101. Compressed Regression over Adaptive Networks
- Author
-
Carpentiero, Marco, Matta, Vincenzo, and Sayed, Ali H.
- Subjects
Signal Processing (eess.SP) ,FOS: Computer and information sciences ,Computer Science - Machine Learning ,Optimization and Control (math.OC) ,Statistics - Machine Learning ,FOS: Electrical engineering, electronic engineering, information engineering ,FOS: Mathematics ,Machine Learning (stat.ML) ,Computer Science - Multiagent Systems ,Electrical Engineering and Systems Science - Signal Processing ,Mathematics - Optimization and Control ,Machine Learning (cs.LG) ,Multiagent Systems (cs.MA) - Abstract
In this work we derive the performance achievable by a network of distributed agents that solve, adaptively and in the presence of communication constraints, a regression problem. Agents employ the recently proposed ACTC (adapt-compress-then-combine) diffusion strategy, where the signals exchanged locally by neighboring agents are encoded with randomized differential compression operators. We provide a detailed characterization of the mean-square estimation error, which is shown to comprise a term related to the error that agents would achieve without communication constraints, plus a term arising from compression. The analysis reveals quantitative relationships between the compression loss and fundamental attributes of the distributed regression problem, in particular, the stochastic approximation error caused by the gradient noise and the network topology (through the Perron eigenvector). We show that knowledge of such relationships is critical to allocate optimally the communication resources across the agents, taking into account their individual attributes, such as the quality of their data or their degree of centrality in the network topology. We devise an optimized allocation strategy where the parameters necessary for the optimization can be learned online by the agents. Illustrative examples show that a significant performance improvement, as compared to a blind (i.e., uniform) resource allocation, can be achieved by optimizing the allocation by means of the provided mean-square-error formulas., This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible
- Published
- 2023