The neural attention mechanism plays an important role in many natural language processing applications. In particular, the use of multi-head attention extends single-head attention by allowing a model to jointly attend information from different perspectives. Without explicit constraining, however, multi-head attention may suffer from attention collapse, an issue that makes different heads extract similar attentive features, thus limiting the model's representation power. In this paper, for the first time, we provide a novel understanding of multi-head attention from a Bayesian perspective. Based on the recently developed particle-optimization sampling techniques, we propose a non-parametric approach that explicitly improves the repulsiveness in multi-head attention and consequently strengthens model's expressiveness. Remarkably, our Bayesian interpretation provides theoretical inspirations on the not-well-understood questions: why and how one uses multi-head attention. Extensive experiments on various attention models and applications demonstrate that the proposed repulsive attention can improve the learned feature diversity, leading to more informative representations with consistent performance improvement on various tasks.

Block modeling is widely used in studies on complex networks. The cornerstone model is the stochastic block model (SBM), widely used over the past decades. However, the SBM is limited in analyzing complex networks as the model is, in essence, a random graph model that cannot reproduce the basic properties of many complex networks, such as sparsity and heavy-tailed degree distribution. In this paper, we provide an edge exchangeable block model that incorporates such basic features and simultaneously infers the latent block structure of a given complex network. Our model is a Bayesian nonparametric model that flexibly estimates the number of blocks and takes into account the possibility of unseen nodes. Using one synthetic dataset and one real-world stock ownership dataset, we show that our model outperforms state-of-the-art SBMs for held-out link prediction tasks.

Following the remarkable success of the AlphaGO series, 2019 was a booming year that witnessed significant advances in multi-agent reinforcement learning (MARL) techniques. MARL corresponds to the learning problem in a multi-agent system in which multiple agents learn simultaneously. MARL is an interdisciplinary domain with a long history that includes game theory, machine learning, stochastic control, psychology, and optimisation. Although MARL has achieved considerable empirical success in solving real-world games, there is a lack of a self-contained overview in the literature that elaborates the game theoretical foundations of modern MARL methods and summarises the recent advances. In fact, the majority of existing surveys are outdated and do not fully cover the recent developments since 2010. In this work, we provide a monograph on MARL that covers both the fundamentals and the latest developments in the research frontier. The goal of our monograph is to provide a self-contained assessment of the current state-of-the-art MARL techniques from a game theoretical perspective. We expect this work to serve as a stepping stone for both new researchers who are about to enter this fast-growing domain and existing domain experts who want to obtain a panoramic view and identify new directions based on recent advances.

Legged robots often use separate control policies that are highly engineered for traversing difficult terrain such as stairs, gaps, and steps, where switching between policies is only possible when the robot is in a region that is common to adjacent controllers. Deep Reinforcement Learning (DRL) is a promising alternative to hand-crafted control design, though typically requires the full set of test conditions to be known before training. DRL policies can result in complex (often unrealistic) behaviours that have few or no overlapping regions between adjacent policies, making it difficult to switch behaviours. In this work we develop multiple DRL policies with Curriculum Learning (CL), each that can traverse a single respective terrain condition, while ensuring an overlap between policies. We then train a network for each destination policy that estimates the likelihood of successfully switching from any other policy. We evaluate our switching method on a previously unseen combination of terrain artifacts and show that it performs better than heuristic methods. While our method is trained on individual terrain types, it performs comparably to a Deep Q Network trained on the full set of terrain conditions. This approach allows the development of separate policies in constrained conditions with embedded prior knowledge about each behaviour, that is scalable to any number of behaviours, and prepares DRL methods for applications in the real world

Potential-based reward shaping provides an approach for designing good reward functions, with the purpose of speeding up learning. However, automatically finding potential functions for complex environments is a difficult problem (in fact, of the same difficulty as learning a value function from scratch). We propose a new framework for learning potential functions by leveraging ideas from graph representation learning. Our approach relies on Graph Convolutional Networks which we use as a key ingredient in combination with the probabilistic inference view of reinforcement learning. More precisely, we leverage Graph Convolutional Networks to perform message passing from rewarding states. The propagated messages can then be used as potential functions for reward shaping to accelerate learning. We verify empirically that our approach can achieve considerable improvements in both small and high-dimensional control problems.

