Abstract | ||
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Although Q-learning is one of the most successful algorithms for finding the best action-value function (and thus the optimal policy) in reinforcement learning, its implementation often suffers from large overestimation of Q-function values incurred by random sampling. The double Q-learning algorithm proposed in~\citet{hasselt2010double} overcomes such an overestimation issue by randomly switching the update between two Q-estimators, and has thus gained significant popularity in practice. However, the theoretical understanding of double Q-learning is rather limited. So far only the asymptotic convergence has been established, which does not characterize how fast the algorithm converges. In this paper, we provide the first non-asymptotic (i.e., finite-time) analysis for double Q-learning. We show that both synchronous and asynchronous double Q-learning are guaranteed to converge to an $\epsilon$-accurate neighborhood of the global optimum by taking $\tilde{\Omega}\left(\left( \frac{1}{(1-\gamma)^6\epsilon^2}\right)^{\frac{1}{\omega}} +\left(\frac{1}{1-\gamma}\right)^{\frac{1}{1-\omega}}\right)$ iterations, where $\omega\in(0,1)$ is the decay parameter of the learning rate, and $\gamma$ is the discount factor. Our analysis develops novel techniques to derive finite-time bounds on the difference between two inter-connected stochastic processes, which is new to the literature of stochastic approximation. |
Year | Venue | DocType |
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2020 | NIPS 2020 | Conference |
Volume | Citations | PageRank |
33 | 0 | 0.34 |
References | Authors | |
0 | 4 |
Name | Order | Citations | PageRank |
---|---|---|---|
Huaqing Xiong | 1 | 1 | 1.37 |
Lin Zhao | 2 | 26 | 3.99 |
Yingbin Liang | 3 | 1646 | 147.64 |
Wei Zhang | 4 | 236 | 33.77 |