A key question in Reinforcement Learning is which representation an agent can learn to efficiently reuse knowledge between different tasks. Recently the Successor Representation was shown to have empirical benefits for transferring knowledge between tasks with shared transition dynamics. This paper presents Model Features: a feature representation that clusters behaviourally equivalent states and that is equivalent to a Model-Reduction. Further, we present a Successor Feature model which shows that learning Successor Features is equivalent to learning a Model-Reduction. A novel optimization objective is developed and we provide bounds showing that minimizing this objective results in an increasingly improved approximation of a Model-Reduction. Further, we provide transfer experiments on randomly generated MDPs which vary in their transition and reward functions but approximately preserve behavioural equivalence between states. These results demonstrate that Model Features are suitable for transfer between tasks with varying transition and reward functions.

We consider doing Bayesian inference by minimizing the KL divergence on the 2-Wasserstein space $\mathcal{P}_2$. By exploring the Riemannian structure of $\mathcal{P}_2$, we develop two inference methods by simulating the gradient flow on $\mathcal{P}_2$ via updating particles, and an acceleration method that speeds up all such particle-simulation-based inference methods. Moreover we analyze the approximation flexibility of such methods, and conceive a novel bandwidth selection method for the kernel that they use. We note that $\mathcal{P}_2$ is quite abstract and general so that our methods can make closer approximation, while it still has a rich structure that enables practical implementation. Experiments show the effectiveness of the two proposed methods and the improvement of convergence by the acceleration method.

In this paper, we propose a new technique named Stochastic Path-Integrated Differential EstimatoR (SPIDER), which can be used to track many deterministic quantities of interest with significantly reduced computational cost. Combining SPIDER with the method of normalized gradient descent, we propose two new algorithms, namely SPIDER-SFO and SPIDER-SSO, that solve non-convex stochastic optimization problems using stochastic gradients only. We provide sharp error-bound results on their convergence rates. Specially, we prove that the SPIDER-SFO and SPIDER-SSO algorithms achieve a record-breaking $\tilde{O}(\epsilon^{-3})$ gradient computation cost to find an $\epsilon$-approximate first-order and $(\epsilon, O(\epsilon^{0.5}))$-approximate second-order stationary point, respectively. In addition, we prove that SPIDER-SFO nearly matches the algorithmic lower bound for finding stationary point under the gradient Lipschitz assumption in the finite-sum setting.

Scalability may also pose a critical bottleneck one should care about. Each of these meta packages deal with it at different ways.

The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP), a well-known non-parametric and interpretable Bayesian model, which suffers from cubic complexity to training size. To improve the scalability while retaining the desirable prediction quality, a variety of scalable GPs have been presented. But they have not yet been comprehensively reviewed and discussed in a unifying way in order to be well understood by both academia and industry. To this end, this paper devotes to reviewing state-of-the-art scalable GPs involving two main categories: global approximations which distillate the entire data and local approximations which divide the data for subspace learning. Particularly, for global approximations, we mainly focus on sparse approximations comprising prior approximations which modify the prior but perform exact inference, and posterior approximations which retain exact prior but perform approximate inference; for local approximations, we highlight the mixture/product of experts that conducts model averaging from multiple local experts to boost predictions. To present a complete review, recent advances for improving the scalability and model capability of scalable GPs are reviewed. Finally, the extensions and open issues regarding the implementation of scalable GPs in various scenarios are reviewed and discussed to inspire novel ideas for future research avenues.

