Descent With Approximate Multipliers is Enough: Generalising Max-Weight

Víctor Valls; Douglas J. Leith

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arXiv · 1511.02517

Descent With Approximate Multipliers is Enough: Generalising Max-Weight

Víctor Valls·Douglas J. Leith

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Abstract

We study the use of approximate Lagrange multipliers and discrete actions in solving convex optimisation problems. We observe that descent, which can be ensured using a wide range of approaches (gradient, subgradient, Newton, etc.), is orthogonal to the choice of multipliers. Using the Skorokhod representation for a queueing process we show that approximate multipliers can be constructed in a number of ways. These observations lead to the generalisation of (i) essentially any descent method to encompass use of discrete actions and queues and (ii) max-weight scheduling to encompass new descent methods including those with unsynchronised updates such as block coordinate descent. This also allows consideration of communication delays and of updates at varying time-scales within the same clean and consistent framework.

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BibTeX RIS

Víctor Valls, Douglas J. Leith. 2015-11-08. Descent With Approximate Multipliers is Enough: Generalising Max-Weight. https://arxiv.org/abs/1511.02517

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