Prompt-based offline methods are commonly used to optimize large language model (LLM) responses, but evaluating these responses is computationally intensive and often fails to accommodate diverse response styles. This study introduces a novel online evaluation framework that employs a multi-agent conversational bandit model to select optimal responses while aligning with user preferences dynamically. To tackle challenges such as high-dimensional features, large response sets, adaptive conversational needs, and multi-device access, we propose MACO, Multi-Agent Conversational Online Learning, which comprises two key components: (1) MACO-A: Executed by local agents, it employs an online elimination mechanism to filter out low-quality responses. (2) MACO-S: Executed by the cloud server, it adaptively adjusts selection strategies based on aggregated preference data. An adaptive preference mechanism triggers asynchronous conversations to enhance alignment efficiency. Theoretical analysis demonstrates that MACO achieves near-optimal regret bounds, matching state-of-the-art performance in various degenerate cases. Extensive experiments utilizing Google and OpenAI text embedding models on the real-world datasets with different response styles, combined with Llama and GPT-4o, show that MACO consistently outperforms baseline methods by at least 8.29% across varying response set sizes and numbers of agents.

Combinatorial multi-armed bandit (CMAB) is a fundamental online learning framework that can optimize cumulative rewards in networked systems under uncertainty. Real-world applications like content delivery and channel allocation often feature binary base arm rewards and nonlinear total reward functions. This paper introduces combinatorial logistic bandits (CLogB), a contextual CMAB framework with the base arm reward modeled as a nonlinear logistic function of the context, and the feedback is governed by a general arm-triggering process. We study CLogB with smooth reward functions, covering applications such as online content delivery, online multi-LLM selection, and dynamic channel allocation. Our first algorithm, CLogUCB, uses a variance-agnostic exploration bonus and achieves a regret bound of Õ(d√κKT), where d is the feature dimension, κ reflects logistic model nonlinearity,Kis the maximum number of triggered arms, and Õ ignores logarithmic factors. This improves on prior results by Õ (√κ). We further propose VA-CLogUCB, a variance-adaptive enhancement achieving regret bounds of Õ(d√KT) under standard smoothness conditions and Õ (d√T) under stronger variance conditions, removing dependence on K. For time-invariant feature maps, we enhance computational efficiency by avoiding nonconvex optimization while maintaining Õ(d√T) regret. Experiments on synthetic and real-world datasets validate the superior performance of our algorithms, demonstrating their effectiveness and scalability for real-world networked systems.

We study a hinted heterogeneous multi-agent multi-armed bandits problem (HMA2B), where agents can query low-cost observations (hints) in addition to pulling arms. In this framework, each of the M agents has a unique reward distribution over K arms, and in T rounds, they can observe the reward of the arm they pull only if no other agent pulls that arm. The goal is to maximize the total utility by querying the minimal necessary hints without pulling arms, achieving time-independent regret. We study HMA2B in both centralized and decentralized setups. Our main centralized algorithm, GP-HCLA, which is an extension of HCLA, uses a central decision-maker for arm-pulling and hint queries, achieving O(M^4 K) regret with O(M K log T) adaptive hints. In decentralized setups, we propose two algorithms, HD-ETC and EBHD-ETC, that allow agents to choose actions independently through collision-based communication and query hints uniformly until stopping, yielding O(M^3 K^2) regret with O(M^3 K log T) hints, where the former requires knowledge of the minimum gap and the latter does not. Finally, we establish lower bounds to prove the optimality of our results and verify them through numerical simulations.

