We study a formalization of the grammar induction problem that models sentences as being generated by a compound probabilistic context-free grammar. In contrast to traditional formulations which learn a single stochastic grammar, our context-free rule probabilities are modulated by a per-sentence continuous latent variable, which induces marginal dependencies beyond the traditional context-free assumptions. Inference in this grammar is performed by collapsed variational inference, in which an amortized variational posterior is placed on the continuous variable, and the latent trees are marginalized with dynamic programming. Experiments on English and Chinese show the effectiveness of our approach compared to recent state-of-the-art methods for grammar induction from words with neural language models.

This paper addresses two challenges facing sampling-based kinodynamic motion planning: a way to identify good candidate states for local transitions and the subsequent computationally intractable steering between these candidate states. Through the combination of sampling-based planning, a Rapidly Exploring Randomized Tree (RRT) and an efficient kinodynamic motion planner through machine learning, we propose an efficient solution to long-range planning for kinodynamic motion planning. First, we use deep reinforcement learning to learn an obstacle-avoiding policy that maps a robot's sensor observations to actions, which is used as a local planner during planning and as a controller during execution. Second, we train a reachability estimator in a supervised manner, which predicts the RL policy's time to reach a state in the presence of obstacles. Lastly, we introduce RL-RRT that uses the RL policy as a local planner, and the reachability estimator as the distance function to bias tree-growth towards promising regions. We evaluate our method on three kinodynamic systems, including physical robot experiments. Results across all three robots tested indicate that RL-RRT outperforms state of the art kinodynamic planners in efficiency, and also provides a shorter path finish time than a steering function free method. The learned local planner policy and accompanying reachability estimator demonstrate transferability to the previously unseen experimental environments, making RL-RRT fast because the expensive computations are replaced with simple neural network inference. Video: https://youtu.be/dDMVMTOI8KY

Partially Observable Markov Decision Processes (POMDPs) are a popular formalism for sequential decision making in partially observable environments. Since solving POMDPs to optimality is a difficult task, point-based value iteration methods are widely used. These methods compute an approximate POMDP solution, and in some cases they even provide guarantees on the solution quality, but these algorithms have been designed for problems with an infinite planning horizon. In this paper we discuss why state-of-the-art point-based algorithms cannot be easily applied to finite-horizon problems that do not include discounting. Subsequently, we present a general point-based value iteration algorithm for finite-horizon problems which provides solutions with guarantees on solution quality. Furthermore, we introduce two heuristics to reduce the number of belief points considered during execution, which lowers the computational requirements. In experiments we demonstrate that the algorithm is an effective method for solving finite-horizon POMDPs.

Batch Reinforcement Learning (Batch RL) consists in training a policy using trajectories collected with another policy, called the behavioural policy. Safe policy improvement (SPI) provides guarantees with high probability that the trained policy performs better than the behavioural policy, also called baseline in this setting. Previous work shows that the SPI objective improves mean performance as compared to using the basic RL objective, which boils down to solving the MDP with maximum likelihood. Here, we build on that work and improve more precisely the SPI with Baseline Bootstrapping algorithm (SPIBB) by allowing the policy search over a wider set of policies. Instead of binarily classifying the state-action pairs into two sets (the \textit{uncertain} and the \textit{safe-to-train-on} ones), we adopt a softer strategy that controls the error in the value estimates by constraining the policy change according to the local model uncertainty. The method can take more risks on uncertain actions all the while remaining provably-safe, and is therefore less conservative than the state-of-the-art methods. We propose two algorithms (one optimal and one approximate) to solve this constrained optimization problem and empirically show a significant improvement over existing SPI algorithms both on finite MDPs and on infinite MDPs with a neural network function approximation.

We propose Stable Yet Memory Bounded Open-Loop (SYMBOL) planning, a general memory bounded approach to partially observable open-loop planning. SYMBOL maintains an adaptive stack of Thompson Sampling bandits, whose size is bounded by the planning horizon and can be automatically adapted according to the underlying domain without any prior domain knowledge beyond a generative model. We empirically test SYMBOL in four large POMDP benchmark problems to demonstrate its effectiveness and robustness w.r.t. the choice of hyperparameters and evaluate its adaptive memory consumption. We also compare its performance with other open-loop planning algorithms and POMCP.

