On the other hand, RL and MSP are Solving large-scale multistage stochastic programming suitable for discrete-time problems. RL utilizes simulated (MSP) problems poses a significant challenge or real-world experience to learn optimal decision-making as commonly used stagewise decomposition through a trial-and-error process, while MSP seeks to find algorithms, including stochastic dual dynamic optimal decisions through mathematical formulation in either programming (SDDP), face growing time complexity continuous or discrete spaces. Therefore, the selection as the subproblem size and problem count of a methodology depends on specific problem characteristics, increase.

Integer Linear Programming (ILP) has been proposed as a formalism for encoding precise structural and semantic constraints for Natural Language Inference (NLI). However, traditional ILP frameworks are non-differentiable, posing critical challenges for the integration of continuous language representations based on deep learning. In this paper, we introduce a novel approach, named Diff-Comb Explainer, a neuro-symbolic architecture for explanation-based NLI based on Differentiable BlackBox Combinatorial Solvers (DBCS). Differently from existing neuro-symbolic solvers, Diff-Comb Explainer does not necessitate a continuous relaxation of the semantic constraints, enabling a direct, more precise, and efficient incorporation of neural representations into the ILP formulation. Our experiments demonstrate that Diff-Comb Explainer achieves superior performance when compared to conventional ILP solvers, neuro-symbolic black-box solvers, and Transformer-based encoders. Moreover, a deeper analysis reveals that Diff-Comb Explainer can significantly improve the precision, consistency, and faithfulness of the constructed explanations, opening new opportunities for research on neuro-symbolic architectures for explainable and transparent NLI in complex domains.

This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which is a special case of Adam with adaptive learning rates but without first-order momentum. Specifically, to solve the challenges due to dependence among adaptive update, unbounded gradient estimate and Lipschitz constant, we demonstrate that the first-order term in the descent lemma converges and its denominator is upper bounded by a function of gradient norm. Based on this result, we show that RMSProp with proper hyperparameters converges to an $\epsilon$-stationary point with an iteration complexity of $\mathcal O(\epsilon^{-4})$. We then generalize our analysis to Adam, where the additional challenge is due to a mismatch between the gradient and first-order momentum. We develop a new upper bound on the first-order term in the descent lemma, which is also a function of the gradient norm. We show that Adam with proper hyperparameters converges to an $\epsilon$-stationary point with an iteration complexity of $\mathcal O(\epsilon^{-4})$. Our complexity results for both RMSProp and Adam match with the complexity lower bound established in \cite{arjevani2023lower}.

Multi-task learning has become increasingly popular in the machine learning field, but its practicality is hindered by the need for large, labeled datasets. Most multi-task learning methods depend on fully labeled datasets wherein each input example is accompanied by ground-truth labels for all target tasks. Unfortunately, curating such datasets can be prohibitively expensive and impractical, especially for dense prediction tasks which require per-pixel labels for each image. With this in mind, we propose Joint-Task Regularization (JTR), an intuitive technique which leverages cross-task relations to simultaneously regularize all tasks in a single joint-task latent space to improve learning when data is not fully labeled for all tasks. JTR stands out from existing approaches in that it regularizes all tasks jointly rather than separately in pairs -- therefore, it achieves linear complexity relative to the number of tasks while previous methods scale quadratically. To demonstrate the validity of our approach, we extensively benchmark our method across a wide variety of partially labeled scenarios based on NYU-v2, Cityscapes, and Taskonomy.

We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for optimal control design. We propose a specific neural network (NN) architecture that yields a hybrid system with piecewise-affine dynamics that is differentiable with respect to the network's parameters, thereby enabling the use of derivative-based training procedures. We show that a careful choice of our NN's weights produces a hybrid system model with structural properties that are highly favourable when used as part of a finite horizon optimal control problem (OCP). Specifically, we show that optimal solutions with strong local optimality guarantees can be computed via nonlinear programming, in contrast to classical OCPs for general hybrid systems which typically require mixed-integer optimization. In addition to being well-suited for optimal control design, numerical simulations illustrate that our NN-based technique enjoys very similar performance to state-of-the-art system identification methodologies for hybrid systems and it is competitive on nonlinear benchmarks.

Hybrid electric vehicles (HEVs) are becoming increasingly popular because they can better combine the working characteristics of internal combustion engines and electric motors. However, the minimum fuel consumption of an HEV for a battery electrical balance case under a specific assembly condition and a specific speed curve still needs to be clarified in academia and industry. Regarding this problem, this work provides the mathematical expression of constrained optimal fuel consumption (COFC) from the perspective of constrained reinforcement learning (CRL) for the first time globally. Also, two mainstream approaches of CRL, constrained variational policy optimization (CVPO) and Lagrangian-based approaches, are utilized for the first time to obtain the vehicle's minimum fuel consumption under the battery electrical balance condition. We conduct case studies on the well-known Prius TOYOTA hybrid system (THS) under the NEDC condition; we give vital steps to implement CRL approaches and compare the performance between the CVPO and Lagrangian-based approaches. Our case study found that CVPO and Lagrangian-based approaches can obtain the lowest fuel consumption while maintaining the SOC balance constraint. The CVPO approach converges stable, but the Lagrangian-based approach can obtain the lowest fuel consumption at 3.95 L/100km, though with more significant oscillations. This result verifies the effectiveness of our proposed CRL approaches to the COFC problem.

