arXiv subjects

John C. S. Lui

Publications and source records attributed to John C. S. Lui.

At least 55 records · Page 3Linked to original sources

arXiv2025

Online Clustering of Dueling Bandits

The contextual multi-armed bandit (MAB) is a widely used framework for problems requiring sequential decision-making under uncertainty, such as recommendation systems. In applications involving a large number of users, the performance of contextual MAB can be significantly improved by facilitating collaboration among multiple users. This has been achieved by the clustering of bandits (CB) methods, which adaptively group the users into different clusters and achieve collaboration by allowing the users in the same cluster to share data. However, classical CB algorithms typically rely on numerical reward feedback, which may not be practical in certain real-world applications. For instance, in recommendation systems, it is more realistic and reliable to solicit preference feedback between pairs of recommended items rather than absolute rewards. To address this limitation, we introduce the first "clustering of dueling bandit algorithms" to enable collaborative decision-making based on preference feedback. We propose two novel algorithms: (1) Clustering of Linear Dueling Bandits (COLDB) which models the user reward functions as linear functions of the context vectors, and (2) Clustering of Neural Dueling Bandits (CONDB) which uses a neural network to model complex, non-linear user reward functions. Both algorithms are supported by rigorous theoretical analyses, demonstrating that user collaboration leads to improved regret bounds. Extensive empirical evaluations on synthetic and real-world datasets further validate the effectiveness of our methods, establishing their potential in real-world applications involving multiple users with preference-based feedback.

cs.LG↗

arXiv2025

Large Language Model-Enhanced Multi-Armed Bandits

Large language models (LLMs) have been adopted to solve sequential decision-making tasks such as multi-armed bandits (MAB), in which an LLM is directly instructed to select the arms to pull in every iteration. However, this paradigm of direct arm selection using LLMs has been shown to be suboptimal in many MAB tasks. Therefore, we propose an alternative approach which combines the strengths of classical MAB and LLMs. Specifically, we adopt a classical MAB algorithm as the high-level framework and leverage the strong in-context learning capability of LLMs to perform the sub-task of reward prediction. Firstly, we incorporate the LLM-based reward predictor into the classical Thompson sampling (TS) algorithm and adopt a decaying schedule for the LLM temperature to ensure a transition from exploration to exploitation. Next, we incorporate the LLM-based reward predictor (with a temperature of 0) into a regression oracle-based MAB algorithm equipped with an explicit exploration mechanism. We also extend our TS-based algorithm to dueling bandits where only the preference feedback between pairs of arms is available, which requires non-trivial algorithmic modifications. We conduct empirical evaluations using both synthetic MAB tasks and experiments designed using real-world text datasets, in which the results show that our algorithms consistently outperform previous baseline methods based on direct arm selection. Interestingly, we also demonstrate that in challenging tasks where the arms lack semantic meanings that can be exploited by the LLM, our approach achieves considerably better performance than LLM-based direct arm selection.

cs.LG↗

arXiv2025

Demystifying Online Clustering of Bandits: Enhanced Exploration Under Stochastic and Smoothed Adversarial Contexts

The contextual multi-armed bandit (MAB) problem is crucial in sequential decision-making. A line of research, known as online clustering of bandits, extends contextual MAB by grouping similar users into clusters, utilizing shared features to improve learning efficiency. However, existing algorithms, which rely on the upper confidence bound (UCB) strategy, struggle to gather adequate statistical information to accurately identify unknown user clusters. As a result, their theoretical analyses require several strong assumptions about the "diversity" of contexts generated by the environment, leading to impractical settings, complicated analyses, and poor practical performance. Removing these assumptions has been a long-standing open problem in the clustering of bandits literature. In this paper, we provide two solutions to this open problem. First, following the i.i.d. context generation setting in existing studies, we propose two novel algorithms, UniCLUB and PhaseUniCLUB, which incorporate enhanced exploration mechanisms to accelerate cluster identification. Remarkably, our algorithms require substantially weaker assumptions while achieving regret bounds comparable to prior work. Second, inspired by the smoothed analysis framework, we propose a more practical setting that eliminates the requirement for i.i.d. context generation used in previous studies, thus enhancing the performance of existing algorithms for online clustering of bandits. Our technique can be applied to both graph-based and set-based clustering of bandits frameworks. Extensive evaluations on both synthetic and real-world datasets demonstrate that our proposed algorithms consistently outperform existing approaches.

