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On the Convergence and Sample Complexity Analysis of Deep Q-Networks with $\epsilon$-Greedy Exploration
Shuai Zhang · Hongkang Li · Meng Wang · Miao Liu · Pin-Yu Chen · Songtao Lu · Sijia Liu · Keerthiram Murugesan · Subhajit Chaudhury

Tue Dec 12 08:45 AM -- 10:45 AM (PST) @ Great Hall & Hall B1+B2 #1419
This paper provides a theoretical understanding of deep Q-Network (DQN) with the $\varepsilon$-greedy exploration in deep reinforcement learning.Despite the tremendous empirical achievement of the DQN, its theoretical characterization remains underexplored.First, the exploration strategy is either impractical or ignored in the existing analysis. Second, in contrast to conventional Q-learning algorithms, the DQN employs the target network and experience replay to acquire an unbiased estimation of the mean-square Bellman error (MSBE) utilized in training the Q-network. However,the existing theoretical analysis of DQNs lacks convergence analysis or bypasses the technical challenges by deploying a significantly overparameterized neural network, which is not computationally efficient. This paper provides the first theoretical convergence and sample complexity analysis of the practical setting of DQNs with $\epsilon$-greedy policy. We prove an iterative procedure with decaying $\epsilon$ converges to the optimal Q-value function geometrically. Moreover, a higher level of $\epsilon$ values enlarges the region of convergence but slows down the convergence, while the opposite holds for a lower level of $\epsilon$ values. Experiments justify our established theoretical insights on DQNs.

Author Information

Shuai Zhang (New Jersey Institute of Technology)
Hongkang Li (Rensselaer Polytechnic Institute)
Meng Wang (Rensselaer Polytechnic Institute (RPI))
Miao Liu (IBM)
Pin-Yu Chen (IBM Research)
Songtao Lu (IBM Thomas J. Watson Research Center)
Sijia Liu (Michigan State University)
Keerthiram Murugesan (IBM Research)
Subhajit Chaudhury (International Business Machines)

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