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Recently, extensive studies on photonic reinforcement learning to acceleratethe process of calculation by exploiting the physical nature of light have beenconducted. Previous studies utilized quantum interference of photons to achievecollective decision-making without choice conflicts when solving thecompetitive multi-armed bandit problem, a fundamental example of reinforcementlearning. However, the bandit problem deals with a static environment where theagent's action does not influence the reward probabilities. This study aims toextend the conventional approach to a more general multi-agent reinforcementlearning targeting the grid world problem. Unlike the conventional approach,the proposed scheme deals with a dynamic environment where the reward changesbecause of agents' actions. A successful photonic reinforcement learning schemerequires both a photonic system that contributes to the quality of learning anda suitable algorithm. This study proposes a novel learning algorithm,discontinuous bandit Q-learning, in view of a potential photonicimplementation. Here, state-action pairs in the environment are regarded asslot machines in the context of the bandit problem and an updated amount ofQ-value is regarded as the reward of the bandit problem. We perform numericalsimulations to validate the effectiveness of the bandit algorithm. In addition,we propose a multi-agent architecture in which agents are indirectly connectedthrough quantum interference of light and quantum principles ensure theconflict-free property of state-action pair selections among agents. Wedemonstrate that multi-agent reinforcement learning can be accelerated owing toconflict avoidance among multiple agents.

Bandit approach to conflict-free multi-agent Q-learning in view of photonic implementation