Year: 2016
Type: preprint
Abstract: A recent trend in probabilistic inference emphasizes the codification of models in a formal syntax, with suitable high-level features such as individuals, relations, and connectives, enabling descriptive clarity, succinctness and circumventing the need for the modeler to engineer a custom solver. Unfortunately, bringing these linguistic and pragmatic benefits to numerical optimization has proven surprisingly challenging. In this paper, we turn to these challenges: we introduce a rich modeling language, for which an interior-point method computes approximate solutions in a generic way. While logical features easily complicates the underlying model, often yielding intricate dependencies, we exploit and cache local structure using algebraic decision diagrams (ADDs). Indeed, standard matrix-vector algebra is efficiently realizable in ADDs, but we argue and show that well-known optimization methods are not ideal for ADDs. Our engine, therefore, invokes a sophisticated matrix-free approach. We demonstrate the flexibility of the resulting symbolic-numeric optimizer on decision making and compressed sensing tasks with millions of non-zero entries.
Source: arXiv (Cornell University)
Institutions: TU Dortmund University, KU Leuven
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G617271991
OpenAlex ID: W2962708207