While in the single-task setting, the l1 norm is computed based on the parameter vector at of the respective task t, whereas for MTL we compute it over our task parameter matrix A.  Depending on what constraint we would like to place on each row, we can use a different lq. In general, we refer to these mixed-norm constraints as l1/lq norms. They are also known as block-sparse regularization, as they lead to entire rows of A being set to 0. 

Block-sparse Regularization

Rather than sparsity, we would thus like to leverage prior knowledge indicating that some tasks are related while others are not. In this scenario, a constraint that enforces a clustering of tasks might be more appropriate. To learn task relationships, we can impose a clustering constraint by penalizing both the norms of our task column vectors a·,1, . . . , a·,t as well as their variance with the following constraint:

 Learning Task Relationships

There are two main ideas that have been pervasive throughout the history of multi-task learning: enforcing sparsity across tasks through norm regularization; and modeling the relationships between tasks.


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In Machine Learning (ML), we typically care about optimizing for a particular metric. While we can generally achieve acceptable performance this way, by only focusing on a single task, we ignore information from training signals of related tasks that might help us do even better on the metric we care about. By contrast, MTL improves generalization by leveraging the domain-specific information contained in the training signals of related tasks. 

Multi-task Learning

Ruder, S. (n.d.). An Overview of Multi-Task Learning in Deep Neural Networks *. Retrieved May 22, 2022, from https://arxiv-download.xixiaoyao.cn/pdf/1706.05098.pdf

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Multi-Task Learning in Deep Neural Networks

1. Biological perspective: we can see multi-task learning as being inspired by human learning. For learning new tasks, we often apply the knowledge we have acquired by learning related tasks. 


2. Pedagogical perspective: we often learn tasks that provide us with the necessary skills to master more complex techniques first.


3. Machine learning perspective: We can view multi-task learning as a form of inductive transfer. Inductive transfer can help improve a model by introducing an inductive bias, which causes a model to prefer some hypotheses over others.


Motivations of MTL

In the context of Deep Learning, multi-task learning is typically done with either hard or soft parameter sharing of hidden layers.


Two MTL Methods for Deep Learning


For all examples, we will assume that we have two related tasks A and B, which rely on a common hidden layer representation F.

Reasons Why MTL Works

MTL in Non-neural Models

While many recent Deep Learning approaches have more or less used multi-task learning as part of their model , they all employed either hard or soft parameter sharing, and sometimes both.


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