Portfolio Selection is an important real-world financial task and has attracted extensive attention in artificial intelligence communities. This task, however, has two main difficulties: (i) the non-stationary price series and complex asset correlations make the learning of feature representation very hard; (ii) the practicality principle in financial markets requires controlling both transaction and risk costs. Most existing methods adopt handcraft features and/or consider no constraints for the costs, which may make them perform unsatisfactorily and fail to control both costs in practice. In this paper, we propose a cost-sensitive portfolio selection method with deep reinforcement learning. Specifically, a novel two-stream portfolio policy network is devised to extract both price series patterns and asset correlations, while a new cost-sensitive reward function is developed to maximize the accumulated return and constrain both costs via reinforcement learning. We theoretically analyze the near-optimality of the proposed reward, which shows that the growth rate of the policy regarding this reward function can approach the theoretical optimum. We also empirically evaluate the proposed method on real-world datasets. Promising results demonstrate the effectiveness and superiority of the proposed method in terms of profitability, cost-sensitivity and representation abilities.

Portfolio Selection is an important real-world financial task and has attracted extensive attention in artificial intelligence communities. This task, however, has two main difficulties: (i) the non-stationary price series and complex asset correlations make the learning of feature representation very hard; (ii) the practicality principle in financial markets requires controlling both transaction and risk costs. Most existing methods adopt handcraft features and/or consider no constraints for the costs, which may make them perform unsatisfactorily and fail to control both costs in practice. In this paper, we propose a cost-sensitive portfolio selection method with deep reinforcement learning. Specifically, a novel two-stream portfolio policy network is devised to extract both price series patterns and asset correlations, while a new cost-sensitive reward function is developed to maximize the accumulated return and constrain both costs via reinforcement learning. We theoretically analyze the near-optimality of the proposed reward, which shows that the growth rate of the policy regarding this reward function can approach the theoretical optimum. We also empirically evaluate the proposed method on real-world datasets. Promising results demonstrate the effectiveness and superiority of the proposed method in terms of profitability, cost-sensitivity and representation abilities.

Kernel-based regression represents an important family of learning techniques for solving challenging regression tasks with non-linear patterns. Despite being studied extensively, most of the existing work suffers from two major drawbacks as follows: (i) they are often designed for solving regression tasks in a batch learning setting, making them not only computationally inefficient and but also poorly scalable in real-world applications where data arrives sequentially; and (ii) they usually assume that a fixed kernel function is given prior to the learning task, which could result in poor performance if the chosen kernel is inappropriate. To overcome these drawbacks, this work presents a novel scheme of Online Multiple Kernel Regression (OMKR), which sequentially learns the kernel-based regressor in an online and scalable fashion, and dynamically explore a pool of multiple diverse kernels to avoid suffering from a single fixed poor kernel so as to remedy the drawback of manual/heuristic kernel selection. The OMKR problem is more challenging than regular kernel-based regression tasks since we have to on-the-fly determine both the optimal kernel-based regressor for each individual kernel and the best combination of the multiple kernel regressors. We propose a family of OMKR algorithms for regression and discuss their application to time series prediction tasks including application to AR, ARMA, and ARIMA time series. We develop novel approaches to make OMKR scalable for large datasets, to counter the problems arising from an unbounded number of support vectors. We also explore the effect of kernel combination at prediction level and at the representation level. Finally, we conduct extensive experiments to evaluate the empirical performance on both real-world regression and times series prediction tasks.

Machine learning and artificial intelligence techniques have been applied to construct online portfolio selection strategies recently. A popular and state-of-the-art family of strategies is to explore the reversion phenomenon through online learning algorithms and statistical prediction models. Despite gaining promising results on some benchmark datasets, these strategies often adopt a single model based on a selection criterion (e.g., breakdown point) for predicting future price. However, such model selection is often unstable and may cause unnecessarily high variability in the final estimation, leading to poor prediction performance in real datasets and thus non-optimal portfolios. To overcome the drawbacks, in this article, we propose to exploit the reversion phenomenon by using combination forecasting estimators and design a novel online portfolio selection strategy, named Combination Forecasting Reversion (CFR), which outputs optimal portfolios based on the improved reversion estimator. We further present two efficient CFR implementations based on online Newton step (ONS) and online gradient descent (OGD) algorithms, respectively, and theoretically analyze their regret bounds, which guarantee that the online CFR model performs as well as the best CFR model in hindsight. We evaluate the proposed algorithms on various real markets with extensive experiments. Empirical results show that CFR can effectively overcome the drawbacks of existing reversion strategies and achieve the state-of-the-art performance.

