One general approach to addressing the domain adaptation problem is to assign instance-dependent weights to the loss function when minimizing the expected loss over the distribution of data. To see why instance weighting may help, let us first briefly review the empirical risk minimization framework for standard supervised learning (Vapnik, 1999), and then informally derive an instance weighting solution to domain adaptation. Let be a model family from which we want to select an optimal model for our classification task. Let
be a loss function. Strictly speaking, we want to minimize the following objective function in order to obtain the optimal model for the distribution :
Now consider the setting of domain adaptation. Ideally, we want to find an optimal model for the target domain that minimizes the expected loss over the target distribution:
It is not possible to compute the exact value of for a pair , especially because we do not have enough labeled instances in the target domain. Section reviews one line of work in which is assumed, while Section reviews another line of work in which is assumed.