Multi-camera SLAM systems offer a plethora of advantages, primarily stemming from their capacity to amalgamate information from a broader field of view, thereby resulting in heightened robustness and improved localization accuracy. In this research, we present a significant extension and refinement of the state-of-the-art stereo SLAM system, known as ORB-SLAM2, with the objective of attaining even higher precision. To accomplish this objective, we commence by mapping measurements from all cameras onto a virtual camera termed BundledFrame. This virtual camera is meticulously engineered to seamlessly adapt to multi-camera configurations, facilitating the effective fusion of data captured from multiple cameras. Additionally, we harness extrinsic parameters in the bundle adjustment (BA) process to achieve precise trajectory estimation.Furthermore, we conduct an extensive analysis of the role of bundle adjustment (BA) in the context of multi-camera scenarios, delving into its impact on tracking, local mapping, and global optimization. Our experimental evaluation entails comprehensive comparisons between ground truth data and the state-of-the-art SLAM system. To rigorously assess the system's performance, we utilize the EuRoC datasets. The consistent results of our evaluations demonstrate the superior accuracy of our system in comparison to existing approaches.

We consider the problem of sequentially conducting multiple experiments where each experiment corresponds to a hypothesis testing task. At each time point, the experimenter must make an irrevocable decision of whether to reject the null hypothesis (or equivalently claim a discovery) before the next experimental result arrives. The goal is to maximize the number of discoveries while maintaining a low error rate at all time points measured by local False Discovery Rate (FDR). We formulate the problem as an online knapsack problem with exogenous random budget replenishment. We start with general arrival distributions and show that a simple policy achieves a $O(\sqrt{T})$ regret. We complement the result by showing that such regret rate is in general not improvable. We then shift our focus to discrete arrival distributions. We find that many existing re-solving heuristics in the online resource allocation literature, albeit achieve bounded loss in canonical settings, may incur a $\Omega(\sqrt{T})$ or even a $\Omega(T)$ regret. With the observation that canonical policies tend to be too optimistic and over claim discoveries, we propose a novel policy that incorporates budget safety buffers. It turns out that a little more safety can greatly enhance efficiency -- small additional logarithmic buffers suffice to reduce the regret from $\Omega(\sqrt{T})$ or even $\Omega(T)$ to $O(\ln^2 T)$. From a practical perspective, we extend the policy to the scenario with continuous arrival distributions as well as time-dependent information structures. We conduct both synthetic experiments and empirical applications on a time series data from New York City taxi passengers to validate the performance of our proposed policies. Our results emphasize how effective policies should be designed in online resource allocation problems with exogenous budget replenishment.

Model generalization ability upon incrementally acquiring dynamically updating knowledge from sequentially arriving tasks is crucial to tackle the sensitivity-stability dilemma in Continual Learning (CL). Weight loss landscape sharpness minimization seeking for flat minima lying in neighborhoods with uniform low loss or smooth gradient is proven to be a strong training regime improving model generalization compared with loss minimization based optimizer like SGD. Yet only a few works have discussed this training regime for CL, proving that dedicated designed zeroth-order sharpness optimizer can improve CL performance. In this work, we propose a Continual Flatness (C-Flat) method featuring a flatter loss landscape tailored for CL. C-Flat could be easily called with only one line of code and is plug-and-play to any CL methods. A general framework of C-Flat applied to all CL categories and a thorough comparison with loss minima optimizer and flat minima based CL approaches is presented in this paper, showing that our method can boost CL performance in almost all cases. Code will be publicly available upon publication.

Multi-robot collaborative navigation is an essential ability where teamwork and synchronization are keys. In complex and uncertain environments, adaptive formation is vital, as rigid formations prove to be inadequate. The ability of robots to dynamically adjust their formation enables navigation through unpredictable spaces, maintaining cohesion, and effectively responding to environmental challenges. In this paper, we introduce a novel approach that uses bi-level learning framework. Specifically, we use graph learning at a high level for group coordination and reinforcement learning for individual navigation. We innovate by integrating a spring-damper model within the reinforcement learning reward mechanism, addressing the rigidity of traditional formation control methods. During execution, our approach enables a team of robots to successfully navigate challenging environments, maintain a desired formation shape, and dynamically adjust their formation scale based on environmental information. We conduct extensive experiments to evaluate our approach across three distinct formation scenarios in multi-robot navigation: circle, line, and wedge. Experimental results show that our approach achieves promising results and scalability on multi-robot navigation with formation adaptation.