Intelligent vehicles (IVs) have gained worldwide attention due to their increased convenience, safety advantages, and potential commercial value. Despite predictions of commercial deployment by 2025, implementation remains limited to small-scale validation, with precise tracking controllers and motion planners being essential prerequisites for IVs. This paper reviews state-of-the-art motion planning methods for IVs, including pipeline planning and end-to-end planning methods. The study examines the selection, expansion, and optimization operations in a pipeline method, while it investigates training approaches and validation scenarios for driving tasks in end-to-end methods. Experimental platforms are reviewed to assist readers in choosing suitable training and validation strategies. A side-by-side comparison of the methods is provided to highlight their strengths and limitations, aiding system-level design choices. Current challenges and future perspectives are also discussed in this survey.

A large variety of real-world Reinforcement Learning (RL) tasks is characterized by a complex and heterogeneous structure that makes end-to-end (or flat) approaches hardly applicable or even infeasible. Hierarchical Reinforcement Learning (HRL) provides general solutions to address these problems thanks to a convenient multi-level decomposition of the tasks, making their solution accessible. Although often used in practice, few works provide theoretical guarantees to justify this outcome effectively. Thus, it is not yet clear when to prefer such approaches compared to standard flat ones. In this work, we provide an option-dependent upper bound to the regret suffered by regret minimization algorithms in finite-horizon problems. We illustrate that the performance improvement derives from the planning horizon reduction induced by the temporal abstraction enforced by the hierarchical structure. Then, focusing on a sub-setting of HRL approaches, the options framework, we highlight how the average duration of the available options affects the planning horizon and, consequently, the regret itself. Finally, we relax the assumption of having pre-trained options to show how in particular situations, learning hierarchically from scratch could be preferable to using a standard approach.

Adaptive learning is an area of educational technology that consists in delivering personalized learning experiences to address the unique needs of each learner. An important subfield of adaptive learning is learning path personalization: it aims at designing systems that recommend sequences of educational activities to maximize students' learning outcomes. Many machine learning approaches have already demonstrated significant results in a variety of contexts related to learning path personalization. However, most of them were designed for very specific settings and are not very reusable. This is accentuated by the fact that they often rely on non-scalable models, which are unable to integrate new elements after being trained on a specific set of educational resources. In this paper, we introduce a flexible and scalable approach towards the problem of learning path personalization, which we formalize as a reinforcement learning problem. Our model is a sequential recommender system based on a graph neural network, which we evaluate on a population of simulated learners. Our results demonstrate that it can learn to make good recommendations in the small-data regime.

The Quran is the holy scripture of Islam, and its recitation is an important aspect of the religion. Recognizing the recitation of the Holy Quran automatically is a challenging task due to its unique rules that are not applied in normal speaking speeches. A lot of research has been done in this domain, but previous works have detected recitation errors as a classification task or used traditional automatic speech recognition (ASR). In this paper, we proposed a novel end-to-end deep learning model for recognizing the recitation of the Holy Quran. The proposed model is a CNN-Bidirectional GRU encoder that uses CTC as an objective function, and a character-based decoder which is a beam search decoder. Moreover, all previous works were done on small private datasets consisting of short verses and a few chapters of the Holy Quran. As a result of using private datasets, no comparisons were done. To overcome this issue, we used a public dataset that has recently been published (Ar-DAD) and contains about 37 chapters that were recited by 30 reciters, with different recitation speeds and different types of pronunciation rules. The proposed model performance was evaluated using the most common evaluation metrics in speech recognition, word error rate (WER), and character error rate (CER). The results were 8.34% WER and 2.42% CER. We hope this research will be a baseline for comparisons with future research on this public new dataset (Ar-DAD).

Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since robust loss functions are usually non-smooth. More recently, computationally fast non-convex approaches via sub-gradient descent are proposed, which, unfortunately, fail to deliver a statistically consistent estimator even under sub-Gaussian noise. In this paper, we introduce a novel Riemannian sub-gradient (RsGrad) algorithm which is not only computationally efficient with linear convergence but also is statistically optimal, be the noise Gaussian or heavy-tailed. Convergence theory is established for a general framework and specific applications to absolute loss, Huber loss, and quantile loss are investigated. Compared with existing non-convex methods, ours reveals a surprising phenomenon of dual-phase convergence. In phase one, RsGrad behaves as in a typical non-smooth optimization that requires gradually decaying stepsizes. However, phase one only delivers a statistically sub-optimal estimator which is already observed in the existing literature. Interestingly, during phase two, RsGrad converges linearly as if minimizing a smooth and strongly convex objective function and thus a constant stepsize suffices. Underlying the phase-two convergence is the smoothing effect of random noise to the non-smooth robust losses in an area close but not too close to the truth. Lastly, RsGrad is applicable for low-rank tensor estimation under heavy-tailed noise where a statistically optimal rate is attainable with the same phenomenon of dual-phase convergence, and a novel shrinkage-based second-order moment method is guaranteed to deliver a warm initialization. Numerical simulations confirm our theoretical discovery and showcase the superiority of RsGrad over prior methods.

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since the robust loss functions are usually non-smooth. More recently, computationally fast non-convex approaches via sub-gradient descent are proposed, which, unfortunately, fail to deliver a statistically consistent estimator even under sub-Gaussian noise. In this paper, we introduce a projected sub-gradient descent algorithm for both the sparse linear regression and low-rank linear regression problems. The algorithm is not only computationally efficient with linear convergence but also statistically optimal, be the noise Gaussian or heavy-tailed with a finite 1 + epsilon moment. The convergence theory is established for a general framework and its specific applications to absolute loss, Huber loss and quantile loss are investigated. Compared with existing non-convex methods, ours reveals a surprising phenomenon of two-phase convergence. In phase one, the algorithm behaves as in typical non-smooth optimization that requires gradually decaying stepsizes. However, phase one only delivers a statistically sub-optimal estimator, which is already observed in the existing literature. Interestingly, during phase two, the algorithm converges linearly as if minimizing a smooth and strongly convex objective function, and thus a constant stepsize suffices. Underlying the phase-two convergence is the smoothing effect of random noise to the non-smooth robust losses in an area close but not too close to the truth. Numerical simulations confirm our theoretical discovery and showcase the superiority of our algorithm over prior methods.

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-$m$ rate, where $m$ is the number of simulated samples. This can lead to significant computational challenges since a large $m$ is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

We study a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. Our robust Bayesian approach involves two adjustment steps: first, we make a correction for prior distributions of the conditional mean function; second, we introduce a recentering term on the posterior distribution of the resulting ATE. We prove asymptotic equivalence of our Bayesian estimator and double robust frequentist estimators by establishing a new semiparametric Bernstein-von Mises theorem under double robustness; i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian point estimator internalizes the bias correction as the frequentist-type doubly robust estimator, and the Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, we find that this robust Bayesian procedure leads to significant bias reduction of point estimation and accurate coverage of confidence intervals, especially when the dimensionality of covariates is large relative to the sample size and the underlying functions become complex. We illustrate our method in an application to the National Supported Work Demonstration.

We address an important yet challenging problem - modeling high-dimensional dependencies across multivariates such as financial indicators in heterogeneous markets. In reality, a market couples and influences others over time, and the financial variables of a market are also coupled. We make the first attempt to integrate variational sequential neural learning with copula-based dependence modeling to characterize both temporal observable and latent variable-based dependence degrees and structures across non-normal multivariates. Our variational neural network WPVC-VLSTM models variational sequential dependence degrees and structures across multivariate time series by variational long short-term memory networks and regular vine copula. The regular vine copula models nonnormal and long-range distributional couplings across multiple dynamic variables. WPVC-VLSTM is verified in terms of both technical significance and portfolio forecasting performance. It outperforms benchmarks including linear models, stochastic volatility models, deep neural networks, and variational recurrent networks in cross-market portfolio forecasting.

We study the complexity of reductions for weighted reachability in parametric Markov decision processes. That is, we say a state p is never worse than q if for all valuations of the polynomial indeterminates it is the case that the maximal expected weight that can be reached from p is greater than the same value from q. In terms of computational complexity, we establish that determining whether p is never worse than q is coETR-complete. On the positive side, we give a polynomial-time algorithm to compute the equivalence classes of the order we study for Markov chains. Additionally, we describe and implement two inference rules to under-approximate the never-worse relation and empirically show that it can be used as an efficient preprocessing step for the analysis of large Markov decision processes.