On-line portfolio selection is a practical financial engineering problem, which aims to sequentially allocate capital among a set of assets in order to maximize long-term return. In recent years, a variety of machine learning algorithms have been proposed to address this challenging problem, but no comprehensive open-source toolbox has been released for various reasons. This article presents the first open-source toolbox for "On-Line Portfolio Selection" (OLPS), which implements a collection of classical and state-of-the-art strategies powered by machine learning algorithms. We hope that OLPS can facilitate the development of new learning methods and enable the performance benchmarking and comparisons of different strategies. OLPS is an open-source project released under Apache License (version 2.0), which is available at github.com/OLPS/OLPS or OLPS.stevenhoi.org.

Online portfolio selection has attracted increasing attention from data mining and machine learning communities in recent years. An important theory in financial markets is mean reversion, which plays a critical role in some state-of-the-art portfolio selection strategies. Although existing mean reversion strategies have been shown to achieve good empirical performance on certain datasets, they seldom carefully deal with noise and outliers in the data, leading to suboptimal portfolios, and consequently yielding poor performance in practice. In this paper, we propose to exploit the reversion phenomenon by using robust$L_1$-median estimators, and design a novel online portfolio selection strategy named “Robust Median Reversion” (RMR), which constructs optimal portfolios based on the improved reversion estimator. We examine the performance of the proposed algorithms on various real markets with extensive experiments. Empirical results show that RMR can overcome the drawbacks of existing mean reversion algorithms and achieve significantly better results. Finally, RMR runs in linear time, and thus is suitable for large-scale real-time algorithmic trading applications.

For many data mining and machine learning tasks, the quality of a similarity measure is the key for their performance. To automatically find a good similarity measure from datasets, metric learning and similarity learning are proposed and studied extensively. Metric learning will learn a Mahalanobis distance based on positive semi-definite (PSD) matrix, to measure the distances between objectives, while similarity learning aims to directly learn a similarity function without PSD constraint so that it is more attractive. Most of the existing similarity learning algorithms are online similarity learning method, since online learning is more scalable than offline learning. However, most existing online similarity learning algorithms learn a full matrix with d2parameters, where d is the dimension of the instances. This is clearly inefficient for high dimensional tasks due to its high memory and computational complexity. To solve this issue, we introduce several Sparse Online Relative Similarity (SORS) learning algorithms, which learn a sparse model during the learning process, so that the memory and computational cost can be significantly reduced. We theoretically analyze the proposed algorithms, and evaluate them on some real-world high dimensional datasets. Encouraging empirical results demonstrate the advantages of our approach in terms of efficiency and efficacy.

On-line portfolio selection, a fundamental problem in computational finance, has attracted increasing interest from artificial intelligence and machine learning communities in recent years. Empirical evidence shows that stock's high and low prices are temporary and stock prices are likely to follow the mean reversion phenomenon. While existing mean reversion strategies are shown to achieve good empirical performance on many real datasets, they often make the single-period mean reversion assumption, which is not always satisfied, leading to poor performance in certain real datasets. To overcome this limitation, this article proposes a multiple-period mean reversion, or so-called “Moving Average Reversion” (MAR), and a new on-line portfolio selection strategy named “On-Line Moving Average Reversion” (OLMAR), which exploits MAR via efficient and scalable online machine learning techniques. From our empirical results on real markets, we found that OLMAR can overcome the drawbacks of existing mean reversion algorithms and achieve significantly better results, especially on the datasets where existing mean reversion algorithms failed. In addition to its superior empirical performance, OLMAR also runs extremely fast, further supporting its practical applicability to a wide range of applications. Finally, we have made all the datasets and source codes of this work publicly available at our project website: http://OLPS.stevenhoi.org/.

