In this work, we propose a data-driven approach for real-time self-collision avoidance in multi-arm systems. The approach consists of modeling the regions in joint-space that lead to collisions via a Self-Collision Avoidance (SCA) boundary and use it as a constraint for a centralized Inverse Kinematics (IK) solver. This problem is particularly challenging as the dimensionality of the joint-configurations is in the order of millions (for a dual-arm system), while the IK solver must run within a control loop of 2ms. Hence, an extremely sparse solution is needed for this big data problem. The SCA region is modeled through a sparse non-linear kernel classification method that yields a runtime of less than 2ms (on a single thread CPU process) and has a False Positive Rate (FPR)=1.5%. Code for generating multi-arm datasets and learning the sparse SCA boundary are available at: https://github.com/nbfigueroa/SCA-Boundary-Learning