Can Jin, Rui Wu, Tong Che, Qixin Zhang, Hongwu Peng, Jiahui Zhao, Zhenting Wang, Wenqi Wei, Ligong Han, Zhao Zhang, Yuan Cao, Ruixiang Tang, Dimitris N. Metaxas. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Coordinating multiple agents to collaboratively maximize submodular functions in unpredictable environments is a critical task with numerous applications in machine learning, robot planning and control. The existing approaches, such as the OSG algorithm, are often hindered by their poor approximation guarantees and the rigid requirement for a fully connected communication graph. To address these challenges, we firstly present a $\textbf{MA-OSMA}$ algorithm, which employs the multi-linear extension to transfer the discrete submodular maximization problem into a continuous optimization, thereby allowing us to reduce the strict dependence on a complete graph through consensus techniques. Moreover, $\textbf{MA-OSMA}$ leverages a novel surrogate gradient to avoid sub-optimal stationary points. To eliminate the computationally intensive projection operations in $\textbf{MA-OSMA}$, we also introduce a projection-free $\textbf{MA-OSEA}$ algorithm, which effectively utilizes the KL divergence by mixing a uniform distribution. Theoretically, we confirm that both algorithms achieve a regret bound of $\widetilde{O}(\sqrt{\frac{C_{T}T}{1-\beta}})$ against a  $(\frac{1-e^{-c}}{c})$-approximation to the best comparator in hindsight, where $C_{T}$ is the deviation of maximizer sequence, $\beta$ is the spectral gap of the network and $c$ is the joint curvature of submodular objectives. This result significantly improves the $(\frac{1}{1+c})$-approximation provided by the state-of-the-art OSG algorithm. Finally, we demonstrate the effectiveness of our proposed algorithms through simulation-based multi-target tracking.

Identifying the most representative subset for a close-to-submodular objective while satisfying the predefined partition constraint is a fundamental task with numerous applications in machine learning. However, the existing distorted local-search methods are often hindered by their prohibitive query complexities and the rigid requirement for prior knowledge of difficult-to-obtain structural parameters. To overcome these limitations, we introduce a novel algorithm titled **Multinoulli-SCG**, which not only is parameter-free, but also can achieve the same approximation guarantees as the distorted local-search methods with significantly fewer function evaluations. The core of our **Multinoulli-SCG** algorithm is an innovative continuous-relaxation framework named Multinoulli Extension(***ME***), which can effectively convert the discrete subset selection problem subject to partition constraints into a solvable continuous maximization focused on learning the optimal multinoulli priors across the considered partition. In sharp contrast with the well-established multi-linear extension for submodular subset selection, a notable advantage of our proposed ***ME*** is its intrinsic capacity to provide a lossless rounding scheme for any set function. Finally, we validate the practical efficacy of our proposed algorithms by applying them to video summarization, bayesian A-optimal design and coverage maximization.

Recently, zeroth-order (ZO) optimization plays an essential role in scenarios where gradient information is inaccessible or unaffordable, such as black-box systems and resource-constrained environments. While existing adaptive methods such as ZO-AdaMM have shown promise, they are fundamentally limited by their underutilization of moment information during optimization, usually resulting in underperforming convergence. To overcome these limitations, this paper introduces *Refined Adaptive Zeroth-Order Optimization* (R-AdaZO). Specifically, we first show the untapped variance reduction effect of first moment estimate on ZO gradient estimation, which improves the accuracy and stability of ZO updates. We then refine the second moment estimate based on these variance-reduced gradient estimates to better capture the geometry of the optimization landscape, enabling a more effective scaling of ZO updates. We present rigorous theoretical analysis to show **_(a)_** *the first analysis* to the variance reduction of first moment estimate in ZO optimization, **_(b)_** *the improved second moment estimates* with a more accurate approximation of its variance-free ideal, **_(c)_** *the first variance-aware convergence framework* for adaptive ZO methods, which may be of independent interest, and **_(d)_** *the faster convergence* of R-AdaZO than existing baselines like ZO-AdaMM. Our extensive experiments, including synthetic problems, black-box adversarial attack, and memory-efficient fine-tuning of large language models (LLMs), further verify the superior convergence of R-AdaZO, indicating that R-AdaZO offers an improved solution for real-world ZO optimization challenges.

