Tensor Completion via Integer Optimization

Xin Chen; Sukanya Kudva; Yongzheng Dai; Anil Aswani; Chen Chen

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arXiv · 2402.05141

Tensor Completion via Integer Optimization

Xin Chen·Sukanya Kudva·Yongzheng Dai·Anil Aswani·Chen Chen

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Abstract

The main challenge with the tensor completion problem is a fundamental tension between computation power and the information-theoretic sample complexity rate. Past approaches either achieve the information-theoretic rate but lack practical algorithms to compute the corresponding solution, or have polynomial-time algorithms that require an exponentially-larger number of samples for low estimation error. This paper develops a novel tensor completion algorithm that resolves this tension by achieving both provable convergence (in numerical tolerance) in a linear number of oracle steps and the information-theoretic rate. Our approach formulates tensor completion as a convex optimization problem constrained using a gauge-based tensor norm, which is defined in a way that allows the use of integer linear optimization to solve linear separation problems over the unit-ball in this new norm. Adaptations based on this insight are incorporated into a Frank-Wolfe variant to build our algorithm. We show our algorithm scales-well using numerical experiments on tensors with up to ten million entries.

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BibTeX RIS

Xin Chen, Sukanya Kudva, Yongzheng Dai, Anil Aswani, Chen Chen. 2024-02-06. Tensor Completion via Integer Optimization. https://arxiv.org/abs/2402.05141

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