Studies on massive open online courses (MOOCs) users discuss the existence of typical profiles and their impact on the learning process of the students. However defining the typical behaviors as well as classifying the users accordingly is a difficult task. In this paper we suggest two methods to model MOOC users behaviour given their log data. We mold their behavior into a Markov Decision Process framework. We associate the user's intentions with the MDP reward and argue that this allows us to classify them.

Language modelling has been an integral part of providing an understanding of the nature of language to capture its meaning. In order to improve the machine understanding of language using sequential models, we seek to explore two prominent areas of statistical language models, the Hidden Markov Model (HMM), and a Recurrent Neural Network (RNN) architecture, known commonly as Long Short-Term Memory (LSTM). Under a discrete stochastic modelling framework, HMM's were first introduced in Rabiner [1] to classify speech signals. First used to automate AT&T's voice activated call center, the revolutionary technology allowed computers to robustly characterise speech, and form a basic understanding of spoken words. HMM's have since become a definitive benchmark for the state-of-the-art for speech recognition, and text recognition. Around the same period, RNN's were introduced by Rumelhart et al. [2], however, the training complexity of the model was far too high and not commensurate with the hardware capabilities at the time. In the 21st century, With the introduction of more advanced hardware for deep learning model training, came a wave of applications for the RNN for both voice, text recognition, [3], [4], [5] and machine translation [6]. In parallel, an early form of neural language model was developed in Bengio et al. [7], displaying promising results in statistical language modelling. LSTM's were the first introduced in Hochreiter and Schmidhuber [8], specifically to combat the vanishing gradient problem, which will be further addressed in Section 1.2.

Reduced models are simplified versions of a given domain, designed to accelerate the planning process. Interest in reduced models has grown since the surprising success of determinization in the first international probabilistic planning competition, leading to the development of several enhanced determinization techniques. To address the drawbacks of previous determinization methods, we introduce a family of reduced models in which probabilistic outcomes are classified as one of two types: primary and exceptional. In each model that belongs to this family of reductions, primary outcomes can occur an unbounded number of times per trajectory, while exceptions can occur at most a finite number of times, specified by a parameter. Distinct reduced models are characterized by two parameters: the maximum number of primary outcomes per action, and the maximum number of occurrences of exceptions per trajectory. This family of reductions generalizes the well-known most-likely-outcome determinization approach, which includes one primary outcome per action and zero exceptional outcomes per plan. We present a framework to determine the benefits of planning with reduced models, and develop a continual planning approach that handles situations where the number of exceptions exceeds the specified bound during plan execution. Using this framework, we compare the performance of various reduced models and consider the challenge of generating good ones automatically. We show that each one of the dimensions---allowing more than one primary outcome or planning for some limited number of exceptions---could improve performance relative to standard determinization. The results place previous work on determinization in a broader context and lay the foundation for a systematic exploration of the space of model reductions.

Variance plays a crucial role in risk-sensitive reinforcement learning, and most risk measures can be analyzed via variance. In this paper, we consider two law-invariant risks as examples: mean-variance risk and exponential utility risk. With the aid of the state-augmentation transformation (SAT), we show that, the two risks can be estimated in Markov decision processes (MDPs) with a stochastic transition-based reward and a randomized policy. To relieve the enlarged state space, a novel definition of isotopic states is proposed for state lumping, considering the special structure of the transformed transition probability. In the numerical experiment, we illustrate state lumping in the SAT, errors from a naive reward simplification, and the validity of the SAT for the two risk estimations.

We propose a neural network architecture, called TransNet, that combines planning and model learning for solving Partially Observable Markov Decision Processes (POMDPs) with non-uniform system dynamics. The past decade has seen a substantial advancement in solving POMDP problems. However, constructing a suitable POMDP model remains difficult. Recently, neural network architectures have been proposed to alleviate the difficulty in acquiring such models. Although the results are promising, existing architectures restrict the type of system dynamics that can be learned --that is, system dynamics must be the same in all parts of the state space. TransNet relaxes such a restriction. Key to this relaxation is a novel neural network module that classifies the state space into classes and then learns the system dynamics of the different classes. TransNet uses this module together with the overall architecture of QMDP-Net[1] to allow solving POMDPs that have more expressive dynamic models, while maintaining efficient data requirement. Its evaluation on typical benchmarks in robot navigation with initially unknown system and environment models indicates that TransNet substantially out-performs the quality of the generated policies and learning efficiency of the state-of-the-art method QMDP-Net.