Motivation: We consider continuous-time Markov chains that describe the stochastic evolution of a dynamical system by a transition-rate matrix $Q$ which depends on a parameter $\theta$. Computing the probability distribution over states at time $t$ requires the matrix exponential $\exp(tQ)$, and inferring $\theta$ from data requires its derivative $\partial\exp\!(tQ)/\partial\theta$. Both are challenging to compute when the state space and hence the size of $Q$ is huge. This can happen when the state space consists of all combinations of the values of several interacting discrete variables. Often it is even impossible to store $Q$. However, when $Q$ can be written as a sum of tensor products, computing $\exp(tQ)$ becomes feasible by the uniformization method, which does not require explicit storage of $Q$. Results: Here we provide an analogous algorithm for computing $\partial\exp\!(tQ)/\partial\theta$, the differentiated uniformization method. We demonstrate our algorithm for the stochastic SIR model of epidemic spread, for which we show that $Q$ can be written as a sum of tensor products. We estimate monthly infection and recovery rates during the first wave of the COVID-19 pandemic in Austria and quantify their uncertainty in a full Bayesian analysis. Availability: Implementation and data are available at https://github.com/spang-lab/TenSIR.

Providing appropriate questions according to a student's knowledge level is imperative in personalized learning. However, It requires a lot of manual effort for teachers to understand students' knowledge status and provide optimal questions accordingly. To address this problem, we introduce a question scheduling model that can effectively boost student knowledge level using Reinforcement Learning (RL). Our proposed method first evaluates students' concept-level knowledge using knowledge tracing (KT) model. Given predicted student knowledge, RL-based recommender predicts the benefits of each question. With curriculum range restriction and duplicate penalty, the recommender selects questions sequentially until it reaches the predefined number of questions. In an experimental setting using a student simulator, which gives 20 questions per day for two weeks, questions recommended by the proposed method increased average student knowledge level by 21.3%, superior to an expert-designed schedule baseline with a 10% increase in student knowledge levels.

These are all supervised learning approaches.

Offline estimation of the dynamical model of a Markov Decision Process (MDP) is a non-trivial task that greatly depends on the data available to the learning phase. Sometimes the dynamics of the model is invariant with respect to some transformations of the current state and action. Recent works showed that an expert-guided pipeline relying on Density Estimation methods as Deep Neural Network based Normalizing Flows effectively detects this structure in deterministic environments, both categorical and continuous-valued. The acquired knowledge can be exploited to augment the original data set, leading eventually to a reduction in the distributional shift between the true and the learnt model. In this work we extend the paradigm to also tackle non deterministic MDPs, in particular 1) we propose a detection threshold in categorical environments based on statistical distances, 2) we introduce a benchmark of the distributional shift in continuous environments based on the Wilcoxon signed-rank statistical test and 3) we show that the former results lead to a performance improvement when solving the learnt MDP and then applying the optimal policy in the real environment.

We consider the challenge of policy simplification and verification in the context of policies learned through reinforcement learning (RL) in continuous environments. In well-behaved settings, RL algorithms have convergence guarantees in the limit. While these guarantees are valuable, they are insufficient for safety-critical applications. Furthermore, they are lost when applying advanced techniques such as deep-RL. To recover guarantees when applying advanced RL algorithms to more complex environments with (i) reachability, (ii) safety-constrained reachability, or (iii) discounted-reward objectives, we build upon the DeepMDP framework introduced by Gelada et al. to derive new bisimulation bounds between the unknown environment and a learned discrete latent model of it. Our bisimulation bounds enable the application of formal methods for Markov decision processes. Finally, we show how one can use a policy obtained via state-of-the-art RL to efficiently train a variational autoencoder that yields a discrete latent model with provably approximately correct bisimulation guarantees. Additionally, we obtain a distilled version of the policy for the latent model.

