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With the end of Moore’s Law and the increasing demand for computing, photonic accelerators are garnering considerable attention. This is due to the physical characteristics of light, such as high bandwidth and multiplicity, and the various synchronization phenomena that emerge in the realm of laser physics. These factors come into play as computer performance approaches its limits. In this study, we explore the application of a laser network, acting as a photonic accelerator, to the competitive multi-armed bandit problem. In this context, conflict avoidance is key to maximizing environmental rewards. We experimentally demonstrate cooperative decision-making using zero-lag and lag synchronization within a network of four semiconductor lasers. Lag synchronization of chaos realizes effective decision-making and zero-lag synchronization is responsible for the realization of the collision avoidance function. We experimentally verified a low collision rate and high reward in a fundamental 2-player, 2-slot scenario, and showed the scalability of this system. This system architecture opens up new possibilities for intelligent functionalities in laser dynamics.

Reinforcement learning involves decision making in dynamic and uncertain environments and constitutes an important element of artificial intelligence (AI). In this work, we experimentally demonstrate that the ultrafast chaotic oscillatory dynamics of lasers efficiently solve the multi-armed bandit problem (MAB), which requires decision making concerning a class of difficult trade-offs called the exploration–exploitation dilemma. To solve the MAB, a certain degree of randomness is required for exploration purposes. However, pseudorandom numbers generated using conventional electronic circuitry encounter severe limitations in terms of their data rate and the quality of randomness due to their algorithmic foundations. We generate laser chaos signals using a semiconductor laser sampled at a maximum rate of 100 GSample/s, and combine it with a simple decision-making principle called tug of war with a variable threshold, to ensure ultrafast, adaptive, and accurate decision making at a maximum adaptation speed of 1 GHz. We found that decision-making performance was maximized with an optimal sampling interval, and we highlight the exact coincidence between the negative autocorrelation inherent in laser chaos and decision-making performance. This study paves the way for a new realm of ultrafast photonics in the age of AI, where the ultrahigh bandwidth of light wave can provide new value.

In recent cross-disciplinary studies involving both optics and computing, single-photon-based decision-making has been demonstrated by utilizing the wave-particle duality of light to solve multi-armed bandit problems. Furthermore, entangled-photon-based decision-making has managed to solve a competitive multi-armed bandit problem in such a way that conflicts of decisions among players are avoided while ensuring equality. However, as these studies are based on the polarization of light, the number of available choices is limited to two, corresponding to two orthogonal polarization states. Here we propose a scalable principle to solve competitive decision-making situations by using the orbital angular momentum of photons based on its high dimensionality, which theoretically allows an unlimited number of arms. Moreover, by extending the Hong-Ou-Mandel effect to more than two states, we theoretically establish an experimental configuration able to generate multi-photon states with orbital angular momentum and conditions that provide conflict-free selections at every turn. We numerically examine total rewards regarding three-armed bandit problems, for which the proposed strategy accomplishes almost the theoretical maximum, which is greater than a conventional mixed strategy intending to realize Nash equilibrium. This is thanks to the quantum interference effect that achieves no-conflict selections, even in the exploring phase to find the best arms.

Decision making using photonic technologies has been intensively researched for solving the multi-armed bandit problem, which is fundamental to reinforcement learning. However, these technologies are yet to be extended to large-scale multi-armed bandit problems. In this study, we conduct a numerical investigation of decision making to solve large-scale multi-armed bandit problems by controlling the biases of chaotic temporal waveforms generated in semiconductor lasers with optical feedback. We generate chaotic temporal waveforms using the semiconductor lasers, and each waveform is assigned to a slot machine (or choice) in the multi-armed bandit problem. The biases in the amplitudes of the chaotic waveforms are adjusted based on rewards using the tug-of-war method. Subsequently, the slot machine that yields the maximum-amplitude chaotic temporal waveform with bias is selected. The scaling properties of the correct decision-making process are examined by increasing the number of slot machines to 1024, and the scaling exponent of the power-law distribution is 0.97. We demonstrate that the proposed method outperforms existing software algorithms in terms of the scaling exponent. This result paves the way for photonic decision making in large-scale multi-armed bandit problems using photonic accelerators.

Dynamic channel selection is among the most important wireless communication elements in dynamically changing electromagnetic environments wherein, a user can experience improved communication quality by choosing a better channel. Multi-armed bandit (MAB) algorithms are a promising approach that resolve the trade-off between channel exploration and exploitation of enhanced communication quality. Ultrafast solution of MAB problems has been demonstrated by utilizing chaotically oscillating time series generated by semiconductor lasers. In this study, we experimentally demonstrate a MAB algorithm incorporating laser chaos time series in a wireless local area network (WLAN). Autonomous and adaptive dynamic channel selection is successfully demonstrated in an IEEE802.11a-based, four-channel WLAN. Although the laser chaos time series is arranged prior to the WLAN experiments, the results confirm the usefulness of ultrafast chaotic sequences for real wireless applications. In addition, we numerically examine the underlying adaptation mechanism of the significantly simplified MAB algorithm implemented in the present study compared with the previously reported chaos-based decision makers. This study provides a first step toward the application of ultrafast chaotic lasers for future high-performance wireless communication networks.

