Geometrically Coupled Monte Carlo Sampling

Monte Carlo sampling in high-dimensional, low-sample settings is important in many machine learning tasks. We improve current methods for sampling in Euclidean spaces by avoiding independence, and instead consider ways to couple samples. We show fundamental connections to optimal transport theory, leading to novel sampling algorithms, and providing new theoretical grounding for existing strategies. We compare our new strategies against prior methods for improving sample efficiency, including QMC, by studying discrepancy. We explore our findings empirically, and observe benefits of our sampling schemes for reinforcement learning and generative modelling.

Authors

• Mark Rowland
• Krzysztof Choromanski Google Brain
• François Chalus Credit Suisse
• Aldo Pacchiano
• Tamas Sarlos Google Research
• Richard Turner
• Adrian Weller The Alan Turing Institute University of Cambridge

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