Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system. However, in practical situations, data is often obtained from multiple sources which results in a collection of matrices rather than a single one. In this work, we consider the problem of collective matrix completion with multiple and heterogeneous matrices, which can be count, binary, continuous, etc. We first investigate the setting where, for each source, the matrix entries are sampled from an exponential family distribution. Then, we relax the assumption of exponential family distribution for the noise and we investigate the distribution-free case. In this setting, we do not assume any specific model for the observations. The estimation procedures are based on minimizing the sum of a goodness-of-fit term and the nuclear norm penalization of the whole collective matrix. We prove that the proposed estimators achieve fast rates of convergence under the two considered settings and we corroborate our results with numerical experiments.

This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under mild assumptions, we show that the asymptotic classification error approaches a deterministic quantity that depends only on the means and covariances associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized discriminant analsysis, in practical large but finite dimensions, and can be used to determine and pre-estimate the optimal regularization parameter that minimizes the misclassification error probability. Despite being theoretically valid only for Gaussian data, our findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from the popular USPS data base, thereby making an interesting connection between theory and practice.

In multi-agent planning, agents jointly compute a plan that achieves mutual goals, keeping certain information private to the individual agents. Agents' coordination is achieved through the transmission of messages. These messages can be a source of privacy leakage as they can permit a malicious agent to collect information about other agents' actions and search states. In this paper, we investigate the usage of novelty techniques in the context of (decentralised) multi-agent privacy-preserving planning, addressing the challenges related to the agents' privacy and performance. In particular, we show that the use of novelty based techniques can significantly reduce the number of messages transmitted among agents, better preserving their privacy and improving their performance. An experimental study analyses the effectiveness of our techniques and compares them with the state-of-the-art. Finally, we evaluate the robustness of our approach, considering different delays in the transmission of messages as they would occur in overloaded networks, due for example to massive attacks or critical situations.

Learning about many things can provide numerous benefits to a reinforcement learning system. For example, learning many auxiliary value functions, in addition to optimizing the environmental reward, appears to improve both exploration and representation learning. The question we tackle in this paper is how to sculpt the stream of experience---how to adapt the system's behaviour---to optimize the learning of a collection of value functions. A simple answer is to compute an intrinsic reward based on the statistics of each auxiliary learner, and use reinforcement learning to maximize that intrinsic reward. Unfortunately, implementing this simple idea has proven difficult, and thus has been the focus of decades of study. It remains unclear which of the many possible measures of learning would work well in a parallel learning setting where environmental reward is extremely sparse or absent. In this paper, we investigate and compare different intrinsic reward mechanisms in a new bandit-like parallel-learning testbed. We discuss the interaction between reward and prediction learners and highlight the importance of introspective prediction learners: those that increase their rate of learning when progress is possible, and decrease when it is not. We provide a comprehensive empirical comparison of 15 different rewards, including well-known ideas from reinforcement learning and active learning. Our results highlight a simple but seemingly powerful principle: intrinsic rewards based on the amount of learning can generate useful behaviour, if each individual learner is introspective.

Solving sequential decision prediction problems, including those in imitation learning settings, requires mitigating the problem of covariate shift. The standard approach, DAgger, relies on capturing expert behaviour in all states that the agent reaches. In real-world settings, querying an expert is costly. We propose a new active learning algorithm that selectively queries the expert, based on both a prediction of agent error and a proxy for agent risk, that maintains the performance of unrestrained expert querying systems while substantially reducing the number of expert queries made. We show that our approach, RadGrad, has the potential to improve upon existing safety-aware algorithms, and matches or exceeds the performance of DAgger and variants (i.e., SafeDAgger) in one simulated environment. However, we also find that a more complex environment poses challenges not only to our proposed method, but also to existing safety-aware algorithms, which do not match the performance of DAgger in our experiments.

Data-driven approaches are becoming more common as problem-solving techniques in many areas of research and industry. In most cases, machine learning models are the key component of these solutions, but a solution involves multiple such models, along with significant levels of reasoning with the models' output and input. Current technologies do not make such techniques easy to use for application experts who are not fluent in machine learning nor for machine learning experts who aim at testing ideas and models on real-world data in the context of the overall AI system. We review key efforts made by various AI communities to provide languages for high-level abstractions over learning and reasoning techniques needed for designing complex AI systems. We classify the existing frameworks based on the type of techniques and the data and knowledge representations they use, provide a comparative study of the way they address the challenges of programming real-world applications, and highlight some shortcomings and future directions.

Efficient exploration is necessary to achieve good sample efficiency for reinforcement learning in general. From small, tabular settings such as gridworlds to large, continuous and sparse reward settings such as robotic object manipulation tasks, exploration through adding an uncertainty bonus to the reward function has been shown to be effective when the uncertainty is able to accurately drive exploration towards promising states. However reward bonuses can still be inefficient since they are non-stationary, which means that we must wait for function approximators to catch up and converge again when uncertainties change. We propose the idea of directed exploration, that is learning a goal-conditioned policy where goals are simply other states, and using that to directly try to reach states with large uncertainty. The goal-conditioned policy is independent of uncertainty and is thus stationary. We show in our experiments how directed exploration is more efficient at exploration and more robust to how the uncertainty is computed than adding bonuses to rewards.

Dyna is an architecture for model-based reinforcement learning (RL), where simulated experience from a model is used to update policies or value functions. A key component of Dyna is search-control, the mechanism to generate the state and action from which the agent queries the model, which remains largely unexplored. In this work, we propose to generate such states by using the trajectory obtained from Hill Climbing (HC) the current estimate of the value function. This has the effect of propagating value from high-value regions and of preemptively updating value estimates of the regions that the agent is likely to visit next. We derive a noisy stochastic projected gradient ascent algorithm for hill climbing, and highlight a connection to Langevin dynamics. We provide an empirical demonstration on four classical domains that our algorithm, HC-Dyna, can obtain significant sample efficiency improvements. We study the properties of different sampling distributions for search-control, and find that there appears to be a benefit specifically from using the samples generated by climbing on current value estimates from low-value to high-value region.

We introduce the Constrained Least-cost Tour (CLT) problem: given an undirected graph with weight and cost functions on the edges, minimise the total cost of a tour rooted at a start vertex such that the total weight lies within a given range. CLT is related to the family of Travelling Salesman Problems with Profits, but differs by defining the weight function on edges instead of vertices, and by requiring the total weight to be within a range instead of being at least some quota. We prove CLT is $\mathcal{NP}$-hard, even in the simple case when the input graph is a path. We derive an informative lower bound by relaxing the integrality of edges and propose a heuristic motivated by this relaxation. For the case that requires the tour to be a simple cycle, we develop two heuristics which exploit Suurballe's algorithm to find low-cost, weight-feasible cycles. We demonstrate our algorithms by addressing a real-world problem that affects urban populations: finding routes that minimise air pollution exposure for walking, running and cycling in the city of London.

Explaining and interpreting the decisions of recommender systems are becoming extremely relevant both, for improving predictive performance, and providing valid explanations to users. While most of the recent interest has focused on providing local explanations, there has been a much lower emphasis on studying the effects of model dynamics and its impact on explanation. In this paper, we perform a focused study on the impact of model interpretability in the context of calibration. Specifically, we address the challenges of both over-confident and under-confident predictions with interpretability using attention distribution. Our results indicate that the means of using attention distributions for interpretability are highly unstable for un-calibrated models. Our empirical analysis on the stability of attention distribution raises questions on the utility of attention for explainability.