A Bayesian Variational Framework for Stochastic Optimization

05/05/2019

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by   Philippe Casgrain, et al.

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This work proposes a theoretical framework for stochastic optimization algorithms, based on a continuous Bayesian variational model for algorithms. Using techniques from stochastic control with asymmetric information, the solution to this variational problem is shown to be equivalent to a system of Forward Backward Differential Equations (FBSDEs). Using an analytical approximation to the solution of these FBSDEs, we recover a variety of existing adaptive stochastic gradient descent methods. This framework establishes a direct connection between stochastic optimization algorithms and a secondary Bayesian inference problem on gradients, where the prior and assumed observation dynamics determine the resulting algorithm.