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Asynchronous stochastic approximations (SAs) are an important class ofmodel-free algorithms, tools and techniques that are popular in multi-agent anddistributed control scenarios. To counter Bellman's curse of dimensionality,such algorithms are coupled with function approximations. Although thelearning/ control problem becomes more tractable, function approximationsaffect stability and convergence. In this paper, we present verifiablesufficient conditions for stability and convergence of asynchronous SAs withbiased approximation errors. The theory developed herein is used to analyzePolicy Gradient methods and noisy Value Iteration schemes. Specifically, weanalyze the asynchronous approximate counterparts of the policy gradient (A2PG)and value iteration (A2VI) schemes. It is shown that the stability of thesealgorithms is unaffected by biased approximation errors, provided they areasymptotically bounded. With respect to convergence (of A2VI and A2PG), arelationship between the limiting set and the approximation errors isestablished. Finally, experimental results are presented that support thetheory.

Asynchronous stochastic approximations with asymptotically biased errors and deep multi-agent learning