This paper introduces a novel reinforcement learning (RL) framework, termed Reward-Guided Conservative Q-learning (RG-CQL), to enhance coordination between ride-pooling and public transit within a multimodal transportation network. We model each ride-pooling vehicle as an agent governed by a Markov Decision Process (MDP) and propose an offline training and online fine-tuning RL framework to learn the optimal operational decisions of the multimodal transportation systems, including rider-vehicle matching, selection of drop-off locations for passengers, and vehicle routing decisions, with improved data efficiency. During the offline training phase, we develop a Conservative Double Deep Q Network (CDDQN) as the action executor and a supervised learning-based reward estimator, termed the Guider Network, to extract valuable insights into action-reward relationships from data batches. In the online fine-tuning phase, the Guider Network serves as an exploration guide, aiding CDDQN in effectively and conservatively exploring unknown state-action pairs. The efficacy of our algorithm is demonstrated through a realistic case study using real-world data from Manhattan. We show that integrating ride-pooling with public transit outperforms two benchmark cases solo rides coordinated with transit and ride-pooling without transit coordination by 17% and 22% in the achieved system rewards, respectively. Furthermore, our innovative offline training and online fine-tuning framework offers a remarkable 81.3% improvement in data efficiency compared to traditional online RL methods with adequate exploration budgets, with a 4.3% increase in total rewards and a 5.6% reduction in overestimation errors. Experimental results further demonstrate that RG-CQL effectively addresses the challenges of transitioning from offline to online RL in large-scale ride-pooling systems integrated with transit.

Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints. The ``space-decoupling" is reflected in several ways. We show that the tangent cone of coupled constraints is the intersection of tangent cones of each constraint. Moreover, we decouple the intertwined bounded-rank and orthogonally invariant constraints into two spaces, leading to optimization on a smooth manifold. Implementing Riemannian algorithms on this manifold is painless as long as the geometry of additional constraints is known. In addition, we unveil the equivalence between the reformulated problem and the original problem. Numerical experiments on real-world applications -- spherical data fitting, graph similarity measuring, low-rank SDP, model reduction of Markov processes, reinforcement learning, and deep learning -- validate the superiority of the proposed framework.

Quantification, or prevalence estimation, is the task of predicting the prevalence of each class within an unknown bag of examples. Most existing quantification methods in the literature rely on prior probability shift assumptions to create a quantification model that uses the predictions of an underlying classifier to make optimal prevalence estimates. In this work, we present an end-to-end neural network that uses Gaussian distributions in latent spaces to obtain invariant representations of bags of examples. This approach addresses the quantification problem using deep learning, enabling the optimization of specific loss functions relevant to the problem and avoiding the need for an intermediate classifier, tackling the quantification problem as a direct optimization problem. Our method achieves state-of-the-art results, both against traditional quantification methods and other deep learning approaches for quantification. The code needed to reproduce all our experiments is publicly available at https://github.com/AICGijon/gmnet.

Predictive models are highly advanced in understanding the mechanisms of brain function. Recent advances in machine learning further underscore the power of prediction for optimal representation in learning. However, there remains a gap in creating a biologically plausible model that explains how the neural system achieves prediction. In this paper, we introduce a framework that employs an energy-based model (EBM) to capture the nuanced processes of predicting observation after action within the neural system, encompassing prediction, learning, and inference. We implement the EBM with a hierarchical structure and integrate a continuous attractor neural network for memory, constructing a biologically plausible model. In experimental evaluations, our model demonstrates efficacy across diverse scenarios. The range of actions includes eye movement, motion in environments, head turning, and static observation while the environment changes. Our model not only makes accurate predictions for environments it was trained on, but also provides reasonable predictions for unseen environments, matching the performances of machine learning methods in multiple tasks. We hope that this study contributes to a deep understanding of how the neural system performs prediction.

What if artificial intelligence could not only solve problems for which it was trained but also learn to teach itself to solve new problems (i.e., meta-learn)? In this study, we demonstrate that a pre-trained transformer fine-tuned with reinforcement learning over multiple episodes develops the ability to solve problems that it has never encountered before - an emergent ability called In-Context Reinforcement Learning (ICRL). This powerful meta-learner not only excels in solving unseen in-distribution environments with remarkable sample efficiency, but also shows strong performance in out-of-distribution environments. In addition, we show that it exhibits robustness to the quality of its training data, seamlessly stitches together behaviors from its context, and adapts to non-stationary environments. These behaviors demonstrate that an RL-trained transformer can iteratively improve upon its own solutions, making it an excellent general-purpose problem solver.

In this work, we leverage a generative data model considering comparison noise to develop a fast, precise, and informative ranking algorithm from pairwise comparisons that produces a measure of confidence on each comparison. The problem of ranking a large number of items from noisy and sparse pairwise comparison data arises in diverse applications, like ranking players in online games, document retrieval or ranking human perceptions. Although different algorithms are available, we need fast, large-scale algorithms whose accuracy degrades gracefully when the number of comparisons is too small. Fitting our proposed model entails solving a non-convex optimization problem, which we tightly approximate by a sum of quasi-convex functions and a regularization term. Resorting to an iterative reweighted minimization and the Primal-Dual Hybrid Gradient method, we obtain PD-Rank, achieving a Kendall tau 0.1 higher than all comparing methods, even for 10\% of wrong comparisons in simulated data matching our data model, and leading in accuracy if data is generated according to the Bradley-Terry model, in both cases faster by one order of magnitude, in seconds. In real data, PD-Rank requires less computational time to achieve the same Kendall tau than active learning methods.

The relations between maximum-likelihood and optimal transport (OT) have already been discussed in multiple works (Rigollet and Weed, 2018; Mena et al., 2020; Diebold et al., 2024). The purpose of this brief note is to provide the key tools used to establish these connections. The primary aim is pedagogical: we will focus on the (discrete) mixtures case, adopting a "computational OT" perspective. Hopefully, readers will find this exercise insightful. Our analysis will largely rely on the approach described in Rigollet and Weed (2018), though adapted to a different formalism and applied to a slightly different problem (mixture estimation rather than Gaussian deconvolution).

Weaknesses: The problem in the paper is that it fails in showing the actual scope of the new results, especially in the global context of BNs learning. In fact their methods apparently can only applied to the continuous case: no mention is ever made if the same method can work with categorical variables. This is reflected to the selected set of "state-of-the-art" methods against which they compare their methods, that is a narrow subset of the whole literature on BNs learning. Saying something like "As mentioned, this paper is most closely related to the fully continuous framework of ... " is definitely not enough: a more precise and thorough description of the limitations of this work, and its position in the whole BNs learning literature, is needed. The title and the abstract should modified as well with same reasoning.

After discussions, there has been consensus that the paper's ideas deserve publication, even though they are somewhat incremental and without guarantees, as they build on NOTEARS. It has been appreciated the discussion on the issues with NOTEARS and an attempt to improve on them.

Summary: This paper introduces Poisson auxiliary variables to facilitate minibatch sampling. The key insight is with the appropriate Poisson parameterization, the joint distribution (Eq. The authors apply this insight to discrete-state Gibbs sampling (Algorithm 2), Metropolis Hastings (Supplement), and continuous-state Gibbs sampling (Alg 3. and 5). The authors also develop spectral gap lower bounds for all proposed Gibbs sampling methods, which provides a rough guideline for choosing a tuning parameter \lambda and comparing the (asymptotic) per iteration runtime of the methods (Table 1). Finally the authors evaluate the Gibbs methods on synthetic data, showing that their proposed method performs similarly to Gibbs while outperforming alternatives.