  This paper investigates the problem of decentralized resource allocation in
the presence of Byzantine attacks. Such attacks occur when an unknown number of
malicious agents send random or carefully crafted messages to their neighbors,
aiming to prevent the honest agents from reaching the optimal resource
allocation strategy. We characterize these malicious behaviors with the
classical Byzantine attacks model, and propose a class of Byzantine-resilient
decentralized resource allocation algorithms augmented with dual-domain
defenses. The honest agents receive messages containing the (possibly
malicious) dual variables from their neighbors at each iteration, and filter
these messages with robust aggregation rules. Theoretically, we prove that the
proposed algorithms can converge to neighborhoods of the optimal resource
allocation strategy, given that the robust aggregation rules are properly
designed. Numerical experiments are conducted to corroborate the theoretical
results.
