In this paper, we present a design method for a wideband non-uniformly spaced linear array (NUSLA), with both symmetric and asymmetric geometries, using the modified reinforcement learning algorithm (MORELA). We designed a cost function that provided freedom to the beam pattern by setting limits only on the beam width (BW) and side-lobe level (SLL) in order to satisfy the desired BW and SLL in the wide band. We added the scan angle condition to the cost function to design the scanned beam pattern, as the ability to scan a beam in the desired direction is important in various applications. In order to prevent possible pointing angle errors for asymmetric NUSLA, we employed a penalty function to ensure the peak at the desired direction. Modified reinforcement learning algorithm (MORELA), which is a reinforcement learning-based algorithm used to determine a global optimum of the cost function, is applied to optimize the spacing and weights of the NUSLA by minimizing the proposed cost function. The performance of the proposed scheme was verified by comparing it with that of existing heuristic optimization algorithms via computer simulations.