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Commonly in reinforcement learning (RL), rewards are discounted over time using an exponential function to model time preference, thereby bounding the expected long-term reward. In contrast, in economics and psychology, it has been shown that humans often adopt a hyperbolic discounting scheme, which is optimal when a specific task termination time distribution is assumed. In this work, we propose a theory for continuous-time model-based reinforcement learning generalized to arbitrary discount functions. This formulation covers the case in which there is a non-exponential random termination time. We derive a Hamilton-Jacobi-Bellman (HJB) equation characterizing the optimal policy and describe how it can be solved using a collocation method, which uses deep learning for function approximation. Further, we show how the inverse RL problem can be approached, in which one tries to recover properties of the discount function given decision data. We validate the applicability of our proposed approach on two simulated problems. Our approach opens the way for the analysis of human discounting in sequential decision-making tasks.

We study the classic facility location setting, where we are given $n$ clients and $m$ possible facility locations in some arbitrary metric space, and want to choose a location to build a facility. The exact same setting also arises in spatial social choice, where voters are the clients and the goal is to choose a candidate or outcome, with the distance from a voter to an outcome representing the cost of this outcome for the voter (e.g., based on their ideological differences). Unlike most previous work, we do not focus on a single objective to optimize (e.g., the total distance from clients to the facility, or the maximum distance, etc.), but instead attempt to optimize several different objectives simultaneously. More specifically, we consider the $l$-centrum family of objectives, which includes the total distance, max distance, and many others. We present tight bounds on how well any pair of such objectives (e.g., max and sum) can be simultaneously approximated compared to their optimum outcomes. In particular, we show that for any such pair of objectives, it is always possible to choose an outcome which simultaneously approximates both objectives within a factor of $1+\sqrt{2}$, and give a precise characterization of how this factor improves as the two objectives being optimized become more similar. For $q>2$ different centrum objectives, we show that it is always possible to approximate all $q$ of these objectives within a small constant, and that this constant approaches 3 as $q\rightarrow \infty$. Our results show that when optimizing only a few simultaneous objectives, it is always possible to form an outcome which is a significantly better than 3 approximation for all of these objectives.

Motivation: A Genomic Dictionary, i.e., the set of the k-mers appearing in a genome, is a fundamental source of genomic information: its collection is the first step in strategic computational methods ranging from assembly to sequence comparison and phylogeny. Unfortunately, it is costly to store. This motivates some recent studies regarding the compression of those k-mer sets. However, such an area does not have the maturity of genomic compression, lacking an homogeneous and methodologically sound experimental foundation that allows to fairly compare the relative merits of the available solutions, and that takes into account also the rich choices of compression methods that can be used. Results: We provide such a foundation here, supporting it with an extensive set of experiments that use reference datasets and a carefully selected set of representative data compressors. Our results highlight the spectrum of compressor choices one has in terms of Pareto Optimality of compression vs. post-processing, this latter being important when the Dictionary needs to be decompressed many times. In addition to the useful indications, not available elsewhere, that this study offers to the researchers interested in storing k-mer dictionaries in compressed form, a software system that can be readily used to explore the Pareto Optimal solutions available r a given Dictionary is also provided. Availability: The software system is available at //github.com/GenGrim76/Pareto-Optimal-GDC, together with user manuals and installation instructions. Contact: [email protected] Supplementary information: Additional data are available in the Supplementary Material.

We present a way to create small yet difficult model counting instances. Our generator is highly parameterizable: the number of variables of the instances it produces, as well as their number of clauses and the number of literals in each clause, can all be set to any value. Our instances have been tested on state of the art model counters, against other difficult model counting instances, in the Model Counting Competition. The smallest unsolved instances of the competition, both in terms of number of variables and number of clauses, were ours. We also observe a peak of difficulty when fixing the number of variables and varying the number of clauses, in both random instances and instances built by our generator. Using these results, we predict the parameter values for which the hardest to count instances will occur.

