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Teradata Vantage is a platform for integrating a broad range of analytical functions and capabilities with the Teradata's SQL engine. One of the main challenges in optimizing the execution of these analytical functions is that many of them are not only black boxes, but also have polymorphic nature, i.e., their behavior and properties may change depending on the invocation context. In this paper, we first demonstrate the inherent complexity in optimizing polymorphic functions, and then present the Vantage's Collaborative Optimizer , which is a cross-platform optimizer designed for optimizing the analytical functions invoked from within the SQL engine. The Collaborative Optimizer is the industry-first effort towards enabling analytics-aware optimizations over polymorphic analytical functions. We present a novel markup language-based approach for expressing the functions' polymorphic properties via a set of well-defined instructions. The Collaborative Optimizer uses these instructions at query time to infer the corresponding properties, and then decide on the applicable optimizations. From several possible optimizations, we showcase two core optimizations, namely "projection push" and "predicate push" , which aim at optimizing the data movement to and from the analytical functions. The experiments using the Teradata-MLE analytical system demonstrate the expressiveness power and flexibility of the proposed markup language. Moreover, benchmark and real-world customer queries show the significant performance gain that the Collaborative Optimizer brings to the Vantage system.