Abstract-The problem of output optimization within a specified input space of neural networks (NNs) with fixed weights is discussed in this paper. The problem is (highly) nonlinear when nonlinear activation functions are used. This global optimization problem is encountered in the reinforcement learning (RL) community. Interval analysis is applied to guarantee that all solutions are found to any degree of accuracy with guaranteed bounds. The major drawbacks of interval analysis, i.e., dependency effect and high-computational load, are both present for the problem of NN output optimization. Taylor models (TMs) are introduced to reduce these drawbacks. They have excellent convergence properties for small intervals. However, the dependency effect still remains and is even made worse when evaluating large input do-