By exploiting ultrafast and irregular time series generated by lasers with delayed feedback, we have previously demonstrated a scalable algorithm to solve multi-armed bandit (MAB) problems utilizing the time-division multiplexing of laser chaos time series. Although the algorithm detects the arm with the highest reward expectation, the correct recognition of the order of arms in terms of reward expectations is not achievable. Here, we present an algorithm where the degree of exploration is adaptively controlled based on confidence intervals that represent the estimation accuracy of reward expectations. We have demonstrated numerically that our approach did improve arm order recognition accuracy significantly, along with reduced dependence on reward environments, and the total reward is almost maintained compared with conventional MAB methods. This study applies to sectors where the order information is critical, such as efficient allocation of resources in information and communications technology.

Photonic reservoir computing is an emergent technology toward beyond-Neumann computing. Although photonic reservoir computing provides superior performance in environments whose characteristics are coincident with the training datasets for the reservoir, the performance is significantly degraded if these characteristics deviate from the original knowledge used in the training phase. Here, we propose a scheme of adaptive model selection in photonic reservoir computing using reinforcement learning. In this scheme, a temporal waveform is generated by different dynamic source models that change over time. The system autonomously identifies the best source model for the task of time series prediction using photonic reservoir computing and reinforcement learning. We prepare two types of output weights for the source models, and the system adaptively selected the correct model using reinforcement learning, where the prediction errors are associated with rewards. We succeed in adaptive model selection when the source signal is temporally mixed, having originally been generated by two different dynamic system models, as well as when the signal is a mixture from the same model but with different parameter values. This study paves the way for autonomous behavior in photonic artificial intelligence and could lead to new applications in load forecasting and multi-objective control, where frequent environment changes are expected.

Situations involving competition for resources among entities can be modeled by the competitive multi-armed bandit (CMAB) problem, which relates to social issues such as maximizing the total outcome and achieving the fairest resource repartition among individuals. In these respects, the intrinsic randomness and global properties of quantum states provide ideal tools for obtaining optimal solutions to this problem. Based on the previous study of the CMAB problem in the two-arm, two-player case, this paper presents the theoretical principles necessary to find polarization-entangled N -photon states that can optimize the total resource output while ensuring equality among players. These principles were applied to two-, three-, four-, and five-player cases by using numerical simulations to reproduce realistic configurations and find the best strategies to overcome potential misalignment between the polarization measurement systems of the players. Although a general formula for the N -player case is not presented here, general derivation rules and a verification algorithm are proposed. This report demonstrates the potential usability of quantum states in collective decision making with limited, probabilistic resources, which could serve as a first step toward quantum-based resource allocation systems.

We experimentally study a Stub photonic lattice and excite their localized linear states originated from an isolated Flat Band at the center of the linear spectrum. By exciting these modes in different regions of the lattice, we observe that they do not diffract across the system and remain well trapped after propagating along the crystal. By using their wave nature, we are able to combine – in phase and out of phase – two neighbor states into a coherent superposition. These observations allow us to propose a novel setup for performing three different all-optical logical operations such as OR, AND, and XOR, positioning Flat Band systems as key setups to perform all-optical operations at any level of power.

Collective decision making is important for maximizing total benefits while preserving equality among individuals in the competitive multi-armed bandit (CMAB) problem, wherein multiple players try to gain higher rewards from multiple slot machines. The CMAB problem represents an essential aspect of applications such as resource management in social infrastructure. In a previous study, we theoretically and experimentally demonstrated that entangled photons can physically resolve the difficulty of the CMAB problem. This decision-making strategy completely avoids decision conflicts while ensuring equality. However, decision conflicts can sometimes be beneficial if they yield greater rewards than non-conflicting decisions, indicating that greedy actions may provide positive effects depending on the given environment. In this study, we demonstrate a mixed strategy of entangled- and correlated-photon-based decision-making so that total rewards can be enhanced when compared to the entangled-photon-only decision strategy. We show that an optimal mixture of entangled- and correlated-photon-based strategies exists depending on the dynamics of the reward environment as well as the difficulty of the given problem. This study paves the way for utilizing both quantum and classical aspects of photons in a mixed manner for decision making and provides yet another example of the supremacy of mixed strategies known in game theory, especially in evolutionary game theory.