  We define and study the problem of predicting the solution to a linear
program (LP) given only partial information about its objective and
constraints. This generalizes the problem of learning to predict the purchasing
behavior of a rational agent who has an unknown objective function, that has
been studied under the name "Learning from Revealed Preferences". We give
mistake bound learning algorithms in two settings: in the first, the objective
of the LP is known to the learner but there is an arbitrary, fixed set of
constraints which are unknown. Each example is defined by an additional known
constraint and the goal of the learner is to predict the optimal solution of
the LP given the union of the known and unknown constraints. This models the
problem of predicting the behavior of a rational agent whose goals are known,
but whose resources are unknown. In the second setting, the objective of the LP
is unknown, and changing in a controlled way. The constraints of the LP may
also change every day, but are known. An example is given by a set of
constraints and partial information about the objective, and the task of the
learner is again to predict the optimal solution of the partially known LP.
