Paper:
Parametric Task Learning
We introduce an extended formulation of multi-task learning (MTL) called parametric task learning (PTL) that can systematically handle infinitely many tasks parameterized by a continuous parameter. Our key finding is that, for a certain class of PTL problems, the path of the optimal task-wise solutions can be represented as piecewise-linear functions of the continuous task parameter. Based on this fact, we employ a parametric programming technique to obtain the common shared representation across all the continuously parameterized tasks. We show that our PTL formulation is useful in various scenarios such as learning under non-stationarity, cost-sensitive learning, and quantile regression. We demonstrate the advantage of our approach in these scenarios.

Review:
This paper extends the popular "multi-task feature 
      learning" formulation to the infinite task scenario: 1) Instead of 
      having a finite number task, the problem has an infinite number of tasks 
      characterized by a continuous task parameter \theta (e.g., \theta could be 
      time t). 2) Instead of having each example belong to only one of the 
      finite tasks, each example can belong to the entire class of infinite 
      tasks where its weight in a task is defined by w(\theta), where \theta is 
      the task parameter. 3) The author shows that it's possible to solve 
      this infinite-task feature learning problem because, under certain 
      conditions, the model parameters \beta(\theta) is piece-wise linear on the 
      task parameter \theta. The Originality, Quality, Clarity and 
      Significance are reviewed as follows. Originality: - The idea 
      of having infinite tasks characterized by a task parameter is novel and 
      interesting. - The authors also discussed and studied a few real-world 
      scenarios, where the infinite-task formulation looks a natural solution. 
      Clarity: - Overall the paper is well written. Examples used to 
      illustrate the applications of infinite-task formulation is clear and 
      interesting. - Discussion/review on related work can be improved. One 
      way to view the presented work is to impose a strong known task structure 
      (characterized by a continuous task parameter) on multi-task feature 
      learning formula (in order to handle infinite tasks). In this sense, the 
      author should discuss previous work that tries to infer (unknown) task 
      structure and incorporate it into multi-task feature learning, e.g., 
      "Learning Multiple Tasks with a Sparse Matrix-Normal Penalty" at NIPS 
      2010. Can we combine the strength of inferring unknown task structure and 
      handling infinite tasks? Quality: - The paper only extend a 
      very specific type of multi-learning method -- the multi-task feature 
      learning -- to the infinite-task case. - The empirical study part is 
      relatively weak, mostly based on simulation or small toy data. I like to 
      see the application of the proposed formulation to some significant 
      problem with real-world impact. Significance: - The 
      infinite-task learning idea is interesting and has potential applications.