Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show that non-sampling-based latent state inference used in HSMM's can be generalized to latent Continuous-Time semi-Markov Chains (CTSMC's). We formulate integro-differential forward and backward equations adjusted to the observation likelihood and introduce an exact integral equation for the Bayesian posterior marginals and a scalable Viterbi-type algorithm for posterior path estimates. The presented equations can be efficiently solved using well-known numerical methods.

We consider the problem of online reinforcement learning when several state representations (mapping histories to a discrete state space) are available to the learning agent. At least one of these representations is assumed to induce a Markov decision process (MDP), and the performance of the agent is measured in terms of cumulative regret against the optimal policy giving the highest average reward in this MDP representation. We propose an algorithm (UCB-MS) with O(sqrt(T)) regret in any communicating Markov decision process. The regret bound shows that UCB-MS automatically adapts to the Markov model. This improves over the currently known best results in the literature that gave regret bounds of order O(T (2/3)).

In this paper, we model the dependencies among the items that are recommended to a user in a collaborative-filtering problem via a Gaussian Markov Random Field (MRF). We build upon Besag's auto-normal parameterization and pseudo-likelihood, which not only enables computationally efficient learning, but also connects the areas of MRFs and sparse inverse covariance estimation with autoencoders and neighborhood models, two successful approaches in collaborative filtering. We propose a novel approximation for learning sparse MRFs, where the trade-off between recommendation-accuracy and training-time can be controlled. At only a small fraction of the training-time compared to various baselines, including deep nonlinear models, the proposed approach achieved competitive ranking-accuracy on all three well-known data-sets used in our experiments, and notably a 20% gain in accuracy on the data-set with the largest number of items.

Reinforcement learning algorithms are widely used in domains where it is desirable to provide a personalized service. In these domains it is common that user data contains sensitive information that needs to be protected from third parties. Motivated by this, we study privacy in the context of finite-horizon Markov Decision Processes (MDPs) by requiring information to be obfuscated on the user side. We formulate this notion of privacy for RL by leveraging the local differential privacy (LDP) framework. We establish a lower bound for regret minimization in finite-horizon MDPs with LDP guarantees which shows that guaranteeing privacy has a multiplicative effect on the regret.

The paper introduces a new algorithm for planning in partially observable Markov decision processes (POMDP) based on the idea of aggregate simulation. The algorithm uses product distributions to approximate the belief state and shows how to build a representation graph of an approximate action-value function over belief space. The algorithm supports large observation spaces using sampling networks, a representation of the process of sampling values of observations, which is integrated into the graph representation. Following previous work in MDPs this approach enables action selection in POMDPs through gradient optimization over the graph representation. This approach complements recent algorithms for POMDPs which are based on particle representations of belief states and an explicit search for action selection.

We study algorithms using randomized value functions for exploration in reinforcement learning. This type of algorithms enjoys appealing empirical performance. We show that when we use 1) a single random seed in each episode, and 2) a Bernstein-type magnitude of noise, we obtain a worst-case \widetilde{O}\left(H\sqrt{SAT}\right) regret bound for episodic time-inhomogeneous Markov Decision Process where S is the size of state space, A is the size of action space, H is the planning horizon and T is the number of interactions. This bound polynomially improves all existing bounds for algorithms based on randomized value functions, and for the first time, matches the \Omega\left(H\sqrt{SAT}\right) lower bound up to logarithmic factors. Our result highlights that randomized exploration can be near-optimal, which was previously achieved only by optimistic algorithms.

This work tackles the problem of robust zero-shot planning in non-stationary stochastic environments. We study Markov Decision Processes (MDPs) evolving over time and consider Model-Based Reinforcement Learning algorithms in this setting. We make two hypotheses: 1) the environment evolves continuously with a bounded evolution rate; 2) a current model is known at each decision epoch but not its evolution. Our contribution can be presented in four points. We introduce the notion of regular evolution by making an hypothesis of Lipschitz-Continuity on the transition and reward functions w.r.t.

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.

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be unfeasible. We propose a new class of methods to overcome these challenges in the common case of sparse constraints, where one has a large number of constraints and each only involves a few elements. Our methods rely on a basis transformation into blocks of constrained versus non-constrained subspaces, and we show that the methods greatly outperform existing alternatives in terms of computational cost. By combining the proposed methods with the stochastic partial differential equation approach for Gaussian random fields, we also show how to formulate Gaussian process regression with linear constraints in a GMRF setting to reduce computational cost.

We study sequential decision-making problems in which each agent aims to maximize the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon Constrained Markov Decision Processes (CMDPs) problem. Specifically, we propose a new Natural Policy Gradient Primal-Dual (NPG-PD) method for CMDPs which updates the primal variable via natural policy gradient ascent and the dual variable via projected sub-gradient descent. Even though the underlying maximization involves a nonconcave objective function and a nonconvex constraint set under the softmax policy parametrization, we prove that our method achieves global convergence with sublinear rates regarding both the optimality gap and the constraint violation. Such a convergence is independent of the size of the state-action space, i.e., it is dimension-free.