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.