Nonparametric contextual bandit is an important model of sequential decision making problems. Under $\alpha$-Tsybakov margin condition, existing research has established a regret bound of $\tilde{O}\left(T^{1-\frac{\alpha+1}{d+2}}\right)$ for bounded supports. However, the optimal regret with unbounded contexts has not been analyzed. The challenge of solving contextual bandit problems with unbounded support is to achieve both exploration-exploitation tradeoff and bias-variance tradeoff simultaneously. In this paper, we solve the nonparametric contextual bandit problem with unbounded contexts. We propose two nearest neighbor methods combined with UCB exploration. The first method uses a fixed $k$. Our analysis shows that this method achieves minimax optimal regret under a weak margin condition and relatively light-tailed context distributions. The second method uses adaptive $k$. By a proper data-driven selection of $k$, this method achieves an expected regret of $\tilde{O}\left(T^{1-\frac{(\alpha+1)\beta}{\alpha+(d+2)\beta}}+T^{1-\beta}\right)$, in which $\beta$ is a parameter describing the tail strength. This bound matches the minimax lower bound up to logarithm factors, indicating that the second method is approximately optimal.

In this paper, we present two effective policy learning algorithms for multi-agent online coordination(MA-OC) problem. The first one, **MA-SPL**, not only can achieve the optimal $(1-\frac{c}{e})$-approximation guarantee for the MA-OC problem with submodular objectives but also can handle the unexplored $\alpha$-weakly DR-submodular and $(\gamma,\beta)$-weakly submodular scenarios, where $c$ is the curvature of the investigated submodular functions, $\alpha$ denotes the diminishing-return(DR) ratio and the tuple$(\gamma,\beta)$ represents the submodularity ratios. Subsequently, in order to reduce the reliance on the unknown parameters $\alpha,\gamma,\beta$ inherent in the **MA-SPL** algorithm, we then introduce the second online algorithm named **MA-MPL**. This **MA-MPL** algorithm is entirely *parameter-free* and simultaneously can maintain the same approximation ratio as the first **MA-SPL** algorithm. The core of our **MA-SPL** and **MA-MPL** algorithms is a novel continuous-relaxation technique term as policy-based continuous extension. Compared with the well-established multi-linear extension, a notable advantage of this new policy-based continuous extension is its ability to provide a lossless rounding scheme for any set function, thereby enabling us to tackle the challenging weakly submodular objective functions. Finally, extensive simulations are conducted to demonstrate the effectiveness of our proposed algorithms.

Optimizing the assortment of products to display to customers is key to increasing revenue for both offline and online retailers. To trade-off between exploring customers’ preferences and exploiting customers’ choices learned from data, in this article, by adopting the Multi-Nomial Logit (MNL) choice model to capture customers’ choices over products, we study the problem of optimizing assortments over a planning horizon$T$for maximizing the profit of the retailer. To make the problem setting more practical, we consider both the inventory constraint and the limited switches constraint, where the retailer is forced to stop the sales when the resources are depleted and is forbidden to switch the assortment shown to customers too many times. Such a setting suits the case when an online retailer wants to optimize the assortment selection for a population of customers dynamically. We develop an efficient UCB-like algorithm to optimize the assortments while learning customers’ choices from data. We prove that our algorithm can achieve a sub-linear regret bound$\tilde{O}(T^{\max \lbrace 2/3-\alpha /3,1/2\rbrace })$if$O(T^\alpha)$switches are allowed. Extensive numerical experiments show that our algorithm outperforms baselines, and the gap between our algorithm's performance and the theoretical upper bound is small.

In this paper, we revisit the online non-monotone continuous DR-submodular maximization problem over a down-closed convex set, which finds wide real-world applications in the domain of machine learning, economics, and operations research. At first, we present the Meta-MFW algorithm achieving a $1/e$-regret of $O(\sqrt{T})$ at the cost of $T^{3/2}$ stochastic gradient evaluations per round. As far as we know, Meta-MFW is the first algorithm to obtain $1/e$-regret of $O(\sqrt{T})$ for the online non-monotone continuous DR-submodular maximization problem over a down-closed convex set. Furthermore, in sharp contrast with ODC algorithm (Thang $&$ Srivastav, 2021), Meta-MFW relies on the simple online linear oracle without discretization, lifting, or rounding operations. Considering the practical restrictions, we then propose the Mono-MFW algorithm, which reduces the per-function stochastic gradient evaluations from $T^{3/2}$ to 1 and achieves a $1/e$-regret bound of $O(T^{4/5})$. Next, we extend Mono-MFW to the bandit setting and propose the Bandit-MFW algorithm which attains a $1/e$-regret bound of $O(T^{8/9})$. To the best of our knowledge, Mono-MFW and Bandit-MFW are the first sublinear-regret algorithms to explore the one-shot and bandit setting for online non-monotone continuous DR-submodular maximization problem over a down-closed convex set, respectively. Finally, we conduct numerical experiments on both synthetic and real-world datasets to verify the effectiveness of our methods.