Emergency shelters, which reflect the city's ability to respond to and deal with major public emergencies to a certain extent, are essential to a modern urban emergency management system. This paper is based on spatial analysis methods, using Analytic Hierarchy Process to analyze the suitability of the 28 emergency shelters in Wuhan City. The Technique for Order Preference by Similarity to an Ideal Solution is further used to evaluate the accommodation capacity of emergency shelters in central urban areas, which provides a reference for the optimization of existing shelters and the site selection of new shelters, and provides a basis for improving the service capacity of shelters. The results show that the overall situation of emergency shelters in Wuhan is good, with 96\% of the places reaching the medium level or above, but the suitability level needs to be further improved, especially the effectiveness and accessibility. Among the seven central urban areas in Wuhan, Hongshan District has the strongest accommodation capacity while Jianghan District has the weakest, with noticeable differences.

Sampling-based methods have become a cornerstone of contemporary approaches to Model Predictive Control (MPC), as they make no restrictions on the differentiability of the dynamics or cost function and are straightforward to parallelize. However, their efficacy is highly dependent on the quality of the sampling distribution itself, which is often assumed to be simple, like a Gaussian. This restriction can result in samples which are far from optimal, leading to poor performance. Recent work has explored improving the performance of MPC by sampling in a learned latent space of controls. However, these methods ultimately perform all MPC parameter updates and warm-starting between time steps in the control space. This requires us to rely on a number of heuristics for generating samples and updating the distribution and may lead to sub-optimal performance. Instead, we propose to carry out all operations in the latent space, allowing us to take full advantage of the learned distribution. Specifically, we frame the learning problem as bi-level optimization and show how to train the controller with backpropagation-through-time. By using a normalizing flow parameterization of the distribution, we can leverage its tractable density to avoid requiring differentiability of the dynamics and cost function. Finally, we evaluate the proposed approach on simulated robotics tasks and demonstrate its ability to surpass the performance of prior methods and scale better with a reduced number of samples.

The widespread use of information and communication technology (ICT) over the course of the last decades has been a primary catalyst behind the digitalization of power systems. Meanwhile, as the utilization rate of the Internet of Things (IoT) continues to rise along with recent advancements in ICT, the need for secure and computationally efficient monitoring of critical infrastructures like the electrical grid and the agents that participate in it is growing. A cyber-physical system, such as the electrical grid, may experience anomalies for a number of different reasons. These may include physical defects, mistakes in measurement and communication, cyberattacks, and other similar occurrences. The goal of this study is to emphasize what the most common incidents are with power systems and to give an overview and classification of the most common ways to find problems, starting with the consumer/prosumer end working up to the primary power producers. In addition, this article aimed to discuss the methods and techniques, such as artificial intelligence (AI) that are used to identify anomalies in the power systems and markets.

The notion of concept drift refers to the phenomenon that the distribution generating the observed data changes over time. If drift is present, machine learning models may become inaccurate and need adjustment. Many technologies for learning with drift rely on the interleaved test-train error (ITTE) as a quantity which approximates the model generalization error and triggers drift detection and model updates. In this work, we investigate in how far this procedure is mathematically justified. More precisely, we relate a change of the ITTE to the presence of real drift, i.e., a changed posterior, and to a change of the training result under the assumption of optimality. We support our theoretical findings by empirical evidence for several learning algorithms, models, and datasets.

A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.

The essence of multivariate sequential learning is all about how to extract dependencies in data. These data sets, such as hourly medical records in intensive care units and multi-frequency phonetic time series, often time exhibit not only strong serial dependencies in the individual components (the "marginal" memory) but also non-negligible memories in the cross-sectional dependencies (the "joint" memory). Because of the multivariate complexity in the evolution of the joint distribution that underlies the data generating process, we take a data-driven approach and construct a novel recurrent network architecture, termed Memory-Gated Recurrent Networks (mGRN), with gates explicitly regulating two distinct types of memories: the marginal memory and the joint memory. Through a combination of comprehensive simulation studies and empirical experiments on a range of public datasets, we show that our proposed mGRN architecture consistently outperforms state-of-the-art architectures targeting multivariate time series.