This thesis is a proof of concept for the potential of Variational Auto-Encoder (VAE) on representation learning of real-world Knowledge Graphs (KG). Inspired by successful approaches to the generation of molecular graphs, we evaluate the capabilities of our model, the Relational Graph Variational Auto-Encoder (RGVAE). The impact of the modular hyperparameter choices, encoding through graph convolutions, graph matching and latent space prior, is compared. The RGVAE is first evaluated on link prediction. The mean reciprocal rank (MRR) scores on the two datasets FB15K-237 and WN18RR are compared to the embedding-based model DistMult. A variational DistMult and a RGVAE without latent space prior constraint are implemented as control models. The results show that between different settings, the RGVAE with relaxed latent space, scores highest on both datasets, yet does not outperform the DistMult. Further, we investigate the latent space in a twofold experiment: first, linear interpolation between the latent representation of two triples, then the exploration of each latent dimension in a $95\%$ confidence interval. Both interpolations show that the RGVAE learns to reconstruct the adjacency matrix but fails to disentangle. For the last experiment we introduce a new validation method for the FB15K-237 data set. The relation type-constrains of generated triples are filtered and matched with entity types. The observed rate of valid generated triples is insignificantly higher than the random threshold. All generated and valid triples are unseen. A comparison between different latent space priors, using the $\delta$-VAE method, reveals a decoder collapse. Finally we analyze the limiting factors of our approach compared to molecule generation and propose solutions for the decoder collapse and successful representation learning of multi-relational KGs.

Variable division and optimization (D\&O) is a frequently utilized algorithm design paradigm in Evolutionary Algorithms (EAs). A D\&O EA divides a variable into partial variables and then optimize them respectively. A complicated problem is thus divided into simple subtasks. For example, a variable of portfolio problem can be divided into two partial variables, i.e. the selection of assets and the allocation of capital. Thereby, we optimize these two partial variables respectively. There is no formal discussion about how are the partial variables iteratively optimized and why can it work for both single- and multi-objective problems in D\&O. In this paper, this gap is filled. According to the discussion, an elitist selection method for partial variables in multiobjective problems is developed. Then this method is incorporated into the Decomposition-Based Multiobjective Evolutionary Algorithm (D\&O-MOEA/D). With the help of a mathematical programming optimizer, it is achieved on the constrained multiobjective portfolio problems. In the empirical study, D\&O-MOEA/D is implemented for 20 instances and recent Chinese stock markets. The results show the superiority and versatility of D\&O-MOEA/D on large-scale instances while the performance of it on small-scale problems is also not bad. The former targets convergence towards the Pareto front and the latter helps promote diversity among the non-dominated solutions during the search process.

Abstract-- This paper presents a novel approach using sensitivity analysis for generalizing Differential Dynamic Programming (DDP) to systems characterized by implicit dynamics, such as those modelled via inverse dynamics and variational or implicit integrators. It leads to a more general formulation of DDP, enabling for example the use of the faster recursive Newton-Euler inverse dynamics. We leverage the implicit formulation for precise and exact contact modelling in DDP, where we focus on two contributions: (1) Contact dynamics in acceleration level that enables high-order integration schemes; (2) Formulation using an invertible contact model in the forward pass and a closed-form solution in the backward pass to improve the numerical resolution of contacts. The performance of the proposed framework is validated (1) by comparing implicit versus explicit DDP for the swing-up of a double pendulum, and (2) by planning motions for two tasks using a single leg model making multi-body contacts with the environment: standing up from ground, where a priori contact enumeration is challenging, and maintaining balance under an external perturbation. A reinforcement learning To date, we still have limited technologies to replicate approach trained by an adaptive terrain curriculum demonstrated animal-or human-level interaction skills on robots.

Solving multi-objective optimization problems is important in various applications where users are interested in obtaining optimal policies subject to multiple (yet often conflicting) objectives. A typical approach to obtain the optimal policies is to first construct a loss function based on the scalarization of individual objectives and then derive optimal policies that minimize the scalarized loss function. Albeit simple and efficient, the typical approach provides no insights/mechanisms on the optimization of multiple objectives due to the lack of ability to quantify the inter-objective relationship. To address the issue, we propose to develop a new efficient gradient-based multi-objective reinforcement learning approach that seeks to iteratively uncover the quantitative inter-objective relationship via finding a minimum-norm point in the convex hull of the set of multiple policy gradients when the impact of one objective on others is unknown a priori. In particular, we first propose a new PAOLS algorithm that integrates pruning and approximate optimistic linear support algorithm to efficiently discover the weight-vector sets of multiple gradients that quantify the inter-objective relationship. Then we construct an actor and a multi-objective critic that can co-learn the policy and the multi-objective vector value function. Finally, the weight discovery process and the policy and vector value function learning process can be iteratively executed to yield stable weight-vector sets and policies. To validate the effectiveness of the proposed approach, we present a quantitative evaluation of the approach based on three case studies.