Maximizing a monotone submodular function is a fundamental task in data mining, machine learning, economics, and statistics. In this paper, we present two communication-efficient decentralized online algorithms for the monotone continuous DR-submodular maximization problem, both of which reduce the number of per-function gradient evaluations and per-round communication complexity from T3/2 to 1. The first one, One-shot Decentralized Meta-Frank-Wolfe~(Mono-DMFW), achieves a (1-1/e)-regret bound of O(T4/5). As far as we know, this is the first one-shot and projection-free decentralized online algorithm for monotone continuous DR-submodular maximization. Next, inspired by the non-oblivious boosting function[29], we propose the Decentralized Online Boosting Gradient Ascent (DOBGA) algorithm, which attains a (1-1/e)-regret of O(√T). To the best of our knowledge, this is the first result to obtain the optimal O(√T) against a (1-1/e)-approximation with only one gradient inquiry for each local objective function per step. Finally, various experimental results confirm the effectiveness of the proposed methods.

In this paper, we investigate the online allocation problem of maximizing the overall revenue subject to both lower and upper bound constraints. Compared to the extensively studied online problems with only resource upper bounds, the two-sided constraints affect the prospects of resource consumption more severely. As a result, only limited violations of constraints or pessimistic competitive bounds could be guaranteed. To tackle the challenge, we define a measure of feasibility $\xi^*$ to evaluate the hardness of this problem, and estimate this measurement by an optimization routine with theoretical guarantees. We propose an online algorithm adopting a constructive framework, where we initialize a threshold price vector using the estimation, then dynamically update the price vector and use it for decision-making at each step. It can be shown that the proposed algorithm is $\big(1-O(\frac{\varepsilon}{\xi^*-\varepsilon})\big)$ or $\big(1-O(\frac{\varepsilon}{\xi^*-\sqrt{\varepsilon}})\big)$ competitive with high probability for $\xi^*$ known or unknown respectively. To the best of our knowledge, this is the first result establishing a nearly optimal competitive algorithm for solving two-sided constrained online allocation problems with a high probability of feasibility.

In this paper, we revisit Stochastic Continuous Submodular Maximization in both offline and online settings, which can benefit wide applications in machine learning and operations research areas. We present a boosting framework covering gradient ascent and online gradient ascent. The fundamental ingredient of our methods is a novel non-oblivious function $F$ derived from a factor-revealing optimization problem, whose any stationary point provides a $(1-e^{-\gamma})$-approximation to the global maximum of the $\gamma$-weakly DR-submodular objective function $f\in C^{1,1}_L(\mathcal{X})$. Under the offline scenario, we propose a boosting gradient ascent method achieving $(1-e^{-\gamma}-\epsilon^{2})$-approximation after $O(1/\epsilon^2)$ iterations, which improves the $(\frac{\gamma^2}{1+\gamma^2})$ approximation ratio of the classical gradient ascent algorithm. In the online setting, for the first time we consider the adversarial delays for stochastic gradient feedback, under which we propose a boosting online gradient algorithm with the same non-oblivious function $F$. Meanwhile, we verify that this boosting online algorithm achieves a regret of $O(\sqrt{D})$ against a $(1-e^{-\gamma})$-approximation to the best feasible solution in hindsight, where $D$ is the sum of delays of gradient feedback. To the best of our knowledge, this is the first result to obtain $O(\sqrt{T})$ regret against a $(1-e^{-\gamma})$-approximation with $O(1)$ gradient inquiry at each time step, when no delay exists, i.e., $D=T$. Finally, numerical experiments demonstrate the effectiveness of our boosting methods.

The Laplacian representation recently gains increasing attention for reinforcement learning as it provides succinct and informative representation for states, by taking the eigenvectors of the Laplacian matrix of the state-transition graph as state embeddings. Such representation captures the geometry of the underlying state space and is beneficial to RL tasks such as option discovery and reward shaping. To approximate the Laplacian representation in large (or even continuous) state spaces, recent works propose to minimize a spectral graph drawing objective, which however has infinitely many global minimizers other than the eigenvectors. As a result, their learned Laplacian representation may differ from the ground truth. To solve this problem, we reformulate the graph drawing objective into a generalized form and derive a new learning objective, which is proved to have eigenvectors as its unique global minimizer. It enables learning high-quality Laplacian representations that faithfully approximate the ground truth. We validate this via comprehensive experiments on a set of gridworld and continuous control environments. Moreover, we show that our learned Laplacian representations lead to more exploratory options and better reward shaping.