optimizing the logistic loss does not improve the 0/1 loss (compared to optimizing the default square loss)? Is this a specific of this particular dataset?</p>