Complex systems optimization is a critical challenge in real production and also the hot spot of academic research. The key factors that raise systems' complexity include (but are not limited to): inestimable structures, computationally intensive evaluations, stochastic noise, and multiple key performance indicators (KPIs). A typical example is a simulation-based optimization for an emergency department. Suppose we aim to optimize the patients' flow cost and departments' closeness by determining the corridors' widths via a simulation model. Due to the characteristics of the simulation model, there exists no explicit expression of the input and output, and the estimations are time-consuming and noise-corrupted. Furthermore, the multilevel performance indicators also lay a burden on optimization problems.

Predictions obtained by, e.g., artificial neural networks have a high accuracy but humans often perceive the models as black boxes. Insights about the decision making are mostly opaque for humans. Particularly understanding the decision making in highly sensitive areas such as healthcare or finance, is of paramount importance. The decision-making behind the black boxes requires it to be more transparent, accountable, and understandable for humans. This survey paper provides essential definitions, an overview of the different principles and methodologies of explainable Supervised Machine Learning (SML). We conduct a state-of-the-art survey that reviews past and recent explainable SML approaches and classifies them according to the introduced definitions. Finally, we illustrate principles by means of an explanatory case study and discuss important future directions.

Adaptive control approaches yield high-performance controllers when a precise system model or suitable parametrizations of the controller are available. Existing data-driven approaches for adaptive control mostly augment standard model-based methods with additional information about uncertainties in the dynamics or about disturbances. In this work, we propose a purely data-driven, model-free approach for adaptive control. Tuning low-level controllers based solely on system data raises concerns on the underlying algorithm safety and computational performance. Thus, our approach builds on GoOSE, an algorithm for safe and sample-efficient Bayesian optimization. We introduce several computational and algorithmic modifications in GoOSE that enable its practical use on a rotational motion system. We numerically demonstrate for several types of disturbances that our approach is sample efficient, outperforms constrained Bayesian optimization in terms of safety, and achieves the performance optima computed by grid evaluation. We further demonstrate the proposed adaptive control approach experimentally on a rotational motion system.

Efficient Global Optimization (EGO) is the canonical form of Bayesian optimization that has been successfully applied to solve global optimization of expensive-to-evaluate black-box problems. However, EGO struggles to scale with dimension, and offers limited theoretical guarantees. In this work, we propose and analyze a trust-region-like EGO method (TREGO). TREGO alternates between regular EGO steps and local steps within a trust region. By following a classical scheme for the trust region (based on a sufficient decrease condition), we demonstrate that our algorithm enjoys strong global convergence properties, while departing from EGO only for a subset of optimization steps. Using extensive numerical experiments based on the well-known COCO benchmark, we first analyze the sensitivity of TREGO to its own parameters, then show that the resulting algorithm is consistently outperforming EGO and getting competitive with other state-of-the-art global optimization methods.

We then consider a class of submodular objectives that Submodular functions are set functions that exhibit a are a summation over non-linear functions of these multilinear diminishing returns property. They naturally arise in functions. Our key observation is that the polynomial many applications, including data summarization [2-4], expansions of these functions are again multilinear; facility location [5], recommendation systems [6], influence hence, compositions of multilinear functions with maximization [7], sensor placement [8], dictionary arbitrary analytic functions, that can be approximated learning [9, 10], and active learning [11]. In these problems, by a Taylor series, can be computed efficiently. A broad the goal is to maximize a submodular function range of problems, e.g., data summarization, influence subject to matroid constraints. These problems are in maximization, facility location, and cache networks (c.f.

As a new generation of Public Bicycle-sharing Systems (PBS), the dockless PBS (DL-PBS) is an important application of cyber-physical systems and intelligent transportation. How to use AI to provide efficient bicycle dispatching solutions based on dynamic bicycle rental demand is an essential issue for DL-PBS. In this paper, we propose a dynamic bicycle dispatching algorithm based on multi-objective reinforcement learning (MORL-BD) to provide the optimal bicycle dispatching solution for DL-PBS. We model the DL-PBS system from the perspective of CPS and use deep learning to predict the layout of bicycle parking spots and the dynamic demand of bicycle dispatching. We define the multi-route bicycle dispatching problem as a multi-objective optimization problem by considering the optimization objectives of dispatching costs, dispatch truck's initial load, workload balance among the trucks, and the dynamic balance of bicycle supply and demand. On this basis, the collaborative multi-route bicycle dispatching problem among multiple dispatch trucks is modeled as a multi-agent MORL model. All dispatch paths between parking spots are defined as state spaces, and the reciprocal of dispatching costs is defined as a reward. Each dispatch truck is equipped with an agent to learn the optimal dispatch path in the dynamic DL-PBS network. We create an elite list to store the Pareto optimal solutions of bicycle dispatch paths found in each action, and finally, get the Pareto frontier. Experimental results on the actual DL-PBS systems show that compared with existing methods, MORL-BD can find a higher quality Pareto frontier with less execution time.