Lexicographic multi-objective problems, which consist of multiple conflicting subtasks with explicit priorities, are common in real-world applications. Despite the advantages of Reinforcement Learning (RL) in single tasks, extending conventional RL methods to prioritized multiple objectives remains challenging. In particular, traditional Safe RL and Multi-Objective RL (MORL) methods have difficulty enforcing priority orderings efficiently. Therefore, Lexicographic Multi-Objective RL (LMORL) methods have been developed to address these challenges. However, existing LMORL methods either rely on heuristic threshold tuning with prior knowledge or are restricted to discrete domains. To overcome these limitations, we propose Lexicographically Projected Policy Gradient RL (LPPG-RL), a novel LMORL framework which leverages sequential gradient projections to identify feasible policy update directions, thereby enabling LPPG-RL broadly compatible with all policy gradient algorithms in continuous spaces. LPPG-RL reformulates the projection step as an optimization problem, and utilizes Dykstra's projection rather than generic solvers to deliver great speedups, especially for small- to medium-scale instances. In addition, LPPG-RL introduces Subproblem Exploration (SE) to prevent gradient vanishing, accelerate convergence and enhance stability. We provide theoretical guarantees for convergence and establish a lower bound on policy improvement. Finally, through extensive experiments in a 2D navigation environment, we demonstrate the effectiveness of LPPG-RL, showing that it outperforms existing state-of-the-art continuous LMORL methods.

Best-of-$N$ reasoning improves the accuracy of language models in solving complex tasks by sampling multiple candidate solutions and then selecting the best one based on some criteria. A critical bottleneck for this strategy is the output diversity limit, which occurs when the model generates similar outputs despite stochastic sampling, and hence recites the same error. To address this lack of variance in reasoning paths, we propose a novel unsupervised activation steering strategy that simultaneously optimizes the steering vectors for multiple reasoning trajectories at test time. At any synchronization anchor along the batch generation process, we find the steering vectors that maximize the total volume spanned by all possible intervened activation subsets. We demonstrate that these steering vectors can be determined by solving a Riemannian optimization problem over the product of spheres with a log-determinant objective function. We then use a Riemannian block-coordinate descent algorithm with a well-tuned learning rate to obtain a stationary point of the problem, and we apply these steering vectors until the generation process reaches the subsequent synchronization anchor. Empirical evaluations on popular mathematical benchmarks demonstrate that our test-time Riemannian activation steering strategy outperforms vanilla sampling techniques in terms of generative diversity and solution accuracy.

Multimodal learning, while contributing to numerous success stories across various fields, faces the challenge of prohibitively expensive manual annotation. To address the scarcity of annotated data, a popular solution is unsupervised domain adaptation, which has been extensively studied in unimodal settings yet remains less explored in multi-modal settings. In this paper, we investigate heterogeneous multimodal domain adaptation, where the primary challenge is the varying domain shifts of different modalities from the source to the target domain. We first introduce the information bottleneck method to learn representations for each modality independently, and then match the source and target domains in the representation space with correlation alignment. To balance the domain alignment of all modalities, we formulate the problem as a multi-objective task, aiming for a Pareto optimal solution. By exploiting the properties specific to our model, the problem can be simplified to a quadratic programming problem. Further approximation yields a closed-form solution, leading to an efficient modality-balanced multimodal domain adaptation algorithm. The proposed method features Balanced multi-objective optimization for multimodal domain adaptation, termed Boomda. Extensive empirical results showcase the effectiveness of the proposed approach and demonstrate that Boomda outperforms the competing schemes.

Imitation Learning (IL) has proven highly effective for robotic and control tasks where manually designing reward functions or explicit controllers is infeasible. However, standard IL methods implicitly assume that the environment dynamics remain fixed between training and deployment. In practice, this assumption rarely holds where modeling inaccuracies, real-world parameter variations, and adversarial perturbations can all induce shifts in transition dynamics, leading to severe performance degradation. We address this challenge through Balance Equation-based Distributionally Robust Offline Imitation Learning, a framework that learns robust policies solely from expert demonstrations collected under nominal dynamics, without requiring further environment interaction. We formulate the problem as a distributionally robust optimization over an uncertainty set of transition models, seeking a policy that minimizes the imitation loss under the worst-case transition distribution. Importantly, we show that this robust objective can be reformulated entirely in terms of the nominal data distribution, enabling tractable offline learning. Empirical evaluations on continuous-control benchmarks demonstrate that our approach achieves superior robustness and generalization compared to state-of-the-art offline IL baselines, particularly under perturbed or shifted environments.

As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a compelling need for multi-objective bilevel learning (MOBL). So far, however, the field of MOBL remains in its infancy and many important problems remain under-explored. This motivates us to fill this gap and systematically investigate the theoretical and algorithmic foundation of MOBL. Specifically, we consider MOBL problems with multiple conflicting objectives guided by preferences at the upper-level subproblem, where part of the inputs depend on the optimal solution of the lower-level subproblem. Our goal is to develop efficient MOBL optimization algorithms to (1) identify a preference-guided Pareto-stationary solution with low oracle complexity; and (2) enable systematic Pareto front exploration. To this end, we propose a unifying algorithmic framework called weighted-Chebyshev multi-hyper-gradient-descent (WC-MHGD) for both deterministic and stochastic settings with finite-time Pareto-stationarity convergence rate guarantees, which not only implies low oracle complexity but also induces systematic Pareto front exploration. We further conduct extensive experiments to confirm our theoretical results.

