Tackling overestimation in Q-learning is an important problem that has been extensively studied in single-agent reinforcement learning, but has received comparatively little attention in the multi-agent setting. In this work, we empirically demonstrate that QMIX, a popular Q-learning algorithm for cooperative multiagent reinforcement learning (MARL), suffers from a more severe overestimation in practice than previously acknowledged, and is not mitigated by existing approaches. We rectify this with a novel regularization-based update scheme that penalizes large joint action-values that deviate from a baseline and demonstrate its effectiveness in stabilizing learning. Furthermore, we propose to employ a softmax operator, which we efficiently approximate in a novel way in the multiagent setting, to further reduce the potential overestimation bias. Our approach, Regularized Softmax (RES) Deep Multi-Agent Q-Learning, is general and can be applied to any Q-learning based MARL algorithm. We demonstrate that, when applied to QMIX, RES avoids severe overestimation and significantly improves performance, yielding state-of-the-art results in a variety of cooperative multi-agent tasks, including the challenging StarCraft II micromanagement benchmarks.

Neural networks have a smooth initial inductive bias, such that small changes in input do not lead to large changes in output. However, in reinforcement learning domains with sparse rewards, value functions have non-smooth structure with a characteristic asymmetric discontinuity whenever rewards arrive. We propose a mechanism that learns an interpolation between a direct value estimate and a projected value estimate computed from the encountered reward and the previous estimate. This reduces the need to learn about discontinuities, and thus improves the value function approximation. Furthermore, as the interpolation is learned and state-dependent, our method can deal with heterogeneous observability. We demonstrate that this one change leads to significant improvements on multiple Atari games, when applied to the state-of-the-art A3C algorithm.

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