Modern reinforcement learning and planning algorithms have achieved tremendous successes on various tasks [Mnih et al., 2015, Silver et al., 2017]. However, most of these algorithms work in the standard Markov decision process (MDP) framework where the goal is to maximize the cumulative reward and thus it can be difficult to apply them to various practical sequential decision-making problems. In this paper, we study planning in generalized MDPs, where instead of maximizing the cumulative reward, the goal is to maximize the objective value induced by a submodular function. To motivate our approach, let us consider the following scenario: a company manufactures cars, and as part of its customer service, continuously monitors the status of all cars produced by the company. Each car is equipped with a number of sensors, each of which constantly produces noisy measurements of some attribute of the car, e.g., speed, location, temperature, etc. Due to bandwidth constraints, at any moment, each car may choose to transmit data generated by a single sensor to the company. The goal is to combine the statistics collected over a fixed period of time, presumably from multiple sensors, to gather as much information about the car as possible. Perhaps one seemingly natural strategy is to transmit only data generated by the most "informative" sensor. However, as the output of a sensor remains the same between two samples, it is pointless to transmit the same data multiple times. One may alternatively try to order sensors by their "informativity" and always choose the most informative sensor that has not yet transmitted data since the last sample was generated.

We study reinforcement learning (RL) for text-based games, which are interactive simulations in the context of natural language. While different methods have been developed to represent the environment information and language actions, existing RL agents are not empowered with any reasoning capabilities to deal with textual games. In this work, we aim to conduct explicit reasoning with knowledge graphs for decision making, so that the actions of an agent are generated and supported by an interpretable inference procedure. We propose a stacked hierarchical attention mechanism to construct an explicit representation of the reasoning process by exploiting the structure of the knowledge graph. We extensively evaluate our method on a number of man-made benchmark games, and the experimental results demonstrate that our method performs better than existing text-based agents.

How can we plan efficiently in real time to control an agent in a complex environment that may involve many other agents? While existing sample-based planners have enjoyed empirical success in large POMDPs, their performance heavily relies on a fast simulator. However, real-world scenarios are complex in nature and their simulators are often computationally demanding, which severely limits the performance of online planners. In this work, we propose influence-augmented online planning, a principled method to transform a factored simulator of the entire environment into a local simulator that samples only the state variables that are most relevant to the observation and reward of the planning agent and captures the incoming influence from the rest of the environment using machine learning methods. Our main experimental results show that planning on this less accurate but much faster local simulator with POMCP leads to higher real-time planning performance than planning on the simulator that models the entire environment.

Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis of non-negative data. In particular, a lot of effort has been devoted to probabilistic NMF, namely estimation or inference tasks in probabilistic models describing the data, based for example on Poisson or exponential likelihoods. When dealing with time series data, several works have proposed to model the evolution of the activation coefficients as a non-negative Markov chain, most of the time in relation with the Gamma distribution, giving rise to so-called temporal NMF models. In this paper, we review four Gamma Markov chains of the NMF literature, and show that they all share the same drawback: the absence of a well-defined stationary distribution. We then introduce a fifth process, an overlooked model of the time series literature named BGAR(1), which overcomes this limitation. These temporal NMF models are then compared in a MAP framework on a prediction task, in the context of the Poisson likelihood.

The airworthiness and safety of a non-pedigreed autopilot must be verified, but the cost to formally do so can be prohibitive. We can bypass formal verification of non-pedigreed components by incorporating Runtime Safety Assurance (RTSA) as mechanism to ensure safety. RTSA consists of a meta-controller that observes the inputs and outputs of a non-pedigreed component and verifies formally specified behavior as the system operates. When the system is triggered, a verified recovery controller is deployed. Recovery controllers are designed to be safe but very likely disruptive to the operational objective of the system, and thus RTSA systems must balance safety and efficiency. The objective of this paper is to design a meta-controller capable of identifying unsafe situations with high accuracy. High dimensional and non-linear dynamics in which modern controllers are deployed along with the black-box nature of the nominal controllers make this a difficult problem. Current approaches rely heavily on domain expertise and human engineering. We frame the design of RTSA with the Markov decision process (MDP) framework and use reinforcement learning (RL) to solve it. Our learned meta-controller consistently exhibits superior performance in our experiments compared to our baseline, human engineered approach.

