  Tackling multi-agent learning problems efficiently is a challenging task in
continuous action domains. While value-based algorithms excel in sample
efficiency when applied to discrete action domains, they are usually
inefficient when dealing with continuous actions. Policy-based algorithms, on
the other hand, attempt to address this challenge by leveraging critic networks
for guiding the learning process and stabilizing the gradient estimation. The
limitations in the estimation of true return and falling into local optima in
these methods result in inefficient and often sub-optimal policies. In this
paper, we diverge from the trend of further enhancing critic networks, and
focus on improving the effectiveness of value-based methods in multi-agent
continuous domains by concurrently evaluating numerous actions. We propose a
novel multi-agent value-based algorithm, Mixed Q-Functionals (MQF), inspired
from the idea of Q-Functionals, that enables agents to transform their states
into basis functions. Our algorithm fosters collaboration among agents by
mixing their action-values. We evaluate the efficacy of our algorithm in six
cooperative multi-agent scenarios. Our empirical findings reveal that MQF
outperforms four variants of Deep Deterministic Policy Gradient through rapid
action evaluation and increased sample efficiency.
