We consider the problem of learning an unknown Markov Decision Process (MDP) that is weakly communicating in the infinite horizon setting. We propose a Thompson Sampling-based reinforcement learning algorithm with dynamic episodes (TSDE). At the beginning of each episode, the algorithm generates a sample from the posterior distribution over the unknown model parameters. It then follows the optimal stationary policy for the sampled model for the rest of the episode. The duration of each episode is dynamically determined by two stopping criteria.

Recently, there has been a surge of interest in using spectral methods for estimating latent variable models. However, it is usually assumed that the distribution of the observations conditioned on the latent variables is either discrete or belongs to a parametric family. In this paper, we study the estimation of an $m$-state hidden Markov model (HMM) with only smoothness assumptions, such as H\olderian conditions, on the emission densities. By leveraging some recent advances in continuous linear algebra and numerical analysis, we develop a computationally efficient spectral algorithm for learning nonparametric HMMs. Our technique is based on computing an SVD on nonparametric estimates of density functions by viewing them as \emph{continuous matrices}. We derive sample complexity bounds via concentration results for nonparametric density estimation and novel perturbation theory results for continuous matrices. We implement our method using Chebyshev polynomial approximations. Our method is competitive with other baselines on synthetic and real problems and is also very computationally efficient.

The correlation between events is ubiquitous and important for temporal events modelling. In many cases, the correlation exists between not only events' emitted observations, but also their arrival times. State space models (e.g., hidden Markov model) and stochastic interaction point process models (e.g., Hawkes process) have been studied extensively yet separately for the two types of correlations in the past. In this paper, we propose a Bayesian nonparametric approach that considers both types of correlations via unifying and generalizing hidden semi-Markov model and interaction point process model. The proposed approach can simultaneously model both the observations and arrival times of temporal events, and determine the number of latent states from data.

Count-based exploration algorithms are known to perform near-optimally when used in conjunction with tabular reinforcement learning (RL) methods for solving small discrete Markov decision processes (MDPs). It is generally thought that count-based methods cannot be applied in high-dimensional state spaces, since most states will only occur once. Recent deep RL exploration strategies are able to deal with high-dimensional continuous state spaces through complex heuristics, often relying on optimism in the face of uncertainty or intrinsic motivation. In this work, we describe a surprising finding: a simple generalization of the classic count-based approach can reach near state-of-the-art performance on various high-dimensional and/or continuous deep RL benchmarks. States are mapped to hash codes, which allows to count their occurrences with a hash table.

Factorial Hidden Markov Models (FHMMs) are powerful models for sequential data but they do not scale well with long sequences. We propose a scalable inference and learning algorithm for FHMMs that draws on ideas from the stochastic variational inference, neural network and copula literatures. Unlike existing approaches, the proposed algorithm requires no message passing procedure among latent variables and can be distributed to a network of computers to speed up learning. Our experiments corroborate that the proposed algorithm does not introduce further approximation bias compared to the proven structured mean-field algorithm, and achieves better performance with long sequences and large FHMMs.

Two seemingly contradictory theories attempt to explain how humans move to intercept an airborne ball. One theory posits that humans predict the ball trajectory to optimally plan future actions; the other claims that, instead of performing such complicated computations, humans employ heuristics to reactively choose appropriate actions based on immediate visual feedback. In this paper, we show that interception strategies appearing to be heuristics can be understood as computational solutions to the optimal control problem faced by a ball-catching agent acting under uncertainty. Modeling catching as a continuous partially observable Markov decision process and employing stochastic optimal control theory, we discover that the four main heuristics described in the literature are optimal solutions if the catcher has sufficient time to continuously visually track the ball. Specifically, by varying model parameters such as noise, time to ground contact, and perceptual latency, we show that different strategies arise under different circumstances. The catcher's policy switches between generating reactive and predictive behavior based on the ratio of system to observation noise and the ratio between reaction time and task duration. Thus, we provide a rational account of human ball-catching behavior and a unifying explanation for seemingly contradictory theories of target interception on the basis of stochastic optimal control.

A fundamental problem in cognitive neuroscience is how humans make decisions, act, and behave in relation to other humans. Here we adopt the hypothesis that when we are in an interactive social setting, our brains perform Bayesian inference of the intentions and cooperativeness of others using probabilistic representations. We employ the framework of partially observable Markov decision processes (POMDPs) to model human decision making in a social context, focusing specifically on the volunteer's dilemma in a version of the classic Public Goods Game. We show that the POMDP model explains both the behavior of subjects as well as neural activity recorded using fMRI during the game. The decisions of subjects can be modeled across all trials using two interpretable parameters. Furthermore, the expected reward predicted by the model for each subject was correlated with the activation of brain areas related to reward expectation in social interactions. Our results suggest a probabilistic basis for human social decision making within the framework of expected reward maximization.

Neural Information Processing Systems http://nips.cc/

This paper introduces the QMDP-net, a neural network architecture for planning under partial observability. The QMDP-net combines the strengths of model-free learning and model-based planning.

Neural Information Processing Systems http://nips.cc/