We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth term and multiple stochastic nonsmooth terms. In each iteration, our splitting technique only requires access to a stochastic gradient of the smooth term and a stochastic proximal operator for each of the nonsmooth terms. We establish nonasymptotic sublinear and linear convergence rates under convexity and strong convexity of the smooth term, respectively, expressed in terms of the KL divergence and Wasserstein distance. We illustrate the efficiency of our sampling technique through numerical simulations on a Bayesian learning task.

We develop a method to combine Markov chain Monte Carlo (MCMC) and variational inference (VI), leveraging the advantages of both inference approaches. Specifically, we improve the variational distribution by running a few MCMC steps. To make inference tractable, we introduce the variational contrastive divergence (VCD), a new divergence that replaces the standard Kullback-Leibler (KL) divergence used in VI. The VCD captures a notion of discrepancy between the initial variational distribution and its improved version (obtained after running the MCMC steps), and it converges asymptotically to the symmetrized KL divergence between the variational distribution and the posterior of interest. The VCD objective can be optimized efficiently with respect to the variational parameters via stochastic optimization. We show experimentally that optimizing the VCD leads to better predictive performance on two latent variable models: logistic matrix factorization and variational autoencoders (VAEs).

Autonomous driving in a crowded environment, e.g., a busy traffic intersection, is an unsolved challenge for robotics. The robot vehicle must contend with a dynamic and partially observable environment, noisy sensors, and many agents. A principled approach is to formalize it as a Partially Observable Markov Decision Process (POMDP) and solve it through online belief-tree search. To handle a large crowd and achieve real-time performance in this very challenging setting, we propose LeTS-Drive, which integrates online POMDP planning and deep learning. It consists of two phases. In the offline phase, we learn a policy and the corresponding value function by imitating the belief tree search. In the online phase, the learned policy and value function guide the belief tree search. LeTS-Drive leverages the robustness of planning and the runtime efficiency of learning to enhance the performance of both. Experimental results in simulation show that LeTS-Drive outperforms either planning or imitation learning alone and develops sophisticated driving skills.

General intelligence, the ability to solve arbitrary solvable problems, is supposed by many to be artificially constructible. Narrow intelligence, the ability to solve a given particularly difficult problem, has seen impressive recent development. Notable examples include self-driving cars, Go engines, image classifiers, and translators. Artificial General Intelligence (AGI) presents dangers that narrow intelligence does not: if something smarter than us across every domain were indifferent to our concerns, it would be an existential threat to humanity, just as we threaten many species despite no ill will. Even the theory of how to maintain the alignment of an AGI's goals with our own has proven highly elusive. We present the first algorithm we are aware of for asymptotically unambitious AGI, where "unambitiousness" includes not seeking arbitrary power. Thus, we identify an exception to the Instrumental Convergence Thesis, which is roughly that by default, an AGI would seek power, including over us.

Often times, we specify tasks for a robot using temporal language that can also span different levels of abstraction. The example command ``go to the kitchen before going to the second floor'' contains spatial abstraction, given that ``floor'' consists of individual rooms that can also be referred to in isolation ("kitchen", for example). There is also a temporal ordering of events, defined by the word "before". Previous works have used Linear Temporal Logic (LTL) to interpret temporal language (such as "before"), and Abstract Markov Decision Processes (AMDPs) to interpret hierarchical abstractions (such as "kitchen" and "second floor"), separately. To handle both types of commands at once, we introduce the Abstract Product Markov Decision Process (AP-MDP), a novel approach capable of representing non-Markovian reward functions at different levels of abstractions. The AP-MDP framework translates LTL into its corresponding automata, creates a product Markov Decision Process (MDP) of the LTL specification and the environment MDP, and decomposes the problem into subproblems to enable efficient planning with abstractions. AP-MDP performs faster than a non-hierarchical method of solving LTL problems in over 95% of tasks, and this number only increases as the size of the environment domain increases. We also present a neural sequence-to-sequence model trained to translate language commands into LTL expression, and a new corpus of non-Markovian language commands spanning different levels of abstraction. We test our framework with the collected language commands on a drone, demonstrating that our approach enables a robot to efficiently solve temporal commands at different levels of abstraction.

