We perform theoretical analysis for a previously proposed method of enhancing performance of an evolutionary algorithm with reinforcement learning. The method adaptively chooses between auxiliary objectives in a single-objective evolutionary algorithm using reinforcement learning. We consider the Q-learning algorithm with ε-greedy strategy (ε > 0), using a benchmark problem based on ONEMAX. For the evolutionary algorithm, we consider the Random Local Search. In our setting, ONEMAX problem should be solved in the presence of the obstructive ZEROMAX objective. This benchmark tests the ability of the reinforcement learning algorithm to ignore such an inefficient objective. It was previously shown that in the case of the greedy strategy (ε = 0), the considered algorithm performs on the described benchmark problem in the best possible time for a conventional evolutionary algorithm. However, the ε-greedy strategy appears to perform in exponential time. Furthermore, every selection algorithm which selects an inefficient auxiliary objective with probability of at least δ is shown to be asymptotically inefficient when δ > 0 is a constant.