Dual-arm manipulation is an area of growing interest in the robotics community. Enabling robots to perform tasks that require the coordinated use of two arms, is essential for complex manipulation tasks such as handling large objects, assembling components, and performing human-like interactions. However, achieving effective dual-arm manipulation is challenging due to the need for precise coordination, dynamic adaptability, and the ability to manage interaction forces between the arms and the objects being manipulated. We propose a novel pipeline that combines the advantages of policy learning based on environment feedback and gradient-based optimization to learn controller gains required for the control outputs. This allows the robotic system to dynamically modulate its impedance in response to task demands, ensuring stability and dexterity in dual-arm operations. We evaluate our pipeline on a trajectory-tracking task involving a variety of large, complex objects with different masses and geometries. The performance is then compared to three other established methods for controlling dual-arm robots, demonstrating superior results. Project page: https://dualarmvil.github.io/Dual-Arm-VIL/