Abstract
The operation of a human-machine interface is increasingly often referred to as a two-learners problem, where both the human and the interface independently adapt their behavior based on shared information to improve joint performance over a specific task. Drawing inspiration from the field of body-machine interfaces, we take a different perspective and propose a framework for studying co-adaptation in scenarios where the evolution of the interface is dependent on the users' behavior and that do not require task goals to be explicitly defined. Our mathematical description of co-adaptation is built upon the assumption that the interface and the user agents co-adapt toward maximizing the interaction efficiency rather than optimizing task performance. This work describes a mathematical framework for body-machine interfaces where a naïve user interacts with an adaptive interface. The interface, modeled as a linear map from a space with high dimension (the user input) to a lower dimensional feedback, acts as an adaptive "tool" whose goal is to minimize transmission loss following an unsupervised learning procedure and has no knowledge of the task being performed by the user. The user is modeled as a non-stationary multivariate Gaussian generative process that produces a sequence of actions that is either statistically independent or correlated. Dependent data is used to model the output of an action selection module concerned with achieving some unknown goal dictated by the task. The framework assumes that in parallel to this explicit objective, the user is implicitly learning a suitable but not necessarily optimal way to interact with the interface. Implicit learning is modeled as use-dependent learning modulated by a reward-based mechanism acting on the generative distribution. Through simulation, the work quantifies how the system evolves as a function of the learning time scales when a user learns to operate a static vs. an adaptive interface. We show that this novel framework can be directly exploited to readily simulate a variety of interaction scenarios, to facilitate the exploration of the parameters that lead to optimal learning dynamics of the joint system, and to provide an empirical proof for the superiority of human-machine co-adaptation over user adaptation.