Meta Learning MPC using Finite-Dimensional Gaussian Process Approximations

Data availability has dramatically increased in recent years, driving model-based control methods to exploit learning techniques for improving the system description, and thus control performance. Two key factors that hinder the practical applicability of learning methods in control are their high computational complexity and limited generalization capabilities to unseen conditions. Meta-learning is a powerful tool that enables efficient learning across a finite set of related tasks, easing adaptation to new unseen tasks. This paper makes use of a meta-learning approach for adaptive model predictive control, by learning a system model that leverages data from previous related tasks, while enabling fast fine-tuning to the current task during closed-loop operation. The dynamics is modeled via Gaussian process regression and, building on the Karhunen-Lo{\`e}ve expansion, can be approximately reformulated as a finite linear combination of kernel eigenfunctions. Using data collected over a set of tasks, the eigenfunction hyperparameters are optimized in a meta-training phase by maximizing a variational bound for the log-marginal likelihood. During meta-testing, the eigenfunctions are fixed, so that only the linear parameters are adapted to the new unseen task in an online adaptive fashion via Bayesian linear regression, providing a simple and efficient inference scheme. Simulation results are provided for autonomous racing with miniature race cars adapting to unseen road conditions

Out of the Box Thinking: Improving Customer Lifetime Value Modelling via Expert Routing and Game Whale Detection

Customer lifetime value (LTV) prediction is essential for mobile game publishers trying to optimize the advertising investment for each user acquisition based on the estimated worth. In mobile games, deploying microtransactions is a simple yet effective monetization strategy, which attracts a tiny group of game whales who splurge on in-game purchases. The presence of such game whales may impede the practicality of existing LTV prediction models, since game whales' purchase behaviours always exhibit varied distribution from general users. Consequently, identifying game whales can open up new opportunities to improve the accuracy of LTV prediction models. However, little attention has been paid to applying game whale detection in LTV prediction, and existing works are mainly specialized for the long-term LTV prediction with the assumption that the high-quality user features are available, which is not applicable in the UA stage. In this paper, we propose ExpLTV, a novel multi-task framework to perform LTV prediction and game whale detection in a unified way. In ExpLTV, we first innovatively design a deep neural network-based game whale detector that can not only infer the intrinsic order in accordance with monetary value, but also precisely identify high spenders (i.e., game whales) and low spenders. Then, by treating the game whale detector as a gating network to decide the different mixture patterns of LTV experts assembling, we can thoroughly leverage the shared information and scenario-specific information (i.e., game whales modelling and low spenders modelling). Finally, instead of separately designing a purchase rate estimator for two tasks, we design a shared estimator that can preserve the inner task relationships. The superiority of ExpLTV is further validated via extensive experiments on three industrial datasets

Task Relationship Modeling in Lifelong Multitask Learning

Multitask Learning is a learning framework which explores the concept of sharing training information among multiple related tasks to improve the generalization error of each task. The benefits of multitask learning have been shown both empirically and theoretically. There are a number of fields that benefit from multitask learning such as toxicology, image annotation, compressive sensing etc. However, majority of multitask learning algorithms make a very important key assumption that all the tasks are related to each other in a similar fashion in multitask learning. The users often do not have the knowledge of which tasks are related and train all tasks together. This results in sharing of training information even among the unrelated tasks. Training unrelated tasks together can cause a negative transfer and deteriorate the performance of multitask learning. For example, consider the case of predicting in vivo toxicity of chemicals at various endpoints from the chemical structure. Toxicity at all the endpoints are not related. Since, biological networks are highly complex, it is also not possible to predetermine which endpoints are related. Training all the endpoints together may cause a negative effect on the overall performance. Therefore, it is important to establish the task relationship models in multitask learning. Multitask learning with task relationship modeling may be explored in three different settings, namely, static learning, online fixed task learning and most recent lifelong learning. The multitask learning algorithms in static setting have been present for more than a decade and there is a lot of literature in this field. However, utilization of task relationships in multitask learning framework has been studied in detail for past several years only. The literature which uses feature selection with task relationship modeling is even further limited. For the cases of online and lifelong learning, task relationship modeling becomes a challenge. In online learning, the knowledge of all the tasks is present before starting the training of the algorithms, and the samples arrive in online fashion. However, in case of lifelong multitask learning, the tasks also arrive in an online fashion. Therefore, modeling the task relationship is even a further challenge in lifelong multitask learning framework as compared to online multitask learning. The main contribution of this thesis is to propose a framework for modeling task relationships in lifelong multitask learning. The initial algorithms are preliminary studies which focus on static setting and learn the clusters of related tasks with feature selection. These algorithms enforce that all the tasks which are related select a common set of features. The later part of the thesis shifts gear to lifelong multitask learning setting. Here, we propose learning functions to represent the relationship between tasks. Learning functions is faster and computationally less expensive as opposed to the traditional manner of learning fixed sized matrices for depicting the task relationship models