We propose a simple model for an atomic switch-based decision maker (ASDM), and show that, as long as its total volume of precipitated Ag atoms is conserved when coupled with suitable operations, an atomic switch system provides a sophisticated "decision-making" capability that is known to be one of the most important intellectual abilities in human beings. We considered the multi-armed bandit problem (MAB); the problem of finding, as accurately and quickly as possible, the most profitable option from a set of options that gives stochastic rewards. These decisions are made as dictated by each volume of precipitated Ag atoms, which is moved in a manner similar to the fluctuations of a rigid body in a tug-of-war game. The "tug-of-war (TOW) dynamics" of the ASDM exhibits higher efficiency than conventional MAB solvers. We show analytical calculations that validate the statistical reasons for the ASDM dynamics to produce such high performance, despite its simplicity. These results imply that various physical systems, in which some conservation law holds, can be used to implement efficient "decision-making objects." Efficient MAB solvers are useful for many practical applications, because MAB abstracts a variety of decision-making problems in real- world situations where an efficient trial-and-error is required. The proposed scheme will introduce a new physics-based analog computing paradigm, which will include such things as "intelligent nano devices" and "intelligent information networks" based on self-detection and self-judgment.
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