Best arm identification (BAI) is a key problem in stochastic multi-armed bandits, where K arms each has an associated reward distribution, and the objective is to minimize the number of queries needed to identify the best arm with high confidence. In this paper, we explore BAI using quantum oracles. For the case where each query probes only one arm (m=1), we devise a quantum algorithm with a query complexity upper bound of O((K/Delta)log(1/delta)), where delta is the confidence parameter and Delta is the reward gap between best and second best arms. This improves on the classical bound by a factor of 1/Delta. For the general case where a single query can probe m arms (1

This paper investigates stochastic multi-armed bandit algorithms that are robust to adversarial attacks, where an attacker can first observe the learner's action and *then* alter their reward observation. We study two cases of this model, with or without the knowledge of an attack budget $C$, defined as an upper bound of the summation of the difference between the actual and altered rewards. For both cases, we devise two types of algorithms with regret bounds having additive or multiplicative $C$ dependence terms. For the known attack budget case, we prove our algorithms achieve the regret bound of ${O}((K/\Delta)\log T + KC)$ and $\tilde{O}(\sqrt{KTC})$ for the additive and multiplicative $C$ terms, respectively, where $K$ is the number of arms, $T$ is the time horizon, $\Delta$ is the gap between the expected rewards of the optimal arm and the second-best arm, and $\tilde{O}$ hides the logarithmic factors. For the unknown case, we prove our algorithms achieve the regret bound of $\tilde{O}(\sqrt{KT} + KC^2)$ and $\tilde{O}(KC\sqrt{T})$ for the additive and multiplicative $C$ terms, respectively. In addition to these upper bound results, we provide several lower bounds showing the tightness of our bounds and the optimality of our algorithms. These results delineate an intrinsic separation between the bandits with attacks and corruption models.

This paper investigates the fusion of absolute (reward) and relative (dueling) feedback in stochastic bandits, where both feedback types are gathered in each decision round. We derive a regret lower bound, demonstrating that an efficient algorithm may incur only the smaller among the reward and dueling-based regret for each individual arm. We propose two fusion approaches: (1) a simple elimination fusion algorithm that leverages both feedback types to explore all arms and unifies collected information by sharing a common candidate arm set, and (2) a decomposition fusion algorithm that selects the more effective feedback to explore the corresponding arms and randomly assigns one feedback type for exploration and the other for exploitation in each round. The elimination fusion experiences a suboptimal multiplicative term of the number of arms in regret due to the intrinsic suboptimality of dueling elimination. In contrast, the decomposition fusion achieves regret matching the lower bound up to a constant under a common assumption. Extensive experiments confirm the efficacy of our algorithms and theoretical results.

In this work, we study the federated multi-armed bandit (FMAB) problem, where a set of distributed agents collaboratively aim to minimize cumulative regret while interacting with a shared set of arms. Unlike traditional centralized bandit models, agents in FMAB settings are connected via a communication graph and cannot share data freely due to bandwidth limitations or privacy constraints. This raises a fundamental challenge: how to achieve optimal learning performance under stringent communication budgets. We propose a novel communication-efficient algorithm that decouples the learning process into two phases: one for eliminating suboptimal arms through early and frequent communication of key decisions, and another for refining global estimates using buffered, quantized, and differentially transmitted statistics. By carefully balancing the communication frequency and precision of shared information, our algorithm achieves the optimal individual regret bound $O(N^{-1}\log T)$ while significantly reducing the total number of communication rounds and transmitted bits. Theoretically, we derive tight upper bounds on both individual cumulative regret and group regret, and prove that our method asymptotically matches the lower bound of regret in federated settings. Experimental results on synthetic data validate the effectiveness of the proposed approach in various graph topologies and under heterogeneous feedback.

In this paper, we focus on the research of federated multi-armed bandit (FMAB) problems where agents can only communicate with their neighbors. All agents aim to solve a common multi-armed bandit (MAB) problem to minimize individual regrets, while group regret can also be minimized. In a federated bandit problem, an agent fails to estimate the global reward means of arms by only using local observations, and hence, the bandit learning algorithm usually adopts a consensus estimation strategy to address the heterogeneity. However, up to now, the existing algorithms with fully distributed communication graphs only achieved a suboptimal result for the problem. To address that, a fully distributed online consensus estimation algorithm (\texttt{CES}) is proposed to estimate the global mean without bias. Integrating this consensus estimator into a distributed successive elimination bandit algorithm framework yields our federated bandit algorithm. Our algorithm significantly improves both individual and group regrets over previous approaches, and we provide an in-depth analysis of the lower bound for this problem.