We establish a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an auxiliary time-reversible Markov Chain. Under certain conditions on the target distribution, we prove that $\tilde O(d^4\epsilon^{-2})$ stochastic gradient evaluations suffice to guarantee $\epsilon$-sampling error in terms of the total variation distance, where $d$ is the problem dimension, which improves existing results on the convergence rate of SGLD (Raginsky et al., 2017; Xu et al., 2018). We further show that provided an additional Hessian Lipschitz condition on the log-density function, SGLD is guaranteed to achieve $\epsilon$-sampling error within $\tilde O(d^{15/4}\epsilon^{-3/2})$ stochastic gradient evaluations. Our proof technique provides a new way to study the convergence of Langevin based algorithms, and sheds some light on the design of fast stochastic gradient based sampling algorithms.

Graph neural network models have been extensively used to learn node representations for graph structured data in an end-to-end setting. These models often rely on localized first order approximations of spectral graph convolutions and hence are unable to capture higher-order relational information between nodes. Probabilistic Graphical Models form another class of models that provide rich flexibility in incorporating such relational information but are limited by inefficient approximate inference algorithms at higher order. In this paper, we propose to combine these approaches to learn better node and graph representations. First, we derive an efficient approximate sum-product loopy belief propagation inference algorithm for higher-order PGMs. We then embed the message passing updates into a neural network to provide the inductive bias of the inference algorithm in end-to-end learning. This gives us a model that is flexible enough to accommodate domain knowledge while maintaining the computational advantage. We further propose methods for constructing higher-order factors that are conditioned on node and edge features and share parameters wherever necessary. Our experimental evaluation shows that our model indeed captures higher-order information, substantially outperforming state-of-the-art $k$-order graph neural networks in molecular datasets.

We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRFs) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying modeling tool for statistical mechanics, probabilistic machine learning, and artificial intelligence. Typically MRFs are complex and high-dimensional with nodes and edges (connections) built in a modular fashion from simpler, low-dimensional probabilistic models and their local connections; in turn, this modularity allows to incorporate available data to MRFs and efficiently simulate them by leveraging their graph-theoretic structure. Learning graphical models from data and/or constructing them from physical modeling and constraints necessarily involves uncertainties inherited from data, modeling choices, or numerical approximations. These uncertainties in the MRF can be manifested either in the graph structure or the probability distribution functions, and necessarily will propagate in predictions for quantities of interest. Here we quantify such uncertainties using tight, information-based bounds on the predictions of quantities of interest; these bounds take advantage of the graphical structure of MRFs and are capable of handling the inherent high-dimensionality of such graphical models. We demonstrate our methods in MRFs for medical diagnostics and statistical mechanics models. In the latter, we develop uncertainty quantification bounds for finite-size effects and phase diagrams, which constitute two of the typical predictions goals of statistical mechanics modeling.

This paper proposes a lexicographic Deep Reinforcement Learning (DeepRL)-based approach to chance-constrained Markov Decision Processes, in which the controller seeks to ensure that the probability of satisfying the constraint is above a given threshold. Standard DeepRL approaches require i) the constraints to be included as additional weighted terms in the cost function, in a multi-objective fashion, and ii) the tuning of the introduced weights during the training phase of the Deep Neural Network (DNN) according to the probability thresholds. The proposed approach, instead, requires to separately train one constraint-free DNN and one DNN associated to each constraint and then, at each time-step, to select which DNN to use depending on the system observed state. The presented solution does not require any hyper-parameter tuning besides the standard DNN ones, even if the probability thresholds changes. A lexicographic version of the well-known DeepRL algorithm DQN is also proposed and validated via simulations.

Model-free reinforcement learning (RL) has been an active area of research and provides a fundamental framework for agent-based learning and decision-making in artificial intelligence. In this paper, we review a specific subset of this literature, namely work that utilizes optimization criteria based on average rewards, in the infinite horizon setting. Average reward RL has the advantage of being the most selective criterion in recurrent (ergodic) Markov decision processes. In comparison to widely-used discounted reward criterion, it also requires no discount factor, which is a critical hyperparameter, and properly aligns the optimization and performance metrics. Motivated by the solo survey by Mahadevan (1996a), we provide an updated review of work in this area and extend it to cover policy-iteration and function approximation methods (in addition to the value-iteration and tabular counterparts). We also identify and discuss opportunities for future work.