Data from: Do cost functions for tracking error generalize across tasks with different noise levels?

Control of human-machine interfaces are well modeled by computational control models, which take into account the behavioral decisions people make in estimating task dynamics and state for a given control law. This control law is optimized according to a cost function, which for the sake of mathematical tractability is typically represented as a series of quadratic terms. Recent studies have found that people actually use cost functions for reaching tasks that are slightly different than a quadratic function, but it is unclear which of several cost functions best explain human behavior and if these cost functions generalize across tasks of similar nature but different scale. In this study, we used an inverse-decision-theory technique to reconstruct the cost function from empirical data collected on 24 able-bodied subjects controlling a myoelectric interface. Compared with previous studies, this experimental paradigm involved a different control source (myoelectric control, which has inherently large multiplicative noise), a different control interface (control signal was mapped to cursor velocity), and a different task (the tracking position dynamically moved on the screen throughout each trial). Several cost functions, including a linear-quadratic; an inverted Gaussian, and a power function, accurately described the behavior of subjects throughout this experiment better than a quadratic cost function or other explored candidate cost functions (p<0.05). Importantly, despite the differences in the experimental paradigm and a substantially larger scale of error, we found only one candidate cost function whose parameter was consistent with the previous studies: a power function (cost ∝ errorα) with a parameter value of α = 1.69 (1.53–1.78 interquartile range). This result suggests that a power-function is a representative function of user’s error cost over a range of noise amplitudes for pointing and tracking tasks.

人机交互界面的控制可通过计算控制模型实现良好建模，这类模型会考量人类在针对给定控制法则（control law）估计任务动态与状态时所做出的行为决策。该控制法则需依据成本函数（cost function）进行优化；出于数学易处理性的考量，此类成本函数通常被表示为一系列二次项形式。近期研究发现，人类在完成抵达任务（reaching tasks）时所使用的成本函数与二次函数存在细微差异，但目前仍存在两个尚未明确的问题：其一，众多候选成本函数中哪一种能最佳解释人类行为；其二，此类成本函数能否在性质相似但尺度不同的任务间实现泛化。本研究采用逆决策理论（inverse-decision-theory）技术，基于24名健康健全受试者操控肌电控制界面（myoelectric interface）时采集的实验数据，重构出对应的成本函数。与既往研究相比，本实验范式采用了不同的控制源：肌电控制（myoelectric control）本身固有的乘性噪声较大；不同的控制界面：控制信号被映射为光标速度；以及不同的任务：每次试次中屏幕上的追踪目标位置会动态移动。包括线性二次型（linear-quadratic）、反高斯型（inverted Gaussian）以及幂函数（power function）在内的多种候选成本函数，均比二次成本函数或其他探究过的候选成本函数能更精准地描述受试者在本实验中的行为表现（p<0.05）。值得注意的是，尽管本实验范式存在差异，且误差尺度显著更大，但我们仅发现一种候选成本函数的参数与既往研究结果保持一致：即幂函数（成本与误差的α次方成正比，cost ∝ error^α），其参数α的取值为1.69（四分位距为1.53–1.78）。该结果表明，对于指向与追踪任务，在一定噪声幅值范围内，幂函数可作为用户误差成本的代表性函数。