Competitive Co-evolution for Dynamic Constrained Optimisation

Dynamic constrained optimisation problems (DCOPs) widely exist in the real world due to frequently changing factors influencing the environment. Many dynamic optimisation methods such as diversity-driven methods, memory and prediction methods offer different strategies to deal with environmental changes. However, when DCOPs change very fast or have very limited time for the algorithm to react, the potential of these methods is limited due to time shortage for re-optimisation and adaptation. This is especially true for population-based dynamic optimisation methods, which normally need quite a few fitness evaluations to find a near-optimum solution. To address this issue, this paper proposes to tackle fast-changing DCOPs through a smart combination of offline and online optimisation. The offline optimisation aims to prepare a set of good solutions for all possible environmental changes beforehand. With this solution set, the online optimisation aims to react quickly to each truly happening environmental change by doing optimisation on the set. To find this solution set, this paper further proposes to use competitive co-evolution for offline optimisation by co-evolving candidate solutions and environmental parameters. The experimental studies on a well-known benchmark test set of DCOPs show that the proposed method outperforms existing methods significantly especially when the environment changes very fast

DynWalks: Global Topology and Recent Changes Awareness Dynamic Network Embedding

Learning topological representation of a network in dynamic environments has recently attracted considerable attention due to the time-evolving nature of many real-world networks i.e. nodes/links might be added/removed as time goes on. Dynamic network embedding aims to learn low dimensional embeddings for unseen and seen nodes by using any currently available snapshots of a dynamic network. For seen nodes, the existing methods either treat them equally important or focus on the $k$ most affected nodes at each time step. However, the former solution is time-consuming, and the later solution that relies on incoming changes may lose the global topology---an important feature for downstream tasks. To address these challenges, we propose a dynamic network embedding method called DynWalks, which includes two key components: 1) An online network embedding framework that can dynamically and efficiently learn embeddings based on the selected nodes; 2) A novel online node selecting scheme that offers the flexible choices to balance global topology and recent changes, as well as to fulfill the real-time constraint if needed. The empirical studies on six real-world dynamic networks under three different slicing ways show that DynWalks significantly outperforms the state-of-the-art methods in graph reconstruction tasks, and obtains comparable results in link prediction tasks. Furthermore, the wall-clock time and complexity analysis demonstrate its excellent time and space efficiency. The source code of DynWalks is available at https://github.com/houchengbin/DynWalks

AlphaStock: A Buying-Winners-and-Selling-Losers Investment Strategy using Interpretable Deep Reinforcement Attention Networks

Recent years have witnessed the successful marriage of finance innovations and AI techniques in various finance applications including quantitative trading (QT). Despite great research efforts devoted to leveraging deep learning (DL) methods for building better QT strategies, existing studies still face serious challenges especially from the side of finance, such as the balance of risk and return, the resistance to extreme loss, and the interpretability of strategies, which limit the application of DL-based strategies in real-life financial markets. In this work, we propose AlphaStock, a novel reinforcement learning (RL) based investment strategy enhanced by interpretable deep attention networks, to address the above challenges. Our main contributions are summarized as follows: i) We integrate deep attention networks with a Sharpe ratio-oriented reinforcement learning framework to achieve a risk-return balanced investment strategy; ii) We suggest modeling interrelationships among assets to avoid selection bias and develop a cross-asset attention mechanism; iii) To our best knowledge, this work is among the first to offer an interpretable investment strategy using deep reinforcement learning models. The experiments on long-periodic U.S. and Chinese markets demonstrate the effectiveness and robustness of AlphaStock over diverse market states. It turns out that AlphaStock tends to select the stocks as winners with high long-term growth, low volatility, high intrinsic value, and being undervalued recently.

Running Time Analysis of the (1+1)-EA for Robust Linear Optimization

Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a series of efforts devoted to analyzing the running time of EAs for optimization under uncertainties. Existing studies mainly focus on noisy and dynamic optimization, while another common type of uncertain optimization, i.e., robust optimization, has been rarely touched. In this paper, we analyze the expected running time of the (1+1)-EA solving robust linear optimization problems (i.e., linear problems under robust scenarios) with a cardinality constraint $k$. Two common robust scenarios, i.e., deletion-robust and worst-case, are considered. Particularly, we derive tight ranges of the robust parameter $d$ or budget $k$ allowing the (1+1)-EA to find an optimal solution in polynomial running time, which disclose the potential of EAs for robust optimization.

