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.人机界面的控制行为可通过计算控制模型进行良好建模，这类模型会考量人类在针对特定控制法则估算任务动态与状态时所做出的行为决策。该控制法则会依据代价函数进行优化，出于数学易处理性的考量，这类代价函数通常被表示为一系列二次项。近期研究发现，人类在完成到达任务（reaching tasks）时所使用的代价函数与二次函数存在细微差异，但目前尚不明确两个核心问题：一是多种候选代价函数中哪一种能最优地解释人类行为，二是这些代价函数是否能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名健康受试者（able-bodied subjects）操控肌电界面（myoelectric interface）时采集的实验数据，重建了对应的代价函数。与以往研究相比，本实验范式采用了不同的控制源（肌电控制，其本身存在较大的乘性噪声（multiplicative noise））、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（trial）中屏幕上的追踪位置会动态移动）。包括线性二次型（linear-quadratic）、反高斯函数（inverted Gaussian）以及幂函数（power function）在内的多种候选代价函数，均比二次代价函数或其他被探索过的候选代价函数更能准确描述受试者在本次实验中的行为表现（p<0.05）。值得注意的是，尽管本次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代价函数的参数与既往研究结果保持一致：即幂函数（代价与误差的α次方成正比，cost ∝ error^α），其参数α的取值为1.69（四分位距（interquartile range）为1.53–1.78）。该结果表明，对于指向与追踪任务，在一定噪声幅度范围内，幂函数能够表征用户的误差代价。