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Tensor decompositions have become a central tool in machine learning to extract interpretable patterns from multiway arrays of data. However, computing the approximate Canonical Polyadic Decomposition (aCPD), one of the most important tensor decomposition model, remains a challenge. In this work, we propose several algorithms based on extrapolation that improve over existing alternating methods for aCPD.

Stochastic mirror descent (SMD) algorithms have recently garnered a great deal of attention in optimization, signal processing, and machine learning. They are similar to stochastic gradient descent (SGD), in that they perform updates along the negative gradient of an instantaneous (or stochastically chosen) loss function. However, rather than update the parameter (or weight) vector directly, they update it in a "mirrored" domain whose transformation is given by the gradient of a strictly convex differentiable potential function.

We consider an oligopoly dynamic pricing problem where the demand model is unknown and the sellers have different marginal costs. We formulate the problem as a repeated game with incomplete information. We develop a dynamic pricing strategy that leads to a Pareto-efficient and subgame-perfect equilibrium and offers a bounded regret over an infinite horizon, where regret is defined as the expected cumulative profit loss as compared to the ideal scenario with a known demand model.

We present an extension of recent semidefinite programming formulations for atomic decomposition over continuous dictionaries, with applications to continuous or 'gridless' compressed sensing. The dictionary considered in this paper is defined in terms of a general matrix pencil and is parameterized by a complex variable that varies over a segment of a line or circle in the complex plane. The main result of the paper is the formulation as a convex semidefinite optimization problem, and a simple constructive proof of the equivalence.