Before revision:  The lower bound represents the minimum possible excess risk achievable by any process using R bits of information from the parameter W. For the upper bound, the optimization is further constrained to use R bits from the training set, a setting which relates MER to information-theoretic bounds on the generalization gap in frequentist learning.
After revision:  The lower bound represents the minimum possible excess risk achievable by any process using R bits of information from the parameter W. For the upper bound, the optimization is further constrained to use R bits from the training set, a setting which relates MER to information-theoretic bounds on the generalization gap in frequentist learning.