Differentiating the Multipoint Expected Improvement for Optimal Batch Design

This work deals with parallel optimization of expensive objective functions which are modelled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis’ formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batchsequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization.

Context Aware e-Learning Objects and their Types from the Perspective of the Object-Oriented Paradigm

The contribution of this article demonstrates how to identify context-aware types of e-Learning objects (eLOs) derived from the subject domains. This perspective is taken from an engineering point of view and is applied during requirements elicitation and analysis relating to present work in constructing an object-oriented (OO), dynamic, and adaptive model to build and deliver packaged e-Learning courses. Consequently, three preliminary subject domains are presented and, as a result, three primitive types of eLOs are posited. These types educed from the subject domains are of structural, conceptual, and granular nature. Structural objects are responsible for the course itself, conceptual objects incorporate adaptive and logical interoperability, while granular objects congregate granular assets. Their differences, interrelationships, and responsibilities are discussed. A major design challenge relates to adaptive behaviour. Future research addresses refinement on the subject domains and adaptive hypermedia systems.