Recent theoretical models suggest that motor learning includes at least two processes: error minimization and memory decay. While learning a novel movement, a motor memory of the movement is gradually formed to minimize the movement error between the desired and actual movements in each training trial, but the memory is slightly forgotten in each trial. The learning effects of error minimization trained with a certain movement are partially available in other non-trained movements, and this transfer of the learning effect can be reproduced by certain theoretical frameworks. Although most theoretical frameworks have assumed that a motor memory trained with a certain movement decays at the same speed during performing the trained movement as non-trained movements, a recent study reported that the motor memory decays faster during performing the trained movement than non-trained movements, i.e., the decay rate of motor memory is movement or context dependent. Although motor learning has been successfully modeled based on an optimization framework, e.g., movement error minimization, the type of optimization that can lead to context-dependent memory decay is unclear. Thus, context-dependent memory decay raises the question of what is optimized in motor learning. To reproduce context-dependent memory decay, I extend a motor primitive framework. Specifically, I introduce motor effort optimization into the framework because some previous studies have reported the existence of effort optimization in motor learning processes and no conventional motor primitive model has yet considered the optimization. Here, I analytically and numerically revealed that context-dependent decay is a result of motor effort optimization. My analyses suggest that context-dependent decay is not merely memory decay but is evidence of motor effort optimization in motor learning.
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