Photonic accelerators have attracted increasing attention for use in artificial intelligence applications. The multi-armed bandit problem is a fundamental problem of decision making using reinforcement learning. However, to the best of our knowledge, the scalability of photonic decision making has not yet been demonstrated in experiments because of the technical difficulties in the physical realization. We propose a parallel photonic decision-making system to solve large-scale multi-armed bandit problems using optical spatiotemporal chaos. We solved a 512-armed bandit problem online, which is larger than those in previous experiments by two orders of magnitude. The scaling property for correct decision making is examined as a function of the number of slot machines, evaluated as an exponent of 0.86. This exponent is smaller than that in previous studies, indicating the superiority of the proposed parallel principle. This experimental demonstration facilitates photonic decision making to solve large-scale multi-armed bandit problems for future photonic accelerators.

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.