Stochastic Approximation for Expensive One-Bit Feedback Systems

One-bit feedback systems generate binary data as their output and the system performance is usually measured by the success rate with a fixed parameter combination. Traditional methods need many executions for parameter optimization. Hence, it is impractical to utilize these methods in Expensive One-Bit Feedback Systems (EOBFSs), where a single system execution is costly in terms of time or money. In this paper, we propose a novel algorithm, named Iterative Regression and Optimization (IRO), for parameter optimization and its corresponding scheme based on the Maximum Likelihood Estimation (MLE) method and Particle Swarm Optimization (PSO) method, named MLEPSO-IRO, for parameter optimization in EOBFSs. The IRO algorithm is an iterative algorithm, with each iteration comprising two parts: regression and optimization. Considering the structure of IRO and the Bernoulli distribution property of the output of EOBFSs, MLE and a modified PSO are selected to implement the regression and optimization sections, respectively, in MLEPSO-IRO. We also provide a theoretical analysis for the convergence of MLEPSO-IRO and provide numerical experiments on hypothesized EOBFSs and one real EOBFS in comparison to traditional methods. The results indicate that MLEPSO-IRO can provide a much better result with only a small amount of system executions.