Co-adaptive learning over a countable space

Co-adaptation is a special form of on-line learning where an algorithm $\mathcal{A}$ must assist an unknown algorithm $\mathcal{B}$ to perform some task. This is a general framework and has applications in recommendation systems, search, education, and much more. Today, the most common use of co-adaptive algorithms is in brain-computer interfacing (BCI), where algorithms help patients gain and maintain control over prosthetic devices. While previous studies have shown strong empirical results Kowalski et al. (2013); Orsborn et al. (2014) or have been studied in specific examples Merel et al. (2013, 2015), there is no general analysis of the co-adaptive learning problem. Here we will study the co-adaptive learning problem in the online, closed-loop setting. We will prove that, with high probability, co-adaptive learning is guaranteed to outperform learning with a fixed decoder as long as a particular condition is met.

Generalization bound for kernel similarity learning

Similarity learning has received a large amount of interest and is an important tool for many scientific and industrial applications. In this framework, we wish to infer the distance (similarity) between points with respect to an arbitrary distance function $d$. Here, we formulate the problem as a regression from a feature space $\mathcal{X}$ to an arbitrary vector space $\mathcal{Y}$, where the Euclidean distance is proportional to $d$. We then give Rademacher complexity bounds on the generalization error. We find that with high probability, the complexity is bounded by the maximum of the radius of $\mathcal{X}$ and the radius of $\mathcal{Y}$.