We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite actions) where the goal of the decision maker is to reach a target set while avoiding an unsafe set(s) with certain probabilistic guarantees. Therefore the underlying Markov chain for any control policy will be multichain since by definition there exists a target set and an unsafe set. The decision maker also has to be optimal (with respect to a cost function) while navigating to the target set. This gives rise to a multi-objective optimization problem. We highlight the fact that Bellman's principle of optimality may not hold for constrained Markov decision problems with an underlying multichain structure (as shown by the counterexample due to Haviv. We resolve the counterexample by formulating the aforementioned multi-objective optimization problem as a zero-sum game and thereafter construct an asynchronous value iteration scheme for the Lagrangian (similar to Shapley's algorithm). Finally, we consider the reinforcement learning problem for the same and construct a modified $Q$-learning algorithm for learning the Lagrangian from data. We also provide a lower bound on the number of iterations required for learning the Lagrangian and corresponding error bounds.
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Deep neural networks have shown remarkable performance when trained on independent and identically distributed data from a fixed set of classes. However, in real-world scenarios, it can be desirable to train models on a continuous stream of data where multiple classification tasks are presented sequentially. This scenario, known as Continual Learning (CL) poses challenges to standard learning algorithms which struggle to maintain knowledge of old tasks while learning new ones. This stability-plasticity dilemma remains central to CL and multiple metrics have been proposed to adequately measure stability and plasticity separately. However, none considers the increasing difficulty of the classification task, which inherently results in performance loss for any model. In that sense, we analyze some limitations of current metrics and identify the presence of setup-induced forgetting. Therefore, we propose new metrics that account for the task's increasing difficulty. Through experiments on benchmark datasets, we demonstrate that our proposed metrics can provide new insights into the stability-plasticity trade-off achieved by models in the continual learning environment.
A significant limitation of one-class classification anomaly detection methods is their reliance on the assumption that unlabeled training data only contains normal instances. To overcome this impractical assumption, we propose two novel classification-based anomaly detection methods. Firstly, we introduce a semi-supervised shallow anomaly detection method based on an unbiased risk estimator. Secondly, we present a semi-supervised deep anomaly detection method utilizing a nonnegative (biased) risk estimator. We establish estimation error bounds and excess risk bounds for both risk minimizers. Additionally, we propose techniques to select appropriate regularization parameters that ensure the nonnegativity of the empirical risk in the shallow model under specific loss functions. Our extensive experiments provide strong evidence of the effectiveness of the risk-based anomaly detection methods.
Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the temporal dependence structure of Hawkes processes is generally a computationally expensive task, all the more with Bayesian estimation methods. In particular, for generalised nonlinear Hawkes processes, Monte-Carlo Markov Chain methods applied to compute the doubly intractable posterior distribution are not scalable to high-dimensional processes in practice. Recently, efficient algorithms targeting a mean-field variational approximation of the posterior distribution have been proposed. In this work, we first unify existing variational Bayes approaches under a general nonparametric inference framework, and analyse the asymptotic properties of these methods under easily verifiable conditions on the prior, the variational class, and the nonlinear model. Secondly, we propose a novel sparsity-inducing procedure, and derive an adaptive mean-field variational algorithm for the popular sigmoid Hawkes processes. Our algorithm is parallelisable and therefore computationally efficient in high-dimensional setting. Through an extensive set of numerical simulations, we also demonstrate that our procedure is able to adapt to the dimensionality of the parameter of the Hawkes process, and is partially robust to some type of model mis-specification.
Effective detection of organizations is essential for fighting crime and maintaining public safety, especially considering the limited human resources and tools to deal with each group that exhibits co-movement patterns. This paper focuses on solving the Network Structure Inference (NSI) challenge. Thus, we introduce two new approaches to detect network structure inferences based on agent trajectories. The first approach is based on the evaluation of graph entropy, while the second considers the quality of clustering indices. To evaluate the effectiveness of the new approaches, we conducted experiments using four scenario simulations based on the animal kingdom, available on the NetLogo platform: Ants, Wolf Sheep Predation, Flocking, and Ant Adaptation. Furthermore, we compare the results obtained with those of an approach previously proposed in the literature, applying all methods to simulations of the NetLogo platform. The results demonstrate that our new detection approaches can more clearly identify the inferences of organizations or networks in the simulated scenarios.
