Employing large antenna arrays is a key characteristic of millimeter wave (mmWave) and terahertz communication systems. However, due to the adoption of fully analog or hybrid analog/digital architectures, as well as non-ideal hardware or arbitrary/unknown array geometries, the accurate channel state information becomes hard to acquire. This impedes the design of beamforming/combining vectors that are crucial to fully exploit the potential of large-scale antenna arrays in providing sufficient receive signal power. In this paper, we develop a novel framework that leverages deep reinforcement learning (DRL) and a Wolpertinger-variant architecture and learns how to iteratively optimize the beam pattern (shape) for serving one or a small set of users relying only on the receive power measurements and without requiring any explicit channel knowledge. The proposed model accounts for key hardware constraints such as the phase-only, constant-modulus, and quantized-angle constraints. Further, the proposed framework can efficiently optimize the beam patterns for systems with non-ideal hardware and for arrays with unknown or arbitrary array geometries. Simulation results show that the developed solution is capable of finding near-optimal beam patterns based only on the receive power measurements.