  One of the most interesting features of Bayesian optimization for direct
policy search is that it can leverage priors (e.g., from simulation or from
previous tasks) to accelerate learning on a robot. In this paper, we are
interested in situations for which several priors exist but we do not know in
advance which one fits best the current situation. We tackle this problem by
introducing a novel acquisition function, called Most Likely Expected
Improvement (MLEI), that combines the likelihood of the priors and the expected
improvement. We evaluate this new acquisition function on a transfer learning
task for a 5-DOF planar arm and on a possibly damaged, 6-legged robot that has
to learn to walk on flat ground and on stairs, with priors corresponding to
different stairs and different kinds of damages. Our results show that MLEI
effectively identifies and exploits the priors, even when there is no obvious
match between the current situations and the priors.