Savage (1972) lays down the foundation of Bayesian decision theory, but asserts that it is not applicable in big worlds where the environment is complex. Using the theory of finite automaton to model belief formation, this paper studies the characteristics of optimal learning behavior in small and big worlds, where the complexity of the environment is low and high, respectively, relative to the cognitive ability of the decision maker. Confirming Savage's claim, optimal learning behavior is closed to Bayesian in small worlds but significantly different in big worlds. In addition, I show that in big worlds, the optimal learning behavior could exhibit a wide range of well-documented non-Bayesian learning behavior, including the use of heuristic, correlation neglect, persistent over-confidence, inattentive learning, and other behaviors of model simplification or misspecification. These results establish a clear and testable relationship between the prominence of non-Bayesian learning behavior, complexity and cognitive ability.

This paper studies the source (event) localization problem in decentralized wireless sensor networks (WSNs) under the fault model without knowing the sensor parameters. Event localizations have many applications such as localizing intruders, Wifi hotspots and users, and faults in power systems. Previous studies assume the true knowledge (or good estimates) of sensor parameters (e.g., fault model probability or Region of Influence (ROI) of the source) for source localization. However, we propose two methods to estimate the source location in this paper under the fault model: hitting set approach and feature selection method, which only utilize the noisy data set at the fusion center for estimation of the source location without knowing the sensor parameters. The proposed methods have been shown to localize the source effectively. We also study the lower bound on the sample complexity requirement for hitting set method. These methods have also been extended for multiple sources localizations. In addition, we modify the proposed feature selection approach to use maximum likelihood. Finally, extensive simulations are carried out for different settings (i.e., the number of sensor nodes and sample complexity) to validate our proposed methods in comparison to centroid, maximum likelihood, FTML, SNAP estimators.

A Pseudo-Random Number Generator (PRNG) is any algorithm generating a sequence of numbers approximating properties of random numbers. These numbers are widely employed in mid-level cryptography and in software applications. Test suites are used to evaluate PRNGs quality by checking statistical properties of the generated sequences. These sequences are commonly represented bit by bit. This paper proposes a Reinforcement Learning (RL) approach to the task of generating PRNGs from scratch by learning a policy to solve a partially observable Markov Decision Process (MDP), where the full state is the period of the generated sequence and the observation at each time step is the last sequence of bits appended to such state. We use a Long-Short Term Memory (LSTM) architecture to model the temporal relationship between observations at different time steps, by tasking the LSTM memory with the extraction of significant features of the hidden portion of the MDP's states. We show that modeling a PRNG with a partially observable MDP and a LSTM architecture largely improves the results of the fully observable feedforward RL approach introduced in previous work.

In recent years, bankruptcy forecasting has gained lot of attention from researchers as well as practitioners in the field of financial risk management. For bankruptcy prediction, various approaches proposed in the past and currently in practice relies on accounting ratios and using statistical modeling or machine learning methods. These models have had varying degrees of successes. Models such as Linear Discriminant Analysis or Artificial Neural Network employ discriminative classification techniques. They lack explicit provision to include prior expert knowledge. In this paper, we propose another route of generative modeling using Expert Bayesian framework. The biggest advantage of the proposed framework is an explicit inclusion of expert judgment in the modeling process. Also the proposed methodology provides a way to quantify uncertainty in prediction. As a result the model built using Bayesian framework is highly flexible, interpretable and intuitive in nature. The proposed approach is well suited for highly regulated or safety critical applications such as in finance or in medical diagnosis. In such cases accuracy in the prediction is not the only concern for decision makers. Decision makers and other stakeholders are also interested in uncertainty in the prediction as well as interpretability of the model. We empirically demonstrate these benefits of proposed framework on real world dataset using Stan, a probabilistic programming language. We found that the proposed model is either comparable or superior to the other existing methods. Also resulting model has much less False Positive Rate compared to many existing state of the art methods. The corresponding R code for the experiments is available at Github repository.

Policy evaluation and, in particular, temporal difference (TD) learning is a key ingredient in reinforcement learning. Here the expected value of future rewards is estimated from simulations of a given policy. When a stationary policy is fixed, the simulated process is a time-homogeneous Markov chain. The convergence of the policy evaluation algorithm is analyzed using stochastic approximation techniques under asynchronous Markovian updates. There is a well-developed theory of stochastic approximation that establishes the convergence of a variety of policy evaluation schemes.