Efficient exploration is one of the most important issues in deep reinforcement learning. To address this issue, recent methods consider the value function parameters as random variables, and resort variational inference to approximate the posterior of the parameters. In this paper, we propose an amortized variational inference framework to approximate the posterior distribution of the action value function in Deep Q Network. We establish the equivalence between the loss of the new model and the amortized variational inference loss. We realize the balance of exploration and exploitation by assuming the posterior as Cauchy and Gaussian, respectively in a two-stage training process. We show that the amortized framework can results in significant less learning parameters than existing state-of-the-art method. Experimental results on classical control tasks in OpenAI Gym and chain Markov Decision Process tasks show that the proposed method performs significantly better than state-of-art methods and requires much less training time.

Planning under partial obervability is essential for autonomous robots. A principled way to address such planning problems is the Partially Observable Markov Decision Process (POMDP). Although solving POMDPs is computationally intractable, substantial advancements have been achieved in developing approximate POMDP solvers in the past two decades. However, computing robust solutions for problems with continuous observation spaces remains challenging. Most on-line solvers rely on discretising the observation space or artificially limiting the number of observations that are considered during planning to compute tractable policies. In this paper we propose a new on-line POMDP solver, called Lazy Belief Extraction for Continuous POMDPs (LABECOP), that combines methods from Monte-Carlo-Tree-Search and particle filtering to construct a policy reprentation which doesn't require discretised observation spaces and avoids limiting the number of observations considered during planning. Experiments on three different problems involving continuous observation spaces indicate that LABECOP performs similar or better than state-of-the-art POMDP solvers.

We describe a framework for research and evaluation in Embodied AI. Our proposal is based on a canonical task: Rearrangement. A standard task can focus the development of new techniques and serve as a source of trained models that can be transferred to other settings. In the rearrangement task, the goal is to bring a given physical environment into a specified state. The goal state can be specified by object poses, by images, by a description in language, or by letting the agent experience the environment in the goal state. We characterize rearrangement scenarios along different axes and describe metrics for benchmarking rearrangement performance. To facilitate research and exploration, we present experimental testbeds of rearrangement scenarios in four different simulation environments. We anticipate that other datasets will be released and new simulation platforms will be built to support training of rearrangement agents and their deployment on physical systems.

Humans interact with the world based on their inner motivations (goals) by performing actions. Those actions might be observable by financial institutions. In turn, financial institutions might log all these observed actions for better understanding human behavior. Examples of such interactions are investment operations (buying or selling options), account-related activities (creating accounts, making transactions, withdrawing money), digital interactions (utilizing the bank's web or mobile app for configuring alerts, or applying for a new credit card), or even illicit operations (such as fraud or money laundering). Once human behavior can be better understood, financial institutions can improve their processes allowing them to deepen the relationship with clients, offering targeted services (marketing), handling complaints-related interactions (operations), or performing fraud or money laundering investigations (compliance) [Borrajo et al., 2020].

Sequential decision making techniques hold great promise to improve the performance of many real-world systems, but computational complexity hampers their principled application. Influence-based abstraction aims to gain leverage by modeling local subproblems together with the 'influence' that the rest of the system exerts on them. While computing exact representations of such influence might be intractable, learning approximate representations offers a promising approach to enable scalable solutions. This paper investigates the performance of such approaches from a theoretical perspective. The primary contribution is the derivation of sufficient conditions on approximate influence representations that can guarantee solutions with small value loss. In particular we show that neural networks trained with cross entropy are well suited to learn approximate influence representations. Moreover, we provide a sample based formulation of the bounds, which reduces the gap to applications. Finally, driven by our theoretical insights, we propose approximation error estimators, which empirically reveal to correlate well with the value loss.

Agents trained via deep reinforcement learning (RL) routinely fail to generalize to unseen environments, even when these share the same underlying dynamics as the training levels. Understanding the generalization properties of RL is one of the challenges of modern machine learning. Towards this goal, we analyze policy learning in the context of Partially Observable Markov Decision Processes (POMDPs) and formalize the dynamics of training levels as instances. We prove that, independently of the exploration strategy, reusing instances introduces significant changes on the effective Markov dynamics the agent observes during training. Maximizing expected rewards impacts the learned belief state of the agent by inducing undesired instance-specific speed-running policies instead of generalizable ones, which are sub-optimal on the training set. We provide generalization bounds to the value gap in train and test environments based on the number of training instances, and use insights based on these to improve performance on unseen levels. We propose training a shared belief representation over an ensemble of specialized policies, from which we compute a consensus policy that is used for data collection, disallowing instance-specific exploitation. We experimentally validate our theory, observations, and the proposed computational solution over the CoinRun benchmark.

