Adding Policy Tree

[OliverSchacht]

• Documentation is extended in 4. Heterogeneous Treatment Effects.
• Example for Policy Tree is added.
• fixing output errors for the example notebooks

[SvenKlaassen]

• False Heading level 4.4.3. This should be 4.5. Please use:
  Policy Learning with Trees
  +++++++++++++++++++++++

• Please add more explanation before the formula. E.g. Explain how a policy is defined

$$\pi: X\mapsto \{0,1\},$$

what is optimized/maximized etc.
Remark that this is a deterministic policy.

[SvenKlaassen]

• Please use
  $$
  \begin{aligned}
  Y_i & = g(W_1,W_2)T_i + \langle W_i,\gamma_0\rangle + \epsilon_i \
  T_i & = \langle W_i,\beta_0\rangle +\eta_i,
  \end{aligned}
  $$
  to display the alignment. Can you also adjust this in the GATE and CATE Notebook?

• Please use print() for pandas.DataFrame

• Please add more interpretation to the results. Why is it helpful that we know the true DGP? What is the ATTE for the policy

[OliverSchacht]

Hi @SvenKlaassen
thank you for your comments. I made the following changes:

• Extend the policy tree notebook, especially making comparisons between original DGP and estimated splits as well as comparison of original ATTE and optimal policy ATTE
• Extend documentation of Policy Tree optimization problem.