A Latent Variational Framework for Stochastic Optimization

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

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Philippe Casgrain


This paper provides a unifying theoretical framework for stochastic optimization algorithms by means of a latent stochastic variational problem. Using techniques from stochastic control, the solution to the variational problem is shown to be equivalent to that of a Forward Backward Stochastic Differential Equation (FBSDE). By solving these equations, we recover a variety of existing adaptive stochastic gradient descent methods. This framework establishes a direct connection between stochastic optimization algorithms and a secondary latent inference problem on gradients, where a prior measure on gradient observations determines the resulting algorithm.