Humans possess a remarkable ability to navigate complex environments by intuitively interpreting visual scenes at a semantic level - effortlessly distinguishing between walkable paths, obstacles, and hazardous areas while adapting to diverse terrain conditions (Dwivedi et al. 2024). This natural ability to understand both the semantic meaning and traversability of environmental elements has inspired the development of visual semantic navigation systems for autonomous robots. Through semantic segmentation of the environment, robots can identify traversable spaces and obstacles, moving closer to achieving human-like navigation capabilities in challenging real-world applications. A motivating scenario is shown in Figure 1. Visual semantic navigation is especially crucial in field robotics applications.

The paper addresses the Vehicle Relocation Problem in free-floating car-sharing services by presenting a solution focused on strategies for repositioning vehicles and transferring personnel with the use of scooters. Our method begins by dividing the service area into zones that group regions with similar temporal patterns of vehicle presence and service demand, allowing the application of discrete optimization methods. In the next stage, we propose a fast ranking-based algorithm that makes its decisions on the basis of the number of cars available in each zone, the projected probability density of demand, and estimated trip durations. The experiments were carried out on the basis of real-world data originating from a major car-sharing service operator in Poland. The results of this algorithm are evaluated against scenarios without optimization that constitute a baseline and compared with the results of an exact algorithm to solve the Mixed Integer Programming (MIP) model. As performance metrics, the total travel time was used. Under identical conditions (number of vehicles, staff, and demand distribution), the average improvements with respect to the baseline of our algorithm and MIP solver were equal to 8.44\% and 19.6\% correspondingly. However, it should be noted that the MIP model also mimicked decisions on trip selection, which are excluded by current services business rules. The analysis of results suggests that, depending on the size of the workforce, the application of the proposed solution allows for improving performance metrics by roughly 3%-10%.

In computational pathology, the gigapixel scale of Whole-Slide Images (WSIs) necessitates their division into thousands of smaller patches. Analyzing these high-dimensional patch embeddings is computationally expensive and risks diluting key diagnostic signals with many uninformative patches. Existing patch selection methods often rely on random sampling or simple clustering heuristics and typically fail to explicitly manage the crucial trade-off between the number of selected patches and the accuracy of the resulting slide representation. To address this gap, we propose EvoPS (Evolutionary Patch Selection), a novel framework that formulates patch selection as a multi-objective optimization problem and leverages an evolutionary search to simultaneously minimize the number of selected patch embeddings and maximize the performance of a downstream similarity search task, generating a Pareto front of optimal trade-off solutions. We validated our framework across four major cancer cohorts from The Cancer Genome Atlas (TCGA) using five pretrained deep learning models to generate patch embeddings, including both supervised CNNs and large self-supervised foundation models. The results demonstrate that EvoPS can reduce the required number of training patch embeddings by over 90% while consistently maintaining or even improving the final classification F1-score compared to a baseline that uses all available patches' embeddings selected through a standard extraction pipeline. The EvoPS framework provides a robust and principled method for creating efficient, accurate, and interpretable WSI representations, empowering users to select an optimal balance between computational cost and diagnostic performance.

This paper addresses the problem of dual-technology scheduling in hybrid Internet of Things (IoT) networks that integrate Optical Wireless Communication (OWC) alongside Radio Frequency (RF). We begin by formulating a Mixed-Integer Nonlinear Programming (MINLP) model that jointly considers throughput maximization and delay minimization between access points and IoT nodes under energy and link availability constraints. However, given the intractability of solving such NP-hard problems at scale and the impractical assumption of full channel observability, we propose the Dual-Graph Embedding with Transformer (DGET) framework, a supervised multi-task learning architecture combining a two-stage Graph Neural Networks (GNNs) with a Transformer-based encoder. The first stage employs a transductive GNN that encodes the known graph topology and initial node and link states (e.g., energy levels, available links, and queued transmissions). The second stage introduces an inductive GNN for temporal refinement, which learns to generalize these embeddings to the evolved states of the same network, capturing changes in energy and queue dynamics over time, by aligning them with ground-truth scheduling decisions through a consistency loss. These enriched embeddings are then processed by a classifier for the communication links with a Transformer encoder that captures cross-link dependencies through multi-head self-attention via classification loss. A further post-processing step refines these predictions using a top-2 feasibility check to further ensure valid link allocations. Simulation results show that hybrid RF-OWC networks outperform standalone RF systems by handling higher traffic loads more efficiently and reducing the Age of Information (AoI) by up to 20%, all while maintaining comparable energy consumption. The proposed DGET framework, compared to traditional optimization-based methods, achieves near-optimal scheduling with over 90% classification accuracy, reduces computational complexity, and demonstrates higher robustness under partial channel observability.

The Schrödinger Bridge provides a principled framework for modeling stochastic processes between distributions; however, existing methods are limited by energy-conservation assumptions, which constrains the bridge's shape preventing it from model varying-energy phenomena. To overcome this, we introduce the non-conservative generalized Schrödinger bridge (NCGSB), a novel, energy-varying reformulation based on contact Hamiltonian mechanics. By allowing energy to change over time, the NCGSB provides a broader class of real-world stochastic processes, capturing richer and more faithful intermediate dynamics. By parameterizing the Wasserstein manifold, we lift the bridge problem to a tractable geodesic computation in a finite-dimensional space. Unlike computationally expensive iterative solutions, our contact Wasserstein geodesic (CWG) is naturally implemented via a ResNet architecture and relies on a non-iterative solver with near-linear complexity. Furthermore, CWG supports guided generation by modulating a task-specific distance metric. We validate our framework on tasks including manifold navigation, molecular dynamics predictions, and image generation, demonstrating its practical benefits and versatility.