  We present a new approach to the problems of evaluating and learning
personalized decision policies from observational data of past contexts,
decisions, and outcomes. Only the outcome of the enacted decision is available
and the historical policy is unknown. These problems arise in personalized
medicine using electronic health records and in internet advertising. Existing
approaches use inverse propensity weighting (or, doubly robust versions) to
make historical outcome (or, residual) data look like it were generated by a
new policy being evaluated or learned. But this relies on a plug-in approach
that rejects data points with a decision that disagrees with the new policy,
leading to high variance estimates and ineffective learning. We propose a new,
balance-based approach that too makes the data look like the new policy but
does so directly by finding weights that optimize for balance between the
weighted data and the target policy in the given, finite sample, which is
equivalent to minimizing worst-case or posterior conditional mean square error.
Our policy learner proceeds as a two-level optimization problem over policies
and weights. We demonstrate that this approach markedly outperforms existing
ones both in evaluation and learning, which is unsurprising given the wider
support of balance-based weights. We establish extensive theoretical
consistency guarantees and regret bounds that support this empirical success.
