  Reward allocation, also known as the credit assignment problem, has been an
important topic in economics, engineering, and machine learning. An important
concept in reward allocation is the core, which is the set of stable
allocations where no agent has the motivation to deviate from the grand
coalition. In previous works, computing the core requires either knowledge of
the reward function in deterministic games or the reward distribution in
stochastic games. However, this is unrealistic, as the reward function or
distribution is often only partially known and may be subject to uncertainty.
In this paper, we consider the core learning problem in stochastic cooperative
games, where the reward distribution is unknown. Our goal is to learn the
expected core, that is, the set of allocations that are stable in expectation,
given an oracle that returns a stochastic reward for an enquired coalition each
round. Within the class of strictly convex games, we present an algorithm named
\texttt{Common-Points-Picking} that returns a point in the expected core given
a polynomial number of samples, with high probability. To analyse the
algorithm, we develop a new extension of the separation hyperplane theorem for
multiple convex sets.
