Optical metasurfaces are becoming increasingly popular as optical components for shaping the amplitude, phase, and polarization of light. Currently, most of these devices are passive in nature and cannot be dynamically reconfigured or optimized according to the user's requirements or changes in the environment. Yet, Existing active control designs often come with a trade-off, where either the amplitude is compromised to control the phase, or the phase control sacrifices the amplitude. These designs are not optimal for achieving high-performance active wavefront control. In this work, we propose and innovative design strategy that harnesses the power of topological singularities - specifically, zeros and poles of the reflection coefficient - to achieve full phase modulation of light reflected from an arbitrary active metasurface with near-unity efficiency. Our active metasurface unit cells consist of asymmetric Gires-Tournois resonators filled with either silicon or heterostructured materials that take advantage of either the thermo-optical or electro-optical effects. Both cases yield full phase modulation with 100% reflection amplitude, even when dealing with very low refractive index changes of around ∆n ≈ 0.01. Furthermore, by utilizing advanced optimization methodologies that rely on statistical learning and considering the near-field coupling between strongly resonant pixels and the nonlocal response, we improve the beam-deflection efficiencies for each deflection angle. This has led to the optimization of active beam-steering designs with ultimate performance exceeding 90% for the thermo-optical effect. Additionally, the optimization of active wavefront shaping using ultrafast electro-optic control has achieved near-92% modulation performance. These high-efficiency active beam-forming techniques operating at high frequencies would open important applications in imaging microscopy, high-resolution image projection, optical communication, and 3D light detection and ranging (LiDAR).