cs.LG↗

arXiv2024

An Enhanced Levenberg--Marquardt Method via Gram Reduction

This paper studied the problem of solving the system of nonlinear equations ${\bf F}({\bf x})={\bf 0}$, where ${\bf F}:{\mathbb R}^{d}\to{\mathbb R}^d$. We propose Gram-Reduced Levenberg--Marquardt method which updates the Gram matrix ${\bf J}(\cdot)^\top{\bf J}(\cdot)$ in every $m$ iterations, where ${\bf J}(\cdot)$ is the Jacobian of ${\bf F}(\cdot)$. Our method has a global convergence guarantee without relying on any step of line-search or solving sub-problems. We prove our method takes at most $\mathcal{O}(m^2+m^{-0.5}ε^{-2.5})$ iterations to find an $ε$-stationary point of $\frac{1}{2}\|{\bf F}(\cdot)\|^2$, which leads to overall computation cost of $\mathcal{O}(d^3ε^{-1}+d^2ε^{-2})$ by taking $m=Θ(ε^{-1})$. Our results are strictly better than the cost of $\mathcal{O}(d^3ε^{-2})$ for existing Levenberg--Marquardt methods. We also show the proposed method enjoys local superlinear convergence rate under the non-degenerate assumption. We provide experiments on real-world applications in scientific computing and machine learning to validate the efficiency of the proposed methods.

math.OC↗

arXiv2024

cRVR: A Stackelberg Game Approach for Joint Privacy-Aware Video Requesting and Edge Caching

As users conveniently stream their favorite online videos, video request records are automatically stored by video content providers, which have a high chance of privacy leakage. Unfortunately, most existing privacy-enhancing approaches are not applicable for protecting user privacy in video requests, because they cannot be easily altered or distorted by users and must be visible for content providers to stream correct videos. To preserve request privacy in online video services, it is possible to request additional videos that are irrelevant to users' interests so that content providers cannot precisely infer users' interest information. However, a naive redundant requesting approach would significantly degrade the performance of edge caches and increase bandwidth overhead. In this paper, we are among the first to propose a Cache-Friendly Redundant Video Requesting (cRVR) algorithm for User Devices (UDs) and its corresponding caching algorithm for the Edge Cache (EC), which can effectively mitigate the problem of request privacy leakage with minimal impact on the EC's performance. To tackle the problem, we first develop a Stackelberg game to analyze the dedicated interaction between UDs and EC, and obtain their optimal strategies to maximize their respective utility. For UDs, the utility function is a combination of both video playback utility and privacy protection utility. We prove the existence and uniqueness of the equilibrium of the Stackelberg game. Extensive experiments are conducted with real traces to demonstrate that cRVR can effectively protect video request privacy by reducing up to 59.03\% of privacy disclosure compared to baseline algorithms. Meanwhile, the caching performance of EC is only slightly affected.

cs.NI↗

arXiv2024

Batch-Size Independent Regret Bounds for Combinatorial Semi-Bandits with Probabilistically Triggered Arms or Independent Arms

In this paper, we study the combinatorial semi-bandits (CMAB) and focus on reducing the dependency of the batch-size $K$ in the regret bound, where $K$ is the total number of arms that can be pulled or triggered in each round. First, for the setting of CMAB with probabilistically triggered arms (CMAB-T), we discover a novel (directional) triggering probability and variance modulated (TPVM) condition that can replace the previously-used smoothness condition for various applications, such as cascading bandits, online network exploration and online influence maximization. Under this new condition, we propose a BCUCB-T algorithm with variance-aware confidence intervals and conduct regret analysis which reduces the $O(K)$ factor to $O(\log K)$ or $O(\log^2 K)$ in the regret bound, significantly improving the regret bounds for the above applications. Second, for the setting of non-triggering CMAB with independent arms, we propose a SESCB algorithm which leverages on the non-triggering version of the TPVM condition and completely removes the dependency on $K$ in the leading regret. As a valuable by-product, the regret analysis used in this paper can improve several existing results by a factor of $O(\log K)$. Finally, experimental evaluations show our superior performance compared with benchmark algorithms in different applications.

