We present a formalisation of finite Markov decision processes with rewards in the Isabelle theorem prover. We focus on the foundations required for dynamic programming and the use of reinforcement learning agents over such processes. In particular, we derive the Bellman equation from first principles (in both scalar and vector form), derive a vector calculation that produces the expected value of any policy p, and go on to prove the existence of a universally optimal policy where there is a discounting factor less than one. Lastly, we prove that the value iteration and the policy iteration algorithms work in finite time, producing an epsilon-optimal and a fully optimal policy respectively.

The idea of representing symbolic knowledge in connectionist systems has been a long-standing endeavour which has attracted much attention recently with the objective of combining machine learning and scalable sound reasoning. Early work has shown a correspondence between propositional logic and symmetrical neural networks which nevertheless did not scale well with the number of variables and whose training regime was inefficient. In this paper, we introduce Logical Boltzmann Machines (LBM), a neurosymbolic system that can represent any propositional logic formula in strict disjunctive normal form. We prove equivalence between energy minimization in LBM and logical satisfiability thus showing that LBM is capable of sound reasoning. We evaluate reasoning empirically to show that LBM is capable of finding all satisfying assignments of a class of logical formulae by searching fewer than 0.75% of the possible (approximately 1 billion) assignments. We compare learning in LBM with a symbolic inductive logic programming system, a state-of-the-art neurosymbolic system and a purely neural network-based system, achieving better learning performance in five out of seven data sets.

Attention is a state of arousal capable of dealing with limited processing bottlenecks in human beings by focusing selectively on one piece of information while ignoring other perceptible information. For decades, concepts and functions of attention have been studied in philosophy, psychology, neuroscience, and computing. Currently, this property has been widely explored in deep neural networks. Many different neural attention models are now available and have been a very active research area over the past six years. From the theoretical standpoint of attention, this survey provides a critical analysis of major neural attention models. Here we propose a taxonomy that corroborates with theoretical aspects that predate Deep Learning. Our taxonomy provides an organizational structure that asks new questions and structures the understanding of existing attentional mechanisms. In particular, 17 criteria derived from psychology and neuroscience classic studies are formulated for qualitative comparison and critical analysis on the 51 main models found on a set of more than 650 papers analyzed. Also, we highlight several theoretical issues that have not yet been explored, including discussions about biological plausibility, highlight current research trends, and provide insights for the future.

Reinforcement learning (RL) has gained increasing attraction in the academia and tech industry with launches to a variety of impactful applications and products. Although research is being actively conducted on many fronts (e.g., offline RL, performance, etc.), many RL practitioners face a challenge that has been largely ignored: determine whether a designed Markov Decision Process (MDP) is valid and meaningful. This study proposes a heuristic-based feature analysis method to validate whether an MDP is well formulated. We believe an MDP suitable for applying RL should contain a set of state features that are both sensitive to actions and predictive in rewards. We tested our method in constructed environments showing that our approach can identify certain invalid environment formulations. As far as we know, performing validity analysis for RL problem formulation is a novel direction. We envision that our tool will serve as a motivational example to help practitioners apply RL in real-world problems more easily.

This paper proposes a new sequential model learning architecture to solve partially observable Markov decision problems. Rather than compressing sequential information at every timestep as in conventional recurrent neural network-based methods, the proposed architecture generates a latent variable in each data block with a length of multiple timesteps and passes the most relevant information to the next block for policy optimization. The proposed blockwise sequential model is implemented based on self-attention, making the model capable of detailed sequential learning in partial observable settings. The proposed model builds an additional learning network to efficiently implement gradient estimation by using self-normalized importance sampling, which does not require the complex blockwise input data reconstruction in the model learning. Numerical results show that the proposed method significantly outperforms previous methods in various partially observable environments.

