Multi-task optimization is a paradigm in the optimization literature that focuses on solving multiple self-contained tasks simultaneously.Gupta, A., Ong, Y. S., & Feng, L. (2018)
Insights on transfer optimization: Because experience is the best teacher
IEEE Transactions on Emerging Topics in Computational Intelligence, 2(1), 51-64.Gupta, A., Ong, Y. S., & Feng, L. (2016)
Multifactorial evolution: toward evolutionary multitasking.
IEEE Transactions on Evolutionary Computation, 20(3), 343-357. The paradigm has been inspired by the well-established concepts of

transfer learning Transfer learning (TL) is a research problem in machine learning (ML) that focuses on storing knowledge gained while solving one problem and applying it to a different but related problem. For example, knowledge gained while learning to recognize ...

and

multi-task learning Multi-task learning (MTL) is a subfield of machine learning in which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. This can result in improved learning efficiency and prediction ac ...

predictive analytics Predictive analytics encompasses a variety of statistical techniques from data mining, predictive modeling, and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events. In busin ...

. The key motivation behind multi-task optimization is that if optimization tasks are related to each other in terms of their optimal solutions or the general characteristics of their function landscapes, the search progress can be transferred to substantially accelerate the search on the other. The success of the paradigm is not necessarily limited to one-way knowledge transfers from simpler to more complex tasks. In practice an attempt is to intentionally solve a more difficult task that may unintentionally solve several smaller problems.Cabi, S., Colmenarejo, S. G., Hoffman, M. W., Denil, M., Wang, Z., & De Freitas, N. (2017)
The intentional unintentional agent: Learning to solve many continuous control tasks simultaneously
arXiv preprint arXiv:1707.03300.

Methods

There are several common approaches for multi-task optimization: Bayesian optimization,

evolutionary computation In computer science, evolutionary computation is a family of algorithms for global optimization inspired by biological evolution, and the subfield of artificial intelligence and soft computing studying these algorithms. In technical terms, ...

, and approaches based on Game theory.

Multi-task Bayesian optimization

Multi-task Bayesian optimization is a modern model-based approach that leverages the concept of knowledge transfer to speed up the automatic

hyperparameter optimization In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process. By contrast, the ...

process of machine learning algorithms.Swersky, K., Snoek, J., & Adams, R. P. (2013)
Multi-task bayesian optimization
Advances in neural information processing systems (pp. 2004-2012). The method builds a multi-task

Gaussian process In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. ...

model on the data originating from different searches progressing in tandem. The captured inter-task dependencies are thereafter utilized to better inform the subsequent sampling of candidate solutions in respective search spaces.

Evolutionary multi-tasking

Evolutionary multi-tasking has been explored as a means of exploiting the

implicit parallelism In computer science, implicit parallelism is a characteristic of a programming language that allows a compiler or interpreter to automatically exploit the parallelism inherent to the computations expressed by some of the language's constructs. ...

of population-based search algorithms to simultaneously progress multiple distinct optimization tasks. By mapping all tasks to a unified search space, the evolving population of candidate solutions can harness the hidden relationships between them through continuous genetic transfer. This is induced when solutions associated with different tasks crossover.Ong, Y. S., & Gupta, A. (2016)
Evolutionary multitasking: a computer science view of cognitive multitasking
Cognitive Computation, 8(2), 125-142. Recently, modes of knowledge transfer that are different from direct solution

crossover Crossover may refer to: Entertainment Albums and songs * ''Cross Over'' (Dan Peek album) * ''Crossover'' (Dirty Rotten Imbeciles album), 1987 * ''Crossover'' (Intrigue album) * ''Crossover'' (Hitomi Shimatani album) * ''Crossover'' (Yoshino ...

have been explored.

Game-theoretic optimization

Game-theoretic approaches to multi-task optimization propose to view the optimization problem as a game, where each task is a player. All players compete through the reward matrix of the game, and try to reach a solution that satisfies all players (all tasks). This view provide insight about how to build efficient algorithms based on

gradient descent In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of ...

optimization (GD), which is particularly important for training

deep neural networks Deep learning (also known as deep structured learning) is part of a broader family of machine learning methods based on artificial neural networks with representation learning. Learning can be supervised, semi-supervised or unsupervised. ...

. In GD for MTL, the problem is that each task provides its own loss, and it is not clear how to combine all losses and create a single unified gradient, leading to several different aggregation strategies. This aggregation problem can be solved by defining a game matrix where the reward of each player is the agreement of its own gradient with the common gradient, and then setting the common gradient to be the Nash Cooperative bargaining of that system.

Applications

Algorithms for multi-task optimization span a wide array of real-world applications. Recent studies highlight the potential for speed-ups in the optimization of engineering design parameters by conducting related designs jointly in a multi-task manner. In

machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...

, the transfer of optimized features across related data sets can enhance the efficiency of the training process as well as improve the generalization capability of learned models. In addition, the concept of multi-tasking has led to advances in automatic

of machine learning models and

ensemble learning In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone. Unlike a statistical ensemble in statist ...

. Applications have also been reported in cloud computing, with future developments geared towards cloud-based on-demand optimization services that can cater to multiple customers simultaneously. Recent work has additionally shown applications in chemistry.Felton, K., Wigh, D., & Lapkin A. (2021, April
Multi-task Bayesian Optimization of Chemical Reactions
ChemRxiv.

References

Machine learning