This paper is a tutorial and literature review on sampling algorithms. We have two main types of sampling in statistics. The first type is survey sampling which draws samples from a set or population. The second type is sampling from probability distribution where we have a probability density or mass function. In this paper, we cover both types of sampling. First, we review some required background on mean squared error, variance, bias, maximum likelihood estimation, Bernoulli, Binomial, and Hypergeometric distributions, the Horvitz-Thompson estimator, and the Markov property. Then, we explain the theory of simple random sampling, bootstrapping, stratified sampling, and cluster sampling. We also briefly introduce multistage sampling, network sampling, and snowball sampling. Afterwards, we switch to sampling from distribution. We explain sampling from cumulative distribution function, Monte Carlo approximation, simple Monte Carlo methods, and Markov Chain Monte Carlo (MCMC) methods. For simple Monte Carlo methods, whose iterations are independent, we cover importance sampling and rejection sampling. For MCMC methods, we cover Metropolis algorithm, Metropolis-Hastings algorithm, Gibbs sampling, and slice sampling. Then, we explain the random walk behaviour of Monte Carlo methods and more efficient Monte Carlo methods, including Hamiltonian (or hybrid) Monte Carlo, Adler's overrelaxation, and ordered overrelaxation. Finally, we summarize the characteristics, pros, and cons of sampling methods compared to each other. This paper can be useful for different fields of statistics, machine learning, reinforcement learning, and computational physics.

This work studies the problem of learning episodic Markov Decision Processes with known transition and bandit feedback. We develop the first algorithm with a ``best-of-both-worlds'' guarantee: it achieves $\mathcal{O}(log T)$ regret when the losses are stochastic, and simultaneously enjoys worst-case robustness with $\tilde{\mathcal{O}}(\sqrt{T})$ regret even when the losses are adversarial, where $T$ is the number of episodes. More generally, it achieves $\tilde{\mathcal{O}}(\sqrt{C})$ regret in an intermediate setting where the losses are corrupted by a total amount of $C$. Our algorithm is based on the Follow-the-Regularized-Leader method from Zimin and Neu (2013), with a novel hybrid regularizer inspired by recent works of Zimmert et al. (2019a, 2019b) for the special case of multi-armed bandits. Crucially, our regularizer admits a non-diagonal Hessian with a highly complicated inverse. Analyzing such a regularizer and deriving a particular self-bounding regret guarantee is our key technical contribution and might be of independent interest.

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many real-world processes that cannot be characterized by a single linear behavior. Alternatively, it is possible to consider a piecewise-linear model which, combined with a switching mechanism, is well suited when several modes of behavior are needed. Nevertheless, switching dynamical systems are intractable because of their computational complexity increases exponentially with time. In this paper, we propose a variational approximation of piecewise linear dynamical systems. We provide full details of the derivation of two variational expectation-maximization algorithms, a filter and a smoother. We show that the model parameters can be split into two sets, static and dynamic parameters, and that the former parameters can be estimated off-line together with the number of linear modes, or the number of states of the switching variable. We apply the proposed method to a visual tracking problem, namely head-pose tracking, and we thoroughly compare our algorithm with several state of the art trackers.

Selective labels are a common feature of consequential decision-making applications, referring to the lack of observed outcomes under one of the possible decisions. This paper reports work in progress on learning decision policies in the face of selective labels. The setting considered is both a simplified homogeneous one, disregarding individuals' features to facilitate determination of optimal policies, and an online one, to balance costs incurred in learning with future utility. For maximizing discounted total reward, the optimal policy is shown to be a threshold policy, and the problem is one of optimal stopping. In contrast, for undiscounted infinite-horizon average reward, optimal policies have positive acceptance probability in all states. Future work stemming from these results is discussed.