cs.LG↗

arXiv2024

Contextual Combinatorial Bandits with Probabilistically Triggered Arms

We study contextual combinatorial bandits with probabilistically triggered arms (C$^2$MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C$^2$-UCB-T algorithm and propose a novel analysis that achieves an $\tilde{O}(d\sqrt{KT})$ regret bound, removing a potentially exponentially large factor $O(1/p_{\min})$, where $d$ is the dimension of contexts, $p_{\min}$ is the minimum positive probability that any arm can be triggered, and batch-size $K$ is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC$^2$-UCB and derive a regret bound $\tilde{O}(d\sqrt{T})$, which is independent of the batch-size $K$. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C$^2$MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets.

cs.LG↗

arXiv2024

Model-based RL as a Minimalist Approach to Horizon-Free and Second-Order Bounds

Learning a transition model via Maximum Likelihood Estimation (MLE) followed by planning inside the learned model is perhaps the most standard and simplest Model-based Reinforcement Learning (RL) framework. In this work, we show that such a simple Model-based RL scheme, when equipped with optimistic and pessimistic planning procedures, achieves strong regret and sample complexity bounds in online and offline RL settings. Particularly, we demonstrate that under the conditions where the trajectory-wise reward is normalized between zero and one and the transition is time-homogenous, it achieves nearly horizon-free and second-order bounds. Nearly horizon-free means that our bounds have no polynomial dependence on the horizon of the Markov Decision Process. A second-order bound is a type of instance-dependent bound that scales with respect to the variances of the returns of the policies which can be small when the system is nearly deterministic and (or) the optimal policy has small values. We highlight that our algorithms are simple, fairly standard, and indeed have been extensively studied in the RL literature: they learn a model via MLE, build a version space around the MLE solution, and perform optimistic or pessimistic planning depending on whether operating in the online or offline mode. These algorithms do not rely on additional specialized algorithmic designs such as learning variances and performing variance-weighted learning and thus can easily leverage non-linear function approximations. The simplicity of the algorithms also implies that our horizon-free and second-order regret analysis is actually standard and mainly follows the general framework of optimism/pessimism in the face of uncertainty.

cs.LG↗

arXiv2024

Quantum Algorithm for Online Exp-concave Optimization

We explore whether quantum advantages can be found for the zeroth-order feedback online exp-concave optimization problem, which is also known as bandit exp-concave optimization with multi-point feedback. We present quantum online quasi-Newton methods to tackle the problem and show that there exists quantum advantages for such problems. Our method approximates the Hessian by quantum estimated inexact gradient and can achieve $O(n\log T)$ regret with $O(1)$ queries at each round, where $n$ is the dimension of the decision set and $T$ is the total decision rounds. Such regret improves the optimal classical algorithm by a factor of $T^{2/3}$.

quant-ph↗

arXiv2024

Quantum Algorithms for Non-smooth Non-convex Optimization

This paper considers the problem for finding the $(δ,ε)$-Goldstein stationary point of Lipschitz continuous objective, which is a rich function class to cover a great number of important applications. We construct a zeroth-order quantum estimator for the gradient of the smoothed surrogate. Based on such estimator, we propose a novel quantum algorithm that achieves a query complexity of $\tilde{\mathcal{O}}(d^{3/2}δ^{-1}ε^{-3})$ on the stochastic function value oracle, where $d$ is the dimension of the problem. We also enhance the query complexity to $\tilde{\mathcal{O}}(d^{3/2}δ^{-1}ε^{-7/3})$ by introducing a variance reduction variant. Our findings demonstrate the clear advantages of utilizing quantum techniques for non-convex non-smooth optimization, as they outperform the optimal classical methods on the dependency of $ε$ by a factor of $ε^{-2/3}$.

