Accurate, high-dimensional, multiphase optimization is increasingly required across industries such as aerospace, energy, and manufacturing to enhance performance and safety in complex fluid interactions. Shock bubble interaction (SBI) serves as a prime example of such a challenging, multiphase phenomenon, where optimizing SBI dynamics and understanding their sensitivity to initial conditions are crucial for advancements in shock mitigation, flow control, and energy applications. Differentiable fluid dynamics, enabled by automatic differentiation (AD), offers a seamless integration of computational fluid dynamics (CFD) and machine learning (ML), creating highly efficient and scalable optimization frameworks for addressing the intricacies of multiphase flow problems. We employ an open-source, fully-compressible solver JAX-Fluids1,2, an AD-based, differentiable CFD framework, to investigate and optimize SBI, emphasizing the value of AD compared to traditional gradient-based methods. While conventional approaches like adjoint optimization often require complex mathematical derivation and are challenging to implement, AD-based optimization offers an efficient, easy-to-use approach. This allows us to perform sensitivity analysis and optimization, precisely quantifying the influence of parameters such as shock Mach number and initial bubble eccentricity on transmitted and reflected shock intensities. Our findings demonstrate the robustness and versatility of AD-based optimization, establishing a scalable and practical framework for sensitivity analysis and optimization within differentiable fluid dynamics. This is an extension of our previous study of AD-based flow control and optimization for single-phase flow3. This work provides a foundation for broader industrial applications of AD-integrated CFD in multiphase flow challenges, reinforcing the potential of differentiable fluid dynamics in advancing fluid mechanics and engineering solutions.