Numerical optimization is arguably the most prominent computational framework in machine learning and AI. It can be seen as an assembly language for hard combinatorial problems ranging from classification and regression in learning, to computing optimal policies and equilibria in decision theory, to entropy minimization in information sciences. Unfortunately, specifying such problems in complex domains involving relations, objects and other logical dependencies is cumbersome at best, requiring considerable expert knowledge, and solvers require models to be painstakingly reduced to standard forms. To overcome this, we introduce a rich modeling framework for optimization problems that allows convenient codification of symbolic structure. Rather than reducing this symbolic structure to a sparse or dense matrix, we represent and exploit it directly using algebraic decision diagrams (ADDs). Combining efficient ADD-based matrix-vector algebra with a matrix-free interior-point method, we develop an engine that can fully leverage the structure of symbolic representations to solve convex linear and quadratic optimization problems. We demonstrate the flexibility of the resulting symbolic-numeric optimizer on decision making and compressed sensing tasks with millions of non-zero entries.
|Title of host publication||Proceedings of The Thirty-First AAAI Conference on Artificial Intelligence (AAAI-17)|
|Number of pages||7|
|Publication status||Published - 12 Feb 2017|
|Event||Thirty-First AAAI Conference on Artificial Intelligence - San Francisco, United States|
Duration: 4 Feb 2017 → 9 Feb 2017
|Conference||Thirty-First AAAI Conference on Artificial Intelligence|
|Period||4/02/17 → 9/02/17|