Abstract
The competitive multi-armed bandit (CMAB) problem is related to social issues such as maximizing total social benefits while preserving equality among individuals by overcoming conflicts between individual decisions, which could seriously decrease social benefits. The study described herein provides experimental evidence that entangled photons physically resolve the CMAB in the 2-arms 2-players case, maximizing the social rewards while ensuring equality. Moreover, we demonstrated that deception, or outperforming the other player by receiving a greater reward, cannot be accomplished in a polarization-entangled-photon-based system, while deception is achievable in systems based on classical polarization-correlated photons with fixed polarizations. Besides, random polarization-correlated photons have been studied numerically and shown to ensure equality between players and deception prevention as well, although the CMAB maximum performance is reduced as compared with entangled photon experiments. Autonomous alignment schemes for polarization bases were also experimentally demonstrated based only on decision conflict information observed by an individual without communications between players. This study paves a way for collective decision making in uncertain dynamically changing environments based on entangled quantum states, a crucial step toward utilizing quantum systems for intelligent functionalities.
Highlights
The competitive multi-armed bandit (CMAB) problem is related to social issues such as maximizing total social benefits while preserving equality among individuals by overcoming conflicts between individual decisions, which could seriously decrease social benefits
The CMAB problem is important in practical applications ranging from traffic control, where everyone choosing the same road may lead to a traffic jam16 to resource allocation in infrastructures, such as communications12,17 where everyone wanting to communicate at the same time leads to congestion for example
Autonomous and dynamic alignment schemes for polarization bases, which are necessary for CMAB applications, are experimentally demonstrated based only on decision conflict information observed by an individual without communications between players
Summary
The competitive multi-armed bandit (CMAB) problem is related to social issues such as maximizing total social benefits while preserving equality among individuals by overcoming conflicts between individual decisions, which could seriously decrease social benefits. Unique physical attributes of photons have been intensively studied for information processing to solve computationally demanding problems such as time-series prediction using photonic reservoir computing, combinatorial optimization based on coherent Ising machines, and deep learning employing nanophotonic circuits for cognition3 Decision making is another important branch of research where the objective is to identify decisions that will maximize benefits in dynamically changing uncertain environments, with direct applications for reinforcement learning. This paper theoretically and experimentally demonstrates the usefulness and superiority of quantum-entangled photons for collective decision making and physically solving the MAB problem on the social level, for example, maximizing the total benefits while preserving equality among individuals by overcoming conflicts between individual decisions. This example manifests itself as players becoming locked in a local minimum due to conflict between their decisions, since everyone wants more rewards and tries to select the higher-reward-probability slot machine, whereas the total team rewards could be increased if they cooperated
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