In this paper we consider distributed optimization problems over a multi-agent network, where each agent can only partially evaluate the objective function, and it is allowed to exchange messages with its immediate neighbors. Differently from all existing works on distributed optimization, our focus is given to optimizing a class of non-convex problems, and under the challenging setting where each agent can only access the zeroth-order information (i.e., the functional values) of its local functions. For different types of network topologies such as undirected connected networks or star networks, we develop efficient distributed algorithms and rigorously analyze their convergence and rate of convergence (to the set of stationary solutions). Numerical results are provided to demonstrate the efficiency of the proposed algorithms. Furthermore, for given J independent samples of {(φ j , ξ j )} J j=1 , we defineḠ µ (z, φ, ξ) as the sample average:ḠLemma 1 [34, Lemma 4.2] Suppose that Assumption A holds true for function ψ : R Q → R. Then we have the followingwhereσ 2 := 2Q[K 2 + σ 2 + µ 2L2 Q].

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Deep Reinforcement Learning has made significant progress in multi-agent systems in recent years. In this review article, we have mostly focused on recent papers on Multi-Agent Reinforcement Learning (MARL) than the older papers, unless it was necessary. Several ideas and papers are proposed with different notations, and we tried our best to unify them with a single notation and categorize them by their relevance. In particular, we have focused on five common approaches on modeling and solving multi-agent reinforcement learning problems: (I) independent-learners, (II) fully observable critic, (III) value function decomposition, (IV) consensus, (IV) learn to communicate. Moreover, we discuss some new emerging research areas in MARL along with the relevant recent papers. In addition, some of the recent applications of MARL in real world are discussed. Finally, a list of available environments for MARL research are provided and the paper is concluded with proposals on the possible research directions.

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