Kernel-based regression represents an important family of learning techniques for solving challenging regression tasks with non-linear patterns. Despite being studied extensively, most of the existing work suffers from two major drawbacks: (i) they are often designed for solving regression tasks in a batch learning setting, making them not only computationally inefficient and but also poorly scalable in real-world applications where data arrives sequentially; and (ii) they usually assume a fixed kernel function is given prior to the learning task, which could result in poor performance if the chosen kernel is inappropriate. To overcome these drawbacks, this paper presents a novel scheme of Online Multiple Kernel Regression (OMKR), which sequentially learns the kernel-based regressor in an online and scalable fashion, and dynamically explore a pool of multiple diverse kernels to avoid suffering from a single fixed poor kernel so as to remedy the drawback of manual/heuristic kernel selection. The OMKR problem is more challenging than regular kernel-based regression tasks since we have to on-the-fly determine both the optimal kernel-based regressor for each individual kernel and the best combination of the multiple kernel regressors. In this paper, we propose a family of OMKR algorithms for regression and discuss their application to time series prediction tasks. We also analyze the theoretical bounds of the proposed OMKR method and conduct extensive experiments to evaluate its empirical performance on both real-world regression and times series prediction tasks.

Online portfolio selection has been attracting increasing attention from the data mining and machine learning communities. All existing online portfolio selection strategies focus on the first order information of a portfolio vector, though the second order information may also be beneficial to a strategy. Moreover, empirical evidence shows that relative stock prices may follow the mean reversion property, which has not been fully exploited by existing strategies. This article proposes a novel online portfolio selection strategy named Confidence Weighted Mean Reversion (CWMR). Inspired by the mean reversion principle in finance and confidence weighted online learning technique in machine learning, CWMR models the portfolio vector as a Gaussian distribution, and sequentially updates the distribution by following the mean reversion trading principle. CWMR’s closed-form updates clearly reflect the mean reversion trading idea. We also present several variants of CWMR algorithms, including a CWMR mixture algorithm that is theoretical universal. Empirically, CWMR strategy is able to effectively exploit the power of mean reversion for online portfolio selection. Extensive experiments on various real markets show that the proposed strategy is superior to the state-of-the-art techniques. The experimental testbed including source codes and data sets is available online.

This article proposes a novel online portfolio selection strategy named “Passive Aggressive Mean Reversion” (PAMR). Unlike traditional trend following approaches, the proposed approach relies upon the mean reversion relation of financial markets. Equipped with online passive aggressive learning technique from machine learning, the proposed portfolio selection strategy can effectively exploit the mean reversion property of markets. By analyzing PAMR’s update scheme, we find that it nicely trades off between portfolio return and volatility risk and reflects the mean reversion trading principle. We also present several variants of PAMR algorithm, including a mixture algorithm which mixes PAMR and other strategies. We conduct extensive numerical experiments to evaluate the empirical performance of the proposed algorithms on various real datasets. The encouraging results show that in most cases the proposed PAMR strategy outperforms all benchmarks and almost all state-of-the-art portfolio selection strategies under various performance metrics. In addition to its superior performance, the proposed PAMR runs extremely fast and thus is very suitable for real-life online trading applications. The experimental testbed including source codes and data sets is available at http://www.cais.ntu.edu.sg/~chhoi/PAMR/ .

Machine learning techniques have been adopted to select portfolios from financial markets in some emerging intelligent business applications. In this article, we propose a novel learning-to-trade algorithm termed COR relation-driven N onparametric learning strategy (CORN) for actively trading stocks. CORN effectively exploits statistical relations between stock market windows via a nonparametric learning approach. We evaluate the empirical performance of our algorithm extensively on several large historical and latest real stock markets, and show that it can easily beat both the market index and the best stock in the market substantially (without or with small transaction costs), and also surpass a variety of state-of-the-art techniques significantly.