We introduce a novel framework of combinatorial multi-armed bandits (CMAB) with multivariant and probabilistically triggering arms (CMAB-MT), where the outcome of each arm is a $d$-dimensional multivariant random variable and the feedback follows a general arm triggering process. Compared with existing CMAB works, CMAB-MT not only enhances the modeling power but also allows improved results by leveraging distinct statistical properties for multivariant random variables. For CMAB-MT, we propose a general 1-norm multivariant and triggering probability-modulated smoothness condition, and an optimistic CUCB-MT algorithm built upon this condition. Our framework can include many important problems as applications, such as episodic reinforcement learning (RL) and probabilistic maximum coverage for goods distribution, all of which meet the above smoothness condition and achieve matching or improved regret bounds compared to existing works. Through our new framework, we build the first connection between the episodic RL and CMAB literature, by offering a new angle to solve the episodic RL through the lens of CMAB, which may encourage more interactions between these two important directions.

Reliable transmission of fragile quantum information requires one to efficiently select and utilize high-fidelity links among multiple noisy quantum links. However, the fidelity, a quality metric of quantum links, is unknown a priori. Uniformly estimating the fidelity of all links can be expensive, especially in networks with numerous links. To address this challenge, we formulate the link selection and fidelity estimation problem as a best arm identification problem and propose an algorithm named LinkSelFiE. The algorithm efficiently identifies the optimal link from a set of quantum links and provides an accurate fidelity estimate of that link with low quantum resource consumption. LinkSelFiE estimates link fidelity based on the feedback of a vanilla network benchmarking subroutine, and adaptively eliminates inferior links throughout the whole fidelity estimation process. This elimination leverages a novel confidence interval derived in this paper for the estimates from the subroutine, which theoretically guarantees that LinkSelFiE outputs the optimal link correctly with high confidence. We also establish a provable upper bound of cost complexity for LinkSelFiE. Moreover, we perform extensive simulations under various scenarios to corroborate that LinkSelFiE outperforms other existing methods in terms of both identifying the optimal link and reducing quantum resource consumption.

Queueing models serve as important building blocks in many networking applications such as task scheduling in mobile edge computing nodes, traffic scheduling in networks, congestion control in Internet, etc. However, queueing theory often needs to make strong assumptions about the arrival process or service rewards at each queue. In addition, fairness in serving workload among all queues is of great importance in many applications. In this paper, we address how to optimize resource allocation among multiple queues with a fairness guarantee and without any a priori knowledge of these queues’ parameters. To characterize queues with unknown parameters and the fairness requirement, we formulate an online learning model with a varying and continuous action space, as well as a nonlinear utility objective. We design an online learning algorithm to tackle the problem. We prove that our algorithm has a regret upper bound of$O(\sqrt{T}\log T)$and our model has a regret lower bound of$\Omega (\sqrt{T})$, where$T$stands for the number of decision rounds. The asymptotic closeness of upper and lower bounds guarantees their near tightness and our algorithm's near optimality. We discuss our model's real-world applications in mobile edge computing, wireless networks, and crowdsourcing, and conduct simulations to validate our algorithm's effectiveness.

This paper studies a cooperative multi-agent multi-armed stochastic bandit problem where agents operate asynchronously – agent pull times and rates are unknown, irregular, and heterogeneous – and face the same instance of a K-armed bandit problem. Agents can share reward information to speed up the learning process at additional communication costs. We propose ODC, an on-demand communication protocol that tailors the communication of each pair of agents based on their empirical pull times. ODC is efficient when the pull times of agents are highly heterogeneous, and its communication complexity depends on the empirical pull times of agents. ODC is a generic protocol that can be integrated into most cooperative bandit algorithms without degrading their performance. We then incorporate ODC into the natural extensions of UCB and AAE algorithms and propose two communication-efficient cooperative algorithms. Our analysis shows that both algorithms are near-optimal in regret.