In many practical applications of RL, it is expensive to observe state transitions from the environment. For example, in the problem of plasma control for nuclear fusion, computing the next state for a given state-action pair requires querying an expensive transition function which can lead to many hours of computer simulation or dollars of scientific research. Such expensive data collection prohibits application of standard RL algorithms which usually require a large number of observations to learn. In this work, we address the problem of efficiently learning a policy while making a minimal number of state-action queries to the transition function. In particular, we leverage ideas from Bayesian optimal experimental design to guide the selection of state-action queries for efficient learning. We propose an acquisition function that quantifies how much information a state-action pair would provide about the optimal solution to a Markov decision process. At each iteration, our algorithm maximizes this acquisition function, to choose the most informative state-action pair to be queried, thus yielding a data-efficient RL approach. We experiment with a variety of simulated continuous control problems and show that our approach learns an optimal policy with up to $5$ -- $1,000\times$ less data than model-based RL baselines and $10^3$ -- $10^5\times$ less data than model-free RL baselines. We also provide several ablated comparisons which point to substantial improvements arising from the principled method of obtaining data.

Cooperation between agents in a multi-agent system (MAS) has become a hot topic in recent years, and many algorithms based on centralized training with decentralized execution (CTDE), such as VDN and QMIX, have been proposed. However, these methods disregard the information hidden in the individual action values. In this paper, we propose HyperGraph CoNvolution MIX (HGCN-MIX), a method that combines hypergraph convolution with value decomposition. By treating action values as signals, HGCN-MIX aims to explore the relationship between these signals via a self-learning hypergraph. Experimental results present that HGCN-MIX matches or surpasses state-of-the-art techniques in the StarCraft II multi-agent challenge (SMAC) benchmark on various situations, notably those with a number of agents.

In mobile manipulation (MM), robots can both navigate within and interact with their environment and are thus able to complete many more tasks than robots only capable of navigation or manipulation. In this work, we explore how to apply imitation learning (IL) to learn continuous visuo-motor policies for MM tasks. Much prior work has shown that IL can train visuo-motor policies for either manipulation or navigation domains, but few works have applied IL to the MM domain. Doing this is challenging for two reasons: on the data side, current interfaces make collecting high-quality human demonstrations difficult, and on the learning side, policies trained on limited data can suffer from covariate shift when deployed. To address these problems, we first propose Mobile Manipulation RoboTurk (MoMaRT), a novel teleoperation framework allowing simultaneous navigation and manipulation of mobile manipulators, and collect a first-of-its-kind large scale dataset in a realistic simulated kitchen setting. We then propose a learned error detection system to address the covariate shift by detecting when an agent is in a potential failure state. We train performant IL policies and error detectors from this data, and achieve over 45% task success rate and 85% error detection success rate across multiple multi-stage tasks when trained on expert data. Codebase, datasets, visualization, and more available at https://sites.google.com/view/il-for-mm/home.

For robots operating in the real world, it is desirable to learn reusable behaviours that can effectively be transferred and adapted to numerous tasks and scenarios. We propose an approach to learn abstract motor skills from data using a hierarchical mixture latent variable model. In contrast to existing work, our method exploits a three-level hierarchy of both discrete and continuous latent variables, to capture a set of high-level behaviours while allowing for variance in how they are executed. We demonstrate in manipulation domains that the method can effectively cluster offline data into distinct, executable behaviours, while retaining the flexibility of a continuous latent variable model. The resulting skills can be transferred and fine-tuned on new tasks, unseen objects, and from state to vision-based policies, yielding better sample efficiency and asymptotic performance compared to existing skill- and imitation-based methods. We further analyse how and when the skills are most beneficial: they encourage directed exploration to cover large regions of the state space relevant to the task, making them most effective in challenging sparse-reward settings.

We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes a subset of the processes at any given time instant and obtains a noisy binary indicator of whether or not the corresponding process is anomalous. In this setting, we develop an anomaly detection algorithm that chooses the processes to be observed at a given time instant, decides when to stop taking observations, and declares the decision on anomalous processes. The objective of the detection algorithm is to identify the anomalies with an accuracy exceeding the desired value while minimizing the delay in decision making. We devise a centralized algorithm where the processes are jointly selected by a common agent as well as a decentralized algorithm where the decision of whether to select a process is made independently for each process. Our algorithms rely on a Markov decision process defined using the marginal probability of each process being normal or anomalous, conditioned on the observations. We implement the detection algorithms using the deep actor-critic reinforcement learning framework. Unlike prior work on this topic that has exponential complexity in the number of processes, our algorithms have computational and memory requirements that are both polynomial in the number of processes. We demonstrate the efficacy of these algorithms using numerical experiments by comparing them with state-of-the-art methods.