Energy Harvesting technology contributes significantly to green cellular networking by ensuring self-sustainability and extinguishing environmental hazards. Due to the imbalance between the harvested energy and traffic load of the base stations (BSs), energy cooperation has become a crucial requirement. However, the decision of optimal energy cooperation among the BSs in a multi-operator cellular network is a challenging task due to the consideration of various factors, such as cost, loss of energy, future information of traffic load, and harvested energy of the BSs, etc. The two conflicting objectives are minimizing the energy buying cost and the loss of energy while transferring through the power links. In this work, we present an optimal energy cooperation framework, formulated as a multi-objective linear programming (MOLP) problem which brings a trade-off between the two above-mentioned conflicting objectives considering the harvested energy and load of the BSs at future time slots. For the prediction of harvested energy of the BSs, we develop a Deep Q-Learning-based prediction method that intelligently increases measurement accuracy through continuous exploration and exploitation. The results of simulation experiments carried out in MATLAB depict that the proposed multi-operator energy cooperation framework outperforms state-of-the-art works in terms of cost, performance, and energy-loss reduction.