We study the multi-fidelity multi-armed bandit ($\texttt{MF-MAB}$), an extension of the canonical multi-armed bandit (MAB) problem. $\texttt{MF-MAB}$ allows each arm to be pulled with different costs (fidelities) and observation accuracy. We study both the best arm identification with fixed confidence ($\texttt{BAI}$) and the regret minimization objectives. For $\texttt{BAI}$, we present (a) a cost complexity lower bound, (b) an algorithmic framework with two alternative fidelity selection procedures, and (c) both procedures' cost complexity upper bounds. From both cost complexity bounds of $\texttt{MF-MAB}$, one can recover the standard sample complexity bounds of the classic (single-fidelity) MAB. For regret minimization of $\texttt{MF-MAB}$, we propose a new regret definition, prove its problem-independent regret lower bound $\Omega(K^{1/3}\Lambda^{2/3})$ and problem-dependent lower bound $\Omega(K\log \Lambda)$, where $K$ is the number of arms and $\Lambda$ is the decision budget in terms of cost, and devise an elimination-based algorithm whose worst-cost regret upper bound matches its corresponding lower bound up to some logarithmic terms and, whose problem-dependent bound matches its corresponding lower bound in terms of $\Lambda$.

This paper studies a cooperative multi-agent bandit scenario in which the rewards observed by agents are heterogeneous—one agent’s meat can be another agent’s poison. Specifically, the total reward observed by each agent is the sum of two values: an arm-specific reward, capturing the intrinsic value of the arm, and a privately-known agent-specific reward, which captures the personal preference/limitations of the agent. This heterogeneity in total reward leads to different local optimal arms for agents but creates an opportunity for \textit{free exploration} in a cooperative setting—an agent can freely explore its local optimal arm with no regret and share this free observation with some other agents who would suffer regrets if they pull this arm since the arm is not optimal for them. We first characterize a regret lower bound that captures free exploration, i.e., arms that can be freely explored have no contribution to the regret lower bound. Then, we present a cooperative bandit algorithm that takes advantage of free exploration and achieves a near-optimal regret upper bound which tightly matches the regret lower bound up to a constant factor. Lastly, we run numerical simulations to compare our algorithm with various baselines without free exploration.

We generalize the multiple-play multi-armed bandits (MP-MAB) problem with a shareable arms setting, in which several plays can share the same arm. Furthermore, each shareable arm has a finite reward capacity and a “per-load” reward distribution, both of which are unknown to the learner. The reward from a shareable arm is load-dependent, which is the “per-load” reward multiplying either the number of plays pulling the arm, or its reward capacity when the number of plays exceeds the capacity limit. When the “per-load” reward follows a Gaussian distribution, we prove a sample complexity lower bound of learning the capacity from load-dependent rewards and also a regret lower bound of this new MP-MAB problem. We devise a capacity estimator whose sample complexity upper bound matches the lower bound in terms of reward means and capacities. We also propose an online learning algorithm to address the problem and prove its regret upper bound. This regret upper bound’s first term is the same as regret lower bound’s, and its second and third terms also evidently correspond to lower bound’s. Extensive experiments validate our algorithm’s performance and also its gain in 5G & 4G base station selection.

Multi-player multi-armed bandits (MMAB) study how decentralized players cooperatively play the same multi-armed bandit so as to maximize their total cumulative rewards. Existing MMAB models mostly assume when more than one player pulls the same arm, they either have a collision and obtain zero rewards or have no collision and gain independent rewards, both of which are usually too restrictive in practical scenarios. In this paper, we propose an MMAB with shareable resources as an extension of the collision and non-collision settings. Each shareable arm has finite shareable resources and a “per-load” reward random variable, both of which are unknown to players. The reward from a shareable arm is equal to the “per-load” reward multiplied by the minimum between the number of players pulling the arm and the arm’s maximal shareable resources. We consider two types of feedback: sharing demand information (SDI) and sharing demand awareness (SDA), each of which provides different signals of resource sharing. We design the DPE-SDI and SIC-SDA algorithms to address the shareable arm problem under these two cases of feedback respectively and prove that both algorithms have logarithmic regrets that are tight in the number of rounds. We conduct simulations to validate both algorithms’ performance and show their utilities in wireless networking and edge computing.