quant-ph↗

arXiv2024

Cost-Effective Online Multi-LLM Selection with Versatile Reward Models

With the rapid advancement of large language models (LLMs), the diversity of multi-LLM tasks and the variability in their pricing structures have become increasingly important, as costs can vary greatly between different LLMs. To tackle these challenges, we introduce the \textit{C2MAB-V}, a \underline{C}ost-effective \underline{C}ombinatorial \underline{M}ulti-armed \underline{B}andit with \underline{V}ersatile reward models for optimal LLM selection and usage. This online model differs from traditional static approaches or those reliant on a single LLM without cost consideration. With multiple LLMs deployed on a scheduling cloud and a local server dedicated to handling user queries, \textit{C2MAB-V} facilitates the selection of multiple LLMs over a combinatorial search space, specifically tailored for various collaborative task types with different reward models. Based on our designed online feedback mechanism and confidence bound technique, \textit{C2MAB-V} can effectively address the multi-LLM selection challenge by managing the exploration-exploitation trade-off across different models, while also balancing cost and reward for diverse tasks. The NP-hard integer linear programming problem for selecting multiple LLMs with trade-off dilemmas is addressed by: i) decomposing the integer problem into a relaxed form by the local server, ii) utilizing a discretization rounding scheme that provides optimal LLM combinations by the scheduling cloud, and iii) continual online updates based on feedback. Theoretically, we prove that \textit{C2MAB-V} offers strict guarantees over versatile reward models, matching state-of-the-art results for regret and violations in some degenerate cases. Empirically, we show that \textit{C2MAB-V} effectively balances performance and cost-efficiency with nine LLMs for three application scenarios.

cs.LG↗

arXiv2024

Stochastic Bandits Robust to Adversarial Attacks

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 ${O}((K/Δ)\log T + KC)$ 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, $Δ$ 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 [Lykouris et al., 2018].

cs.LG↗

arXiv2024

AxiomVision: Accuracy-Guaranteed Adaptive Visual Model Selection for Perspective-Aware Video Analytics

The rapid evolution of multimedia and computer vision technologies requires adaptive visual model deployment strategies to effectively handle diverse tasks and varying environments. This work introduces AxiomVision, a novel framework that can guarantee accuracy by leveraging edge computing to dynamically select the most efficient visual models for video analytics under diverse scenarios. Utilizing a tiered edge-cloud architecture, AxiomVision enables the deployment of a broad spectrum of visual models, from lightweight to complex DNNs, that can be tailored to specific scenarios while considering camera source impacts. In addition, AxiomVision provides three core innovations: (1) a dynamic visual model selection mechanism utilizing continual online learning, (2) an efficient online method that efficiently takes into account the influence of the camera's perspective, and (3) a topology-driven grouping approach that accelerates the model selection process. With rigorous theoretical guarantees, these advancements provide a scalable and effective solution for visual tasks inherent to multimedia systems, such as object detection, classification, and counting. Empirically, AxiomVision achieves a 25.7\% improvement in accuracy.

cs.MM↗

arXiv2024

Merit-based Fair Combinatorial Semi-Bandit with Unrestricted Feedback Delays

We study the stochastic combinatorial semi-bandit problem with unrestricted feedback delays under merit-based fairness constraints. This is motivated by applications such as crowdsourcing, and online advertising, where immediate feedback is not immediately available and fairness among different choices (or arms) is crucial. We consider two types of unrestricted feedback delays: reward-independent delays where the feedback delays are independent of the rewards, and reward-dependent delays where the feedback delays are correlated with the rewards. Furthermore, we introduce merit-based fairness constraints to ensure a fair selection of the arms. We define the reward regret and the fairness regret and present new bandit algorithms to select arms under unrestricted feedback delays based on their merits. We prove that our algorithms all achieve sublinear expected reward regret and expected fairness regret, with a dependence on the quantiles of the delay distribution. We also conduct extensive experiments using synthetic and real-world data and show that our algorithms can fairly select arms with different feedback delays.

