  Value methods for solving stochastic games with partial observability model
the uncertainty about states of the game as a probability distribution over
possible states. The dimension of this belief space is the number of states.
For many practical problems, for example in security, there are exponentially
many possible states which causes an insufficient scalability of algorithms for
real-world problems. To this end, we propose an abstraction technique that
addresses this issue of the curse of dimensionality by projecting
high-dimensional beliefs to characteristic vectors of significantly lower
dimension (e.g., marginal probabilities). Our two main contributions are (1)
novel compact representation of the uncertainty in partially observable
stochastic games and (2) novel algorithm based on this compact representation
that is based on existing state-of-the-art algorithms for solving stochastic
games with partial observability. Experimental evaluation confirms that the new
algorithm over the compact representation dramatically increases the
scalability compared to the state of the art.
