Summary: IEEE TRANSACTIONS ON AUTOMATIC CONTROL, YOLo AC-31, NO.9, SEPTEMBER1986 803
JOHN N. TSITSIKLIS, MEMBER,IEEE,DIMITRI P. BERTSEKAS, FELLOW,IEEE,ANDMICHAEL ATHANS, FELLOW,IEEE
Abstract-We presenta model for asynchronousdistributed computa-
tion and then proceedto analyze the convergenceof natural asynchron-
ous distributed versions of a large classof deterministic and stochastic
gradient-like algorithms. Wc show that such algorithms retain the
desirable convergenceproperties of their centralized counterparts, pro-
vided that the time betweenconsecutiveinterprocessor communications
and the communication delaysare not too large.
M ANY deterministic andstochasticiterative algorithms admit
a natural distributed implementation [IJ, [3J-[5J, [7J
whereby severalprocessorsperform computationsand exchange
messageswith the end-goalof minimizing a certain costfunction.
If all processorscommunicateto each other their partial results at
each instanceof time and perform computations synchronously,
the distributed algorithm is mathematically equivalentto a single
processor(serial) algorithm and its convergence may be studied
by conventional means. Synchronous algorithms may have,
however, certain drawbacks, which have beendiscussedin [9J.