Reinforcement learning (RL) is a central problem in artificial intelligence. This problem consists of defining artificial agents that can learn optimal behaviour by interacting with an environment -- where the optimal behaviour is defined with respect to a reward signal that the agent seeks to maximize. Reward machines (RMs) provide a structured, automata-based representation of a reward function that enables an RL agent to decompose an RL problem into structured subproblems that can be efficiently learned via off-policy learning. Here we show that RMs can be learned from experience, instead of being specified by the user, and that the resulting problem decomposition can be used to effectively solve partially observable RL problems. We pose the task of learning RMs as a discrete optimization problem where the objective is to find an RM that decomposes the problem into a set of subproblems such that the combination of their optimal memoryless policies is an optimal policy for the original problem. We show the effectiveness of this approach on three partially observable domains, where it significantly outperforms A3C, PPO, and ACER, and discuss its advantages, limitations, and broader potential.

The Partially Observable Markov Decision Process (POMDP) is a powerful framework for capturing decision-making problems that involve state and transition uncertainty. However, most current POMDP planners cannot effectively handle very high-dimensional observations they often encounter in the real world (e.g. image observations in robotic domains). In this work, we propose Visual Tree Search (VTS), a learning and planning procedure that combines generative models learned offline with online model-based POMDP planning. VTS bridges offline model training and online planning by utilizing a set of deep generative observation models to predict and evaluate the likelihood of image observations in a Monte Carlo tree search planner. We show that VTS is robust to different observation noises and, since it utilizes online, model-based planning, can adapt to different reward structures without the need to re-train. This new approach outperforms a baseline state-of-the-art on-policy planning algorithm while using significantly less offline training time.

Clinical decision support tools rooted in machine learning and optimization can provide significant value to healthcare providers, including through better management of intensive care units. In particular, it is important that the patient discharge task addresses the nuanced trade-off between decreasing a patient's length of stay (and associated hospitalization costs) and the risk of readmission or even death following the discharge decision. This work introduces an end-to-end general framework for capturing this trade-off to recommend optimal discharge timing decisions given a patient's electronic health records. A data-driven approach is used to derive a parsimonious, discrete state space representation that captures a patient's physiological condition. Based on this model and a given cost function, an infinite-horizon discounted Markov decision process is formulated and solved numerically to compute an optimal discharge policy, whose value is assessed using off-policy evaluation strategies. Extensive numerical experiments are performed to validate the proposed framework using real-life intensive care unit patient data.

We focus on the task of creating a reinforcement learning agent that is inherently explainable -- with the ability to produce immediate local explanations by thinking out loud while performing a task and analyzing entire trajectories post-hoc to produce causal explanations. This Hierarchically Explainable Reinforcement Learning agent (HEX-RL), operates in Interactive Fictions, text-based game environments in which an agent perceives and acts upon the world using textual natural language. These games are usually structured as puzzles or quests with long-term dependencies in which an agent must complete a sequence of actions to succeed -- providing ideal environments in which to test an agent's ability to explain its actions. Our agent is designed to treat explainability as a first-class citizen, using an extracted symbolic knowledge graph-based state representation coupled with a Hierarchical Graph Attention mechanism that points to the facts in the internal graph representation that most influenced the choice of actions. Experiments show that this agent provides significantly improved explanations over strong baselines, as rated by human participants generally unfamiliar with the environment, while also matching state-of-the-art task performance.

Reinforcement learning (RL) techniques have shown great success in quantitative investment tasks, such as portfolio management and algorithmic trading. Especially, intraday trading is one of the most profitable and risky tasks because of the intraday behaviors of the financial market that reflect billions of rapidly fluctuating values. However, it is hard to apply existing RL methods to intraday trading due to the following three limitations: 1) overlooking micro-level market information (e.g., limit order book); 2) only focusing on local price fluctuation and failing to capture the overall trend of the whole trading day; 3) neglecting the impact of market risk. To tackle these limitations, we propose DeepScalper, a deep reinforcement learning framework for intraday trading. Specifically, we adopt an encoder-decoder architecture to learn robust market embedding incorporating both macro-level and micro-level market information. Moreover, a novel hindsight reward function is designed to provide the agent a long-term horizon for capturing the overall price trend. In addition, we propose a risk-aware auxiliary task by predicting future volatility, which helps the agent take market risk into consideration while maximizing profit. Finally, extensive experiments on two stock index futures and four treasury bond futures demonstrate that DeepScalper achieves significant improvement against many state-of-the-art approaches.