Though reinforcement learning has greatly benefited from the incorporation of neural networks, the inability to verify the correctness of such systems limits their use. Current work in explainable deep learning focuses on explaining only a single decision in terms of input features, making it unsuitable for explaining a sequence of decisions. To address this need, we introduce Abstracted Policy Graphs, which are Markov chains of abstract states. This representation concisely summarizes a policy so that individual decisions can be explained in the context of expected future transitions. Additionally, we propose a method to generate these Abstracted Policy Graphs for deterministic policies given a learned value function and a set of observed transitions, potentially off-policy transitions used during training. Since no restrictions are placed on how the value function is generated, our method is compatible with many existing reinforcement learning methods. We prove that the worst-case time complexity of our method is quadratic in the number of features and linear in the number of provided transitions, $O(|F|^2 |tr\_samples|)$. By applying our method to a family of domains, we show that our method scales well in practice and produces Abstracted Policy Graphs which reliably capture relationships within these domains.

Capsule Networks are a recently proposed alternative for constructing Neural Networks, and early indications suggest that they can provide greater generalisation capacity using fewer parameters. In capsule networks scalar neurons are replaced with capsule vectors or matrices, whose entries represent different properties of objects. The relationships between objects and its parts are learned via trainable viewpoint-invariant transformation matrices, and the presence of a given object is decided by the level of agreement among votes from its parts. This interaction occurs between capsule layers and is a process called routing-by-agreement. Although promising, capsule networks remain underexplored by the community, and in this paper we present a new capsule routing algorithm based of Variational Bayes for a mixture of transforming gaussians. Our Bayesian approach addresses some of the inherent weaknesses of EM routing such as the 'variance collapse' by modelling uncertainty over the capsule parameters in addition to the routing assignment posterior probabilities. We test our method on public domain datasets and outperform the state-of-the-art performance on smallNORB using 50% less capsules.

We study the problem of learning the transition matrices of a set of Markov chains from a single stream of observations on each chain. We assume that the Markov chains are ergodic but otherwise unknown. The learner can sample Markov chains sequentially to observe their states. The goal of the learner is to sequentially select various chains to learn transition matrices uniformly well with respect to some loss function. We introduce a notion of loss that naturally extends the squared loss for learning distributions to the case of Markov chains, and further characterize the notion of being \emph{uniformly good} in all problem instances. We present a novel learning algorithm that efficiently balances \emph{exploration} and \emph{exploitation} intrinsic to this problem, without any prior knowledge of the chains. We provide finite-sample PAC-type guarantees on the performance of the algorithm. Further, we show that our algorithm asymptotically attains an optimal loss.

Dialogue policy plays an important role in task-oriented spoken dialogue systems. It determines how to respond to users. The recently proposed deep reinforcement learning (DRL) approaches have been used for policy optimization. However, these deep models are still challenging for two reasons: 1) Many DRL-based policies are not sample-efficient. 2) Most models don't have the capability of policy transfer between different domains. In this paper, we propose a universal framework, AgentGraph, to tackle these two problems. The proposed AgentGraph is the combination of GNN-based architecture and DRL-based algorithm. It can be regarded as one of the multi-agent reinforcement learning approaches. Each agent corresponds to a node in a graph, which is defined according to the dialogue domain ontology. When making a decision, each agent can communicate with its neighbors on the graph. Under AgentGraph framework, we further propose Dual GNN-based dialogue policy, which implicitly decomposes the decision in each turn into a high-level global decision and a low-level local decision. Experiments show that AgentGraph models significantly outperform traditional reinforcement learning approaches on most of the 18 tasks of the PyDial benchmark. Moreover, when transferred from the source task to a target task, these models not only have acceptable initial performance but also converge much faster on the target task.

Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static graphs. However, many applications involve evolving graphs. This introduces important challenges for learning and inference since nodes, attributes, and edges change over time. In this survey, we review the recent advances in representation learning for dynamic graphs, including dynamic knowledge graphs. We describe existing models from an encoder-decoder perspective, categorize these encoders and decoders based on the techniques they employ, and analyze the approaches in each category. We also review several prominent applications and widely used datasets, and highlight directions for future research.