Distributed optimization has important applications in the practical implementation of machine learning and signal processing setup by providing means to allow interconnected network of processors to work towards the optimization of a global objective with intermittent communication. Existing works on distributed optimization predominantly assume all the processors storing related data to perform updates for the optimization task in each iteration. However, such optimization processes are typically executed at shared computing/data centers along with other concurrent tasks. Therefore, it is necessary to develop efficient distributed optimization methods that possess the flexibility to share the computing resources with other ongoing tasks. In this work, we propose a new first-order framework that allows for this flexibility through a probabilistic computing resource allocation strategy while guaranteeing the satisfactory performance of distributed optimization. Our results, both analytical and numerical, show that by controlling a flexibility parameter, our suite of algorithms (designed for various scenarios) can achieve the lower computation and communication costs of distributed optimization than their inflexible counterparts. This framework also enables the fair sharing of the common resources with other concurrent tasks being processed by the processing network.
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