  We discuss an online decentralized decision making problem where the agents
are coupled with affine inequality constraints. Alternating Direction Method of
Multipliers (ADMM) is used as the computation engine and we discuss the
convergence of the algorithm in an online setting. To be specific, when
decisions have to be made sequentially with a fixed time step, there might not
be enough time for the ADMM to converge before the scenario changes and the
decision needs to be updated. In this case, a suboptimal solution is employed
and we analyze the optimality gap given the convergence condition. Moreover, in
many cases, the decision making problem changes gradually over time. We propose
a warm-start scheme to accelerate the convergence of ADMM and analyze the
benefit of the warm-start. The proposed method is demonstrated in a
decentralized multiagent control barrier function problem with simulation.
