Sharp Time-Data Tradeoffs for Linear Inverse Problems

• Published in: IEEE transactions on information theory Vol. 64; no. 6; pp. 4129 - 4158
• Main Authors: Oymak, Samet, Recht, Benjamin, Soltanolkotabi, Mahdi
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Complexity theory; Convergence; Cost function; Economic models; Empirical analysis; Inverse problems; Least squares; linear inverse problems; Noise measurement; noncovex and nonsmooth optimization; Penalty function; Phase transitions; Prediction algorithms; projected gradient descent; run time prediction of optimization algorithms; Time-data tradeoffs; Tradeoffs; Transition points

In this paper, we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a penalty function. We present a unified convergence analysis...