  Loss minimization is a dominant paradigm in machine learning, where a
predictor is trained to minimize some loss function that depends on an
uncertain event (e.g., "will it rain tomorrow?''). Different loss functions
imply different learning algorithms and, at times, very different predictors.
While widespread and appealing, a clear drawback of this approach is that the
loss function may not be known at the time of learning, requiring the algorithm
to use a best-guess loss function. We suggest a rigorous new paradigm for loss
minimization in machine learning where the loss function can be ignored at the
time of learning and only be taken into account when deciding an action.
  We introduce the notion of an (${\mathcal{L}},\mathcal{C}$)-omnipredictor,
which could be used to optimize any loss in a family ${\mathcal{L}}$. Once the
loss function is set, the outputs of the predictor can be post-processed (a
simple univariate data-independent transformation of individual predictions) to
do well compared with any hypothesis from the class $\mathcal{C}$. The post
processing is essentially what one would perform if the outputs of the
predictor were true probabilities of the uncertain events. In a sense,
omnipredictors extract all the predictive power from the class $\mathcal{C}$,
irrespective of the loss function in $\mathcal{L}$.
  We show that such "loss-oblivious'' learning is feasible through a connection
to multicalibration, a notion introduced in the context of algorithmic
fairness. In addition, we show how multicalibration can be viewed as a solution
concept for agnostic boosting, shedding new light on past results. Finally, we
transfer our insights back to the context of algorithmic fairness by providing
omnipredictors for multi-group loss minimization.
