Vehicle-to-anything connectivity, especially for autonomous vehicles, promises to increase passenger comfort and safety of road traffic, for example, by sharing perception and driving intention. Cooperative maneuver planning uses connectivity to enhance traffic efficiency, which has, so far, been mainly considered for automated intersection management. In this article, we present a novel cooperative maneuver planning approach that is generalized to various situations found in urban traffic. Our framework handles challenging mixed traffic, that is, traffic comprising both cooperative connected vehicles and other vehicles at any distribution. Our solution is based on an optimization approach accompanied by an efficient heuristic method for high-load scenarios. We extensively evaluate the proposed planer in a distinctly realistic simulation framework and show significant efficiency gains already at a cooperation rate of 40%. Traffic throughput increases, while the average waiting time and the number of stopped vehicles are reduced, without impacting traffic safety.

Designing regulatory DNA sequences that achieve precise cell-type-specific gene expression is crucial for advancements in synthetic biology, gene therapy and precision medicine. Although transformer-based language models (LMs) can effectively capture patterns in regulatory DNA, their generative approaches often struggle to produce novel sequences with reliable cell-specific activity. Here, we introduce Ctrl-DNA, a novel constrained reinforcement learning (RL) framework tailored for designing regulatory DNA sequences with controllable cell-type specificity. By formulating regulatory sequence design as a biologically informed constrained optimization problem, we apply RL to autoregressive genomic LMs, enabling the models to iteratively refine sequences that maximize regulatory activity in targeted cell types while constraining off-target effects. Our evaluation on human promoters and enhancers demonstrates that Ctrl-DNA consistently outperforms existing generative and RL-based approaches, generating high-fitness regulatory sequences and achieving state-of-the-art cell-type specificity. Moreover, Ctrl-DNA-generated sequences capture key cell-type-specific transcription factor binding sites (TFBS), short DNA motifs recognized by regulatory proteins that control gene expression, demonstrating the biological plausibility of the generated sequences.

Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained bilevel problems, the constrained setting remains relatively underexplored. We present first-order linearly constrained optimization methods with finite-time hypergradient stationarity guarantees. For linear equality constraints, we attain \epsilon -stationarity in \widetilde{O}(\epsilon {-2}) gradient oracle calls, which is nearly-optimal. Finally, we obtain for the linear inequality setting dimension-free rates of \widetilde{O}({\delta {-1} \epsilon {-4}}) oracle complexity under the additional assumption of oracle access to the optimal dual variable.

This paper investigates simple bilevel optimization problems where we minimize a convex upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic convergence, have slow sublinear rates, or require strong assumptions. To address these challenges, we propose a penalization framework that delineates the relationship between approximate solutions of the original problem and its reformulated counterparts. Specifically, when both upper- and lower-level objectives are composite convex functions, under an \alpha -Hölderian error bound condition and certain mild assumptions, our algorithm attains an (\epsilon,\epsilon {\beta}) -optimal solution of the original problem for any \beta 0 within \mathcal{O}\left(\sqrt{{1}/{\epsilon {\max\\{\alpha,\beta\\}}}}\right) iterations. The result can be improved further if the smooth part of the upper-level objective is strongly convex.

We develop a theoretically-grounded learning method for the Generalized Linear Programming Value Function (GVF), which models the optimal value of a linear programming (LP) problem as its objective and constraint bounds vary. This function plays a fundamental role in algorithmic techniques for large-scale optimization, particularly in decomposition for two-stage mixed-integer linear programs (MILPs). This paper establishes a structural characterization of the GVF that enables it to be modeled as a particular neural network architecture, which we then use to learn the GVF in a way that benefits from three notable properties. First, our method produces a true under-approximation of the value function with respect to the constraint bounds. Second, the model is input-convex in the constraint bounds, which not only matches the structure of the GVF but also enables the trained model to be efficiently optimized over using LP.

This paper proposes Mutual Information Regularized Assignment (MIRA), a pseudo-labeling algorithm for unsupervised representation learning inspired by information maximization. We formulate online pseudo-labeling as an optimization problem to find pseudo-labels that maximize the mutual information between the label and data while being close to a given model probability. We derive a fixed-point iteration method and prove its convergence to the optimal solution. In contrast to baselines, MIRA combined with pseudo-label prediction enables a simple yet effective clustering-based representation learning without incorporating extra training techniques or artificial constraints such as sampling strategy, equipartition constraints, etc. With relatively small training epochs, representation learned by MIRA achieves state-of-the-art performance on various downstream tasks, including the linear/ {\it k} -NN evaluation and transfer learning.

We propose a new framework for formulating optimal transport distances between Markov chains. Previously known formulations studied couplings between the entire joint distribution induced by the chains, and derived solutions via a reduction to dynamic programming (DP) in an appropriately defined Markov decision process. This formulation has, however, not led to particularly efficient algorithms so far, since computing the associated DP operators requires fully solving a static optimal transport problem, and these operators need to be applied numerous times during the overall optimization process. In this work, we develop an alternative perspective by considering couplings between a flattened'' version of the joint distributions that we call discounted occupancy couplings, and show that calculating optimal transport distances in the full space of joint distributions can be equivalently formulated as solving a linear program (LP) in this reduced space. This LP formulation formulation allows us to port several algorithmic ideas from other areas of optimal transport theory.

Local Bayesian optimization is a promising practical approach to solve the high dimensional black-box function optimization problem. Among them is the approximated gradient class of methods, which implements a strategy similar to gradient descent. These methods have achieved good experimental results and theoretical guarantees. However, given the distributional properties of the Gaussian processes applied on these methods, there may be potential to further exploit the information of the Gaussian processes to facilitate the BO search. In this work, we develop the relationship between the steps of the gradient descent method and one that minimizes the Upper Confidence Bound (UCB), and show that the latter can be a better strategy than direct gradient descent when a Gaussian process is applied as a surrogate.

The Area Under the ROC Curve (AUC) is a well-known metric for evaluating instance-level long-tail learning problems. In the past two decades, many AUC optimization methods have been proposed to improve model performance under long-tail distributions. In this paper, we explore AUC optimization methods in the context of pixel-level long-tail semantic segmentation, a much more complicated scenario. This task introduces two major challenges for AUC optimization techniques. On one hand, AUC optimization in a pixel-level task involves complex coupling across loss terms, with structured inner-image and pairwise inter-image dependencies, complicating theoretical analysis. On the other hand, we find that mini-batch estimation of AUC loss in this case requires a larger batch size, resulting in an unaffordable space complexity.

Radiation therapy, treating over half of all cancer patients, involves using specialized machines to direct high-energy beams at tumors, aiming to damage cancer cells while minimizing harm to nearby healthy tissues. Customizing the shape and intensity of radiation beams for each patient leads to solving large-scale constrained optimization problems that need to be solved within tight clinical time-frame. At the core of these challenges is a large matrix that is commonly sparsified for computational efficiency by neglecting small elements. Such a crude approximation can degrade the quality of treatment, potentially causing unnecessary radiation exposure to healthy tissues--this may lead to significant radiation-induced side effects--or delivering inadequate radiation to the tumor, which is crucial for effective tumor treatment. In this work, we demonstrate, for the first time, that randomized sketch tools can effectively sparsify this matrix without sacrificing treatment quality.