Fair calibration is a widely desirable fairness criteria in risk prediction contexts. One way to measure and achieve fair calibration is with multicalibration. Multicalibration constrains calibration error among flexibly-defined subpopulations while maintaining overall calibration. However, multicalibrated models can exhibit a higher percent calibration error among groups with lower base rates than groups with higher base rates. As a result, it is possible for a decision-maker to learn to trust or distrust model predictions for specific groups. To alleviate this, we propose \emph{proportional multicalibration}, a criteria that constrains the percent calibration error among groups and within prediction bins. We prove that satisfying proportional multicalibration bounds a model's multicalibration as well its \emph{differential calibration}, a fairness criteria that directly measures how closely a model approximates sufficiency. Therefore, proportionally calibrated models limit the ability of decision makers to distinguish between model performance on different patient groups, which may make the models more trustworthy in practice. We provide an efficient algorithm for post-processing risk prediction models for proportional multicalibration and evaluate it empirically. We conduct simulation studies and investigate a real-world application of PMC-postprocessing to prediction of emergency department patient admissions. We observe that proportional multicalibration is a promising criteria for controlling simultaneous measures of calibration fairness of a model over intersectional groups with virtually no cost in terms of classification performance.
We present a framework for approximate Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained due to computational constraints, which is becoming increasingly common for applications of complex models. We model the log-likelihood function using a Gaussian process (GP) and the main methodological innovation is to apply this model to emulate the progression that an exact Metropolis-Hastings (MH) sampler would take if it was applicable. Informative log-likelihood evaluation locations are selected using a sequential experimental design strategy until the MH accept/reject decision is done accurately enough according to the GP model. The resulting approximate sampler is conceptually simple and sample-efficient. It is also more robust to violations of GP modelling assumptions compared with earlier, related "Bayesian optimisation-like" methods tailored for Bayesian inference. We discuss some theoretical aspects and various interpretations of the resulting approximate MH sampler, and demonstrate its benefits in the context of Bayesian and generalised Bayesian likelihood-free inference for simulator-based statistical models.
We present our approach for the development, validation and deployment of a data-driven decision-making function for the automated control of a vehicle. The decisionmaking function, based on an artificial neural network is trained to steer the mobile robot SPIDER towards a predefined, static path to a target point while avoiding collisions with obstacles along the path. The training is conducted by means of proximal policy optimisation (PPO), a state of the art algorithm from the field of reinforcement learning. The resulting controller is validated using KPIs quantifying its capability to follow a given path and its reactivity on perceived obstacles along the path. The corresponding tests are carried out in the training environment. Additionally, the tests shall be performed as well in the robotics situation Gazebo and in real world scenarios. For the latter the controller is deployed on a FPGA-based development platform, the FRACTAL platform, and integrated into the SPIDER software stack.
Non-autoregressive approaches aim to improve the inference speed of translation models, particularly those that generate output in a one-pass forward manner. However, these approaches often suffer from a significant drop in translation quality compared to autoregressive models. This paper introduces a series of innovative techniques to enhance the translation quality of Non-Autoregressive Translation (NAT) models while maintaining a substantial acceleration in inference speed. We propose fine-tuning Pretrained Multilingual Language Models (PMLMs) with the CTC loss to train NAT models effectively. Furthermore, we adopt the MASK insertion scheme for up-sampling instead of token duplication, and we present an embedding distillation method to further enhance performance. In our experiments, our model outperforms the baseline autoregressive model (Transformer \textit{base}) on multiple datasets, including WMT'14 DE$\leftrightarrow$EN, WMT'16 RO$\leftrightarrow$EN, and IWSLT'14 DE$\leftrightarrow$EN. Notably, our model achieves better performance than the baseline autoregressive model on the IWSLT'14 En$\leftrightarrow$De and WMT'16 En$\leftrightarrow$Ro datasets, even without using distillation data during training. It is worth highlighting that on the IWSLT'14 DE$\rightarrow$EN dataset, our model achieves an impressive BLEU score of 39.59, setting a new state-of-the-art performance. Additionally, our model exhibits a remarkable speed improvement of 16.35 times compared to the autoregressive model.
Explaining artificial intelligence (AI) predictions is increasingly important and even imperative in many high-stakes applications where humans are the ultimate decision-makers. In this work, we propose two novel architectures of self-interpretable image classifiers that first explain, and then predict (as opposed to post-hoc explanations) by harnessing the visual correspondences between a query image and exemplars. Our models consistently improve (by 1 to 4 points) on out-of-distribution (OOD) datasets while performing marginally worse (by 1 to 2 points) on in-distribution tests than ResNet-50 and a $k$-nearest neighbor classifier (kNN). Via a large-scale, human study on ImageNet and CUB, our correspondence-based explanations are found to be more useful to users than kNN explanations. Our explanations help users more accurately reject AI's wrong decisions than all other tested methods. Interestingly, for the first time, we show that it is possible to achieve complementary human-AI team accuracy (i.e., that is higher than either AI-alone or human-alone), in ImageNet and CUB image classification tasks.
Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.
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