cs.LG↗

arXiv2024

FedConPE: Efficient Federated Conversational Bandits with Heterogeneous Clients

Conversational recommender systems have emerged as a potent solution for efficiently eliciting user preferences. These systems interactively present queries associated with "key terms" to users and leverage user feedback to estimate user preferences more efficiently. Nonetheless, most existing algorithms adopt a centralized approach. In this paper, we introduce FedConPE, a phase elimination-based federated conversational bandit algorithm, where $M$ agents collaboratively solve a global contextual linear bandit problem with the help of a central server while ensuring secure data management. To effectively coordinate all the clients and aggregate their collected data, FedConPE uses an adaptive approach to construct key terms that minimize uncertainty across all dimensions in the feature space. Furthermore, compared with existing federated linear bandit algorithms, FedConPE offers improved computational and communication efficiency as well as enhanced privacy protections. Our theoretical analysis shows that FedConPE is minimax near-optimal in terms of cumulative regret. We also establish upper bounds for communication costs and conversation frequency. Comprehensive evaluations demonstrate that FedConPE outperforms existing conversational bandit algorithms while using fewer conversations.

cs.LG↗

arXiv2024

Variance-Dependent Regret Bounds for Non-stationary Linear Bandits

We investigate the non-stationary stochastic linear bandit problem where the reward distribution evolves each round. Existing algorithms characterize the non-stationarity by the total variation budget $B_K$, which is the summation of the change of the consecutive feature vectors of the linear bandits over $K$ rounds. However, such a quantity only measures the non-stationarity with respect to the expectation of the reward distribution, which makes existing algorithms sub-optimal under the general non-stationary distribution setting. In this work, we propose algorithms that utilize the variance of the reward distribution as well as the $B_K$, and show that they can achieve tighter regret upper bounds. Specifically, we introduce two novel algorithms: Restarted Weighted$\text{OFUL}^+$ and Restarted $\text{SAVE}^+$. These algorithms address cases where the variance information of the rewards is known and unknown, respectively. Notably, when the total variance $V_K$ is much smaller than $K$, our algorithms outperform previous state-of-the-art results on non-stationary stochastic linear bandits under different settings. Experimental evaluations further validate the superior performance of our proposed algorithms over existing works.

cs.LG↗

arXiv2024

Online Search with Predictions: Pareto-optimal Algorithm and its Applications in Energy Markets

This paper develops learning-augmented algorithms for energy trading in volatile electricity markets. The basic problem is to sell (or buy) $k$ units of energy for the highest revenue (lowest cost) over uncertain time-varying prices, which can framed as a classic online search problem in the literature of competitive analysis. State-of-the-art algorithms assume no knowledge about future market prices when they make trading decisions in each time slot, and aim for guaranteeing the performance for the worst-case price sequence. In practice, however, predictions about future prices become commonly available by leveraging machine learning. This paper aims to incorporate machine-learned predictions to design competitive algorithms for online search problems. An important property of our algorithms is that they achieve performances competitive with the offline algorithm in hindsight when the predictions are accurate (i.e., consistency) and also provide worst-case guarantees when the predictions are arbitrarily wrong (i.e., robustness). The proposed algorithms achieve the Pareto-optimal trade-off between consistency and robustness, where no other algorithms for online search can improve on the consistency for a given robustness. Further, we extend the basic online search problem to a more general inventory management setting that can capture storage-assisted energy trading in electricity markets. In empirical evaluations using traces from real-world applications, our learning-augmented algorithms improve the average empirical performance compared to benchmark algorithms, while also providing improved worst-case performance.

cs.LG↗

arXiv2024

Federated Contextual Cascading Bandits with Asynchronous Communication and Heterogeneous Users

We study the problem of federated contextual combinatorial cascading bandits, where $|\mathcal{U}|$ agents collaborate under the coordination of a central server to provide tailored recommendations to the $|\mathcal{U}|$ corresponding users. Existing works consider either a synchronous framework, necessitating full agent participation and global synchronization, or assume user homogeneity with identical behaviors. We overcome these limitations by considering (1) federated agents operating in an asynchronous communication paradigm, where no mandatory synchronization is required and all agents communicate independently with the server, (2) heterogeneous user behaviors, where users can be stratified into $J \le |\mathcal{U}|$ latent user clusters, each exhibiting distinct preferences. For this setting, we propose a UCB-type algorithm with delicate communication protocols. Through theoretical analysis, we give sub-linear regret bounds on par with those achieved in the synchronous framework, while incurring only logarithmic communication costs. Empirical evaluation on synthetic and real-world datasets validates our algorithm's superior performance in terms of regrets and communication costs.

cs.LG↗