Abstract
In this letter, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the incremental proximal gradient algorithm. We explicitly model the update rules of the incremental proximal gradient method and develop a systematic approach to propagate the uncertainty of the solution estimate over iterations. The PIPG algorithm takes the form of Bayesian filtering updates for a state-space model constructed by using the cost function. Our framework makes it possible to utilize well-known exact or approximate Bayesian filters, such as Kalman or extended Kalman filters, to solve large-scale regularized optimization problems.
Original language | English |
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Article number | 8755451 |
Pages (from-to) | 1257-1261 |
Number of pages | 5 |
Journal | IEEE Signal Processing Letters |
Volume | 26 |
Issue number | 8 |
Early online date | 4 Jul 2019 |
DOIs | |
Publication status | Published - 1 Aug 2019 |
Keywords / Materials (for Non-textual outputs)
- extended Kalman filtering
- Probabilistic optimization
- proximal algorithms
- stochastic gradient