Bayesian optimization offers the possibility of optimizing black-box operations not accessible through traditional techniques. The success of Bayesian optimization methods such as Expected Improvement (EI) are significantly affected by the degree of trade-off between exploration and exploitation. Too much exploration can lead to inefficient optimization protocols, whilst too much exploitation leaves the protocol open to strong initial biases, and a high chance of getting stuck in a local minimum. Typically, a constant margin is used to control this trade-off, which results in yet another hyper-parameter to be optimized. We propose contextual improvement as a simple, yet effective heuristic to counter this - achieving a one-shot optimization strategy. Our proposed heuristic can be swiftly calculated and improves both the speed and robustness of discovery of optimal solutions. We demonstrate its effectiveness on both synthetic and real world problems and explore the unaccounted for uncertainty in the pre-determination of search hyperparameters controlling explore-exploit trade-off.

In this article, we proposed the Coopetititve Soft Gating Ensemble or CSGE for general machine learning tasks. The goal of machine learning is to create models which poses a high generalisation capability. But often problems are too complex to be solved by a single model. Therefore, ensemble methods combine predictions of multiple models. The CSGE comprises a comprehensible combination based on three different aspects relating to the overall global historical performance, the local-/situation-dependent and time-dependent performance of its ensemble members. The CSGE can be optimised according to arbitrary loss functions making it accessible for a wider range of problems. We introduce a novel training procedure including a hyper-parameter initialisation at its heart. We show that the CSGE approach reaches state-of-the-art performance for both classification and regression tasks. Still, the CSGE allows to quantify the influence of all base estimators by means of the three weighting aspects in a comprehensive way. In terms of Organic computing (OC), our CSGE approach combines multiple base models towards a self-organising complex system. Moreover, we provide a scikit-learn compatible implementation.

Tensor decompositions are powerful tools for large data analytics as they jointly model multiple aspects of data into one framework and enable the discovery of the latent structures and higher-order correlations within the data. One of the most widely studied and used decompositions, especially in data mining and machine learning, is the Canonical Polyadic or CP decomposition. However, today's datasets are not static and these datasets often dynamically growing and changing with time. To operate on such large data, we present OCTen the first ever compression-based online parallel implementation for the CP decomposition. We conduct an extensive empirical analysis of the algorithms in terms of fitness, memory used and CPU time, and in order to demonstrate the compression and scalability of the method, we apply OCTen to big tensor data. Indicatively, OCTen performs on-par or better than state-of-the-art online and online methods in terms of decomposition accuracy and efficiency, while saving up to 40-200 % memory space.

Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this algorithm as the approximate survey propagation (ASP) and derive it for a class of low-rank matrix estimation problems. We derive the state evolution for the ASP algorithm and prove that it reproduces the one-step replica symmetry breaking (1RSB) fixed-point equations, well-known in physics of disordered systems. Our derivation thus gives a concrete algorithmic meaning to the 1RSB equations that is of independent interest. We characterize the performance of ASP in terms of convergence and mean-squared error as a function of the free Parisi parameter s. We conclude that when there is a model mismatch between the true generative model and the inference model, the performance of AMP rapidly degrades both in terms of MSE and of convergence, while ASP converges in a larger regime and can reach lower errors. Among other results, our analysis leads us to a striking hypothesis that whenever s (or other parameters) can be set in such a way that the Nishimori condition $M=Q>0$ is restored, then the corresponding algorithm is able to reach mean-squared error as low as the Bayes-optimal error obtained when the model and its parameters are known and exactly matched in the inference procedure.

Classification problems involving high dimensional data are extensive in many fields such as finance, marketing, and bioinformatics. Unique challenges with high dimensional datasets are numerous and well known, with many classifiers built under traditional low dimensional frameworks simply unable to be applied to such high dimensional data. Discriminant Analysis (DA) is one such example (Fisher, 1936). DA classifiers work by assuming the distribution of the features is strictly Gaussian at the class level, and assign a particular point to the class label which minimises the Mahalanobis (for linear discriminant analysis (LDA)) distance between that point and the mean of the multivariate normal corresponding to such class. Although extraordinary simple and easy to use in low dimensional settings, DA is well known to be unusable in high dimensions due to the maximum likelihood estimate of the corresponding covariance matrix being singular when the number of features is greater than that of the observations.