Before revision:  Minimum Excess Risk (MER) in Bayesian learning is defined as the difference between the minimum expected loss achievable when learning from data and the minimum expected loss that could be achieved if the underlying parameter W was observed.
After revision: In parametric Bayesian learning, a prior is assumed on the parameter W which determines the distribution of samples. In this setting, Minimum Excess Risk (MER) in Bayesian learning is defined as the difference between the minimum expected loss achievable when learning from data and the minimum expected loss that could be achieved if the underlying parameter W was observed.