  In this paper, we consider groups of agents in a network that select actions
in order to satisfy a set of constraints that vary arbitrarily over time and
minimize a time-varying function of which they have only local observations.
The selection of actions, also called a strategy, is causal and decentralized,
i.e., the dynamical system that determines the actions of a given agent depends
only on the constraints at the current time and on its own actions and those of
its neighbors. To determine such a strategy, we propose a decentralized saddle
point algorithm and show that the corresponding global fit and regret are
bounded by functions of the order of $\sqrt{T}$. Specifically, we define the
global fit of a strategy as a vector that integrates over time the global
constraint violations as seen by a given node. The fit is a performance loss
associated with online operation as opposed to offline clairvoyant operation
which can always select an action if one exists, that satisfies the constraints
at all times. If this fit grows sublinearly with the time horizon it suggests
that the strategy approaches the feasible set of actions. Likewise, we define
the regret of a strategy as the difference between its accumulated cost and
that of the best fixed action that one could select knowing beforehand the time
evolution of the objective function. Numerical examples support the theoretical
conclusions.