Decision Making with Machine Learning and ROC Curves

The Receiver Operating Characteristic (ROC) curve is a representation of the statistical information discovered in binary classification problems and is a key concept in machine learning and data science. This paper studies the statistical properties of ROC curves and its implication on model selection. We analyze the implications of different models of incentive heterogeneity and information asymmetry on the relation between human decisions and the ROC curves. Our theoretical discussion is illustrated in the context of a large data set of pregnancy outcomes and doctor diagnosis from the Pre-Pregnancy Checkups of reproductive age couples in Henan Province provided by the Chinese Ministry of Health.

Stochastic Gradient Descent for Nonconvex Learning without Bounded Gradient Assumptions

Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing theoretical results for SGD applied to nonconvex objective functions are far from mature. For example, existing results require to impose a nontrivial assumption on the uniform boundedness of gradients for all iterates encountered in the learning process, which is hard to verify in practical implementations. In this paper, we establish a rigorous theoretical foundation for SGD in nonconvex learning by showing that this boundedness assumption can be removed without affecting convergence rates. In particular, we establish sufficient conditions for almost sure convergence as well as optimal convergence rates for SGD applied to both general nonconvex objective functions and gradient-dominated objective functions. A linear convergence is further derived in the case with zero variances.

A Parallel Divide-and-Conquer based Evolutionary Algorithm for Large-scale Optimization

Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to solve the emerging large-scale problems both effectively and efficiently. In this paper, we propose a novel Divide-and-Conquer (DC) based EA that can not only produce high-quality solution by solving sub-problems separately, but also highly utilizes the power of parallel computing by solving the sub-problems simultaneously. Existing DC-based EAs that were deemed to enjoy the same advantages of the proposed algorithm, are shown to be practically incompatible with the parallel computing scheme, unless some trade-offs are made by compromising the solution quality.

Attributed Network Embedding for Incomplete Structure Information

An attributed network enriches a pure network by encoding a part of widely accessible node auxiliary information into node attributes. Learning vector representation of each node a.k.a. Network Embedding (NE) for such an attributed network by considering both structure and attribute information has recently attracted considerable attention, since each node embedding is simply a unified low-dimension vector representation that makes downstream tasks e.g. link prediction more efficient and much easier to realize. Most of previous works have not considered the significant case of a network with incomplete structure information, which however, would often appear in our real-world scenarios e.g. the abnormal users in a social network who intentionally hide their friendships. And different networks obviously have different levels of incomplete structure information, which imposes more challenges to balance two sources of information. To tackle that, we propose a robust NE method called Attributed Biased Random Walks (ABRW) to employ attribute information for compensating incomplete structure information by using transition matrices. The experiments of link prediction and node classification tasks on real-world datasets confirm the robustness and effectiveness of our method to the different levels of the incomplete structure information.

Maximizing Monotone DR-submodular Continuous Functions by Derivative-free Optimization

In this paper, we study the problem of monotone (weakly) DR-submodular continuous maximization. While previous methods require the gradient information of the objective function, we propose a derivative-free algorithm LDGM for the first time. We define $\beta$ and $\alpha$ to characterize how close a function is to continuous DR-submodulr and submodular, respectively. Under a convex polytope constraint, we prove that LDGM can achieve a $(1-e^{-\beta}-\epsilon)$-approximation guarantee after $O(1/\epsilon)$ iterations, which is the same as the best previous gradient-based algorithm. Moreover, in some special cases, a variant of LDGM can achieve a $((\alpha/2)(1-e^{-\alpha})-\epsilon)$-approximation guarantee for (weakly) submodular functions. We also compare LDGM with the gradient-based algorithm Frank-Wolfe under noise, and show that LDGM can be more robust. Empirical results on budget allocation verify the effectiveness of LDGM.