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This approach greatly reduces the measurement effort required, but it requires some prior knowledge on the smoothness of the function in the form of an aggregation function and computational issues limit the number of alternatives that can be easily considered to the thousands. We propose a hierarchical aggregation technique that uses the common features shared by alternatives to learn about many alternatives from even a single measurement. This policy myopically optimizes the expected increment in the value of sampling information in each time period. We use a Bayesian probability model for the unknown reward of each alternative and follow a fully sequential sampling policy called the knowledge-gradient policy. Each alternative may be characterized by a multidimensional vector of categorical and numerical attributes and has independent normal rewards. We prove that our policy is consistent, finding a globally optimal alternative when given enough measurements, and show through simulations that it performs competitively with or significantly better than other policies.Ībstract = "We propose a sequential sampling policy for noisy discrete global optimization and ranking and selection, in which we aim to efficiently explore a finite set of alternatives before selecting an alternative as best when exploration stops. This accelerates almost all quantum-classical hybrid algorithms readily and would be a key tool for harnessing near-term quantum devices.We propose a sequential sampling policy for noisy discrete global optimization and ranking and selection, in which we aim to efficiently explore a finite set of alternatives before selecting an alternative as best when exploration stops. We find that the proposed method substantially outperforms the existing optimization algorithms and converges to a solution almost independent of the initial choice of the parameters. We perform numerical simulations and compare the proposed method with existing gradient-free and gradient-based optimization algorithms. By repeatedly performing this procedure, we can optimize the parameterized quantum circuits so that the cost function becomes as small as possible. Furthermore, even in general cases, the cost function is given by a simple sum of trigonometric functions with certain periods and hence can be minimized by using a classical computer. In fact, if we choose a single parameter, the cost function becomes a simple sine curve with period 2 π, and hence we can exactly minimize with respect to the chosen parameter. Specifically, the optimization problem of the parameterized quantum circuits is divided into solvable subproblems by considering only a subset of the parameters. We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, robust against statistical error, and hyperparameter-free.
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