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In this paper, we propose AsyncQVI, an asynchronous-parallel Q-valueiteration for discounted Markov decision processes whose transition and rewardcan only be sampled through a generative model. Given such a problem with$|\mathcal{S}|$ states, $|\mathcal{A}|$ actions, and a discounted factor$\gamma\in(0,1)$, AsyncQVI uses memory of size $\mathcal{O}(|\mathcal{S}|)$ andreturns an $\varepsilon$-optimal policy with probability at least $1-\delta$using$$\tilde{\mathcal{O}}\big(\frac{|\mathcal{S}||\mathcal{A}|}{(1-\gamma)^5\varepsilon^2}\log(\frac{1}{\delta})\big)$$samples. AsyncQVI is also the first asynchronous-parallel algorithm fordiscounted Markov decision processes that has a sample complexity, which nearlymatches the theoretical lower bound. The relatively low memory footprint andparallel ability make AsyncQVI suitable for large-scale applications. Innumerical tests, we compare AsyncQVI with four sample-based value iterationmethods. The results show that our algorithm is highly efficient and achieveslinear parallel speedup.

AsyncQVI: Asynchronous-Parallel Q-Value Iteration for Discounted Markov Decision Processes with Near-Optimal Sample Complexity