  This paper addresses the pointing acquisition phase of the Laser
Interferometer Space Antenna (LISA) mission as a guidance problem. It is
formulated in a cooperative game setup, which solution is a sequence of
corrections that can be used as a tracking reference to align all the
spacecraft' laser beams simultaneously within the tolerances required for
gravitational wave detection. We propose a model-free learning algorithm based
on residual-feedback and momentum, for accelerated convergence to stable
solutions, i.e. Nash Equilibria. Each spacecraft has 4 degrees of freedom, and
the only measured output considered are laser misalignments with the local
interferometer sensors. Simulation results demonstrate that the proposed
strategy manages to achieve absolute misalignment errors $<1\mu$rad in a timely
manner.
