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Deep Q-Networks algorithm (DQN) was the first reinforcement learning algorithm using deep neural network to successfully surpass human level performance in a number of Atari learning environments. However, divergent and unstable behaviour have been long standing issues in DQNs. The unstable behaviour is often characterised by overestimation in the Q -values, commonly referred to as the overestimation bias. To address the overestimation bias and the divergent behaviour, a number of heuristic extensions have been proposed. Notably, multi-step updates have been shown to drastically reduce unstable behaviour while improving agent's training performance. However, agents are often highly sensitive to the selection of the multi-step update horizon (n), and our empirical experiments show that a poorly chosen static value for n can in many cases lead to worse performance than single-step DQN. Inspired by the success of n -step DQN and the effects that multi-step updates have on overestimation bias, this paper proposes a new algorithm that we call 'Elastic Step DQN' (ES-DQN) to alleviate overestimation bias in DQNs. ES-DQN dynamically varies the step size horizon in multi-step updates based on the similarity between states visited. Our empirical evaluation shows that ES-DQN out-performs n -step with fixed n updates, Double DQN and Average DQN in several OpenAI Gym environments while at the same time alleviating the overestimation bias. [ABSTRACT FROM AUTHOR]