Iterative distributed optimization algorithms involve multiple agents that communicate with each other, over time, in order to minimize/maximize a global objective. In the presence of unreliable communication networks, the Age-of-Information (AoI), which measures the freshness of data received, may be large and hence hinder algorithmic convergence. In this paper, we study the convergence of general distributed gradient-based optimization algorithms in the presence of communication that neither happens periodically nor at stochastically independent points in time. We show that convergence is guaranteed provided the random variables associated with the AoI processes are stochastically dominated by a random variable with finite first moment. This improves on previous requirements of boundedness of more than the first moment. We then introduce stochastically strongly connected (SSC) networks, a new stochastic form of strong connectedness for time-varying networks. We show: If for any $p \ge0$ the processes that describe the success of communication between agents in a SSC network are $\alpha$-mixing with $n^{p-1}\alpha(n)$ summable, then the associated AoI processes are stochastically dominated by a random variable with finite $p$-th moment. In combination with our first contribution, this implies that distributed stochastic gradient descend converges in the presence of AoI, if $\alpha(n)$ is summable.

We present sufficient conditions that ensure convergence of the multi-agent Deep Deterministic Policy Gradient (DDPG) algorithm. It is an example of one of the most popular paradigms of Deep Reinforcement Learning (DeepRL) for tackling continuous action spaces: the actor-critic paradigm. In the setting considered herein, each agent observes a part of the global state space in order to take local actions, for which it receives local rewards. For every agent, DDPG trains a local actor (policy) and a local critic (Q-function). The analysis shows that multi-agent DDPG using neural networks to approximate the local policies and critics converge to limits with the following properties: The critic limits minimize the average squared Bellman loss; the actor limits parameterize a policy that maximizes the local critic's approximation of $Q_i^*$, where $i$ is the agent index. The averaging is with respect to a probability distribution over the global state-action space. It captures the asymptotics of all local training processes. Finally, we extend the analysis to a fully decentralized setting where agents communicate over a wireless network prone to delays and losses; a typical scenario in, e.g., robotic applications.