Stochastic proximal ADMM for stochastic tensor Tucker optimization with deterministic constraints

Leveraging Tucker low-rank decomposition for dimensionality reduction and over-fitting mitigation, this study investigates stochastic tensor Tucker optimization problems subject to deterministic constraints, with an emphasis on designing a Stochastic Proximal Alternating Direction Method of Multipliers (SPADMM). Instead of treating the underlying polynomial structures as general smooth nonlinear functions, we introduce block conservative functions based on the tensor Tucker decomposition, and further analyse the convergence rate and high probability performance for the proposed stochastic algorithm. Both numerical tests and background/foreground separation experiments demonstrate that our approach is promising in time efficiency and solution accuracy.