Jinhang Zuo

Xutong Liu, Jinhang Zuo, Siwei Wang et al. · uw

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.

Xutong Liu, Jinhang Zuo, Siwei Wang et al. · uw

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.

Yi Hu, Jinhang Zuo, Bob Iannucci et al. · cmu

Internet of Things (IoT) technologies have enabled numerous data-driven mobile applications and have the potential to significantly improve environmental monitoring and hazard warnings through the deployment of a network of IoT sensors. However, these IoT devices are often power-constrained and utilize wireless communication schemes with limited bandwidth. Such power constraints limit the amount of information each device can share across the network, while bandwidth limitations hinder sensors' coordination of their transmissions. In this work, we formulate the communication planning problem of IoT sensors that track the state of the environment. We seek to optimize sensors' decisions in collecting environmental data under stringent resource constraints. We propose a multi-agent reinforcement learning (MARL) method to find the optimal communication policies for each sensor that maximize the tracking accuracy subject to the power and bandwidth limitations. MARL learns and exploits the spatial-temporal correlation of the environmental data at each sensor's location to reduce the redundant reports from the sensors. Experiments on wildfire spread with LoRA wireless network simulators show that our MARL method can learn to balance the need to collect enough data to predict wildfire spread with unknown bandwidth limitations.

Jinhang Zuo, Songwen Hu, Tong Yu et al.

The recent advances of conversational recommendations provide a promising way to efficiently elicit users' preferences via conversational interactions. To achieve this, the recommender system conducts conversations with users, asking their preferences for different items or item categories. Most existing conversational recommender systems for cold-start users utilize a multi-armed bandit framework to learn users' preference in an online manner. However, they rely on a pre-defined conversation frequency for asking about item categories instead of individual items, which may incur excessive conversational interactions that hurt user experience. To enable more flexible questioning about key-terms, we formulate a new conversational bandit problem that allows the recommender system to choose either a key-term or an item to recommend at each round and explicitly models the rewards of these actions. This motivates us to handle a new exploration-exploitation (EE) trade-off between key-term asking and item recommendation, which requires us to accurately model the relationship between key-term and item rewards. We conduct a survey and analyze a real-world dataset to find that, unlike assumptions made in prior works, key-term rewards are mainly affected by rewards of representative items. We propose two bandit algorithms, Hier-UCB and Hier-LinUCB, that leverage this observed relationship and the hierarchical structure between key-terms and items to efficiently learn which items to recommend. We theoretically prove that our algorithm can reduce the regret bound's dependency on the total number of items from previous work. We validate our proposed algorithms and regret bound on both synthetic and real-world data.

Baran Atalar, Xutong Liu, Jinhang Zuo et al.

As Large Language Models (LLMs) become increasingly popular, caching responses so that they can be reused by users with semantically similar queries has become a vital strategy for reducing inference costs and latency. Existing caching frameworks have proposed to decide which query responses to cache by assuming a finite, known universe of discrete queries and learning their serving costs and arrival probabilities. As LLMs' pool of users and queries expands, however, such an assumption becomes increasingly untenable: real-world LLM queries reside in an infinite, continuous embedding space. In this paper, we establish the first rigorous theoretical framework for semantic LLM response caching in continuous query space under uncertainty. To bridge the gap between discrete optimization and continuous representation spaces, we introduce dynamic $ε$-net discretization coupled with Kernel Ridge Regression. This design enables the system to formally quantify estimation uncertainty and generalize partial feedback on LLM query costs across continuous semantic query neighborhoods. We develop both offline learning and online adaptive algorithms optimized to reduce switching costs incurred by changing the cached responses. We prove that our online algorithm achieves a sublinear regret bound against an optimal continuous oracle, which reduces to existing bounds for discrete query models. Extensive empirical evaluations demonstrate that our framework approximates the continuous optimal cache well while also reducing computational and switching overhead compared to existing methods.

Xuchuang Wang, Jinhang Zuo, Xutong Liu et al. · uw

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].

Qirun Zeng, Xuchuang Wang, Jiayi Shen et al.

We study fixed-confidence best arm identification in generalized linear bandits under a hybrid feedback model: at each round, the learner may query either (i) absolute reward feedback from a single arm or (ii) relative (dueling) feedback from an arm pair, both governed by generalized linear models. We introduce a likelihood-ratio--based confidence sequence that unifies heterogeneous generalized linear observations and yields an explicit ellipsoidal confidence set under a self-concordance assumption. Building on this confidence set, we propose a hybrid Track-and-Stop algorithm that adaptively allocates queries by tracking a minimax-optimal design over a joint action space of arms and pairs. We establish $δ$-correctness and provide high-probability upper bounds on the stopping time. We further extend the framework to a cost-aware setting that accounts for heterogeneous acquisition costs across feedback modalities. Empirical experiments demonstrate that the proposed algorithms significantly improve sample efficiency over baseline methods.

Tian Wu, Liming Wang, Zijian Wen et al.

The emergence of Mixture-of-Experts (MoE) has transformed the scaling of large language models by enabling vast model capacity through sparse activation. Yet, converting these performance gains into practical edge deployment remains difficult, as the massive memory footprint and communication demands often overwhelm resource-limited environments. While centralized cloud-based solutions are available, they are frequently plagued by prohibitive infrastructure costs, latency issues, and privacy concerns. Moreover, existing edge-oriented optimizations largely overlook the complexities of heterogeneous hardware, focusing instead on isolated or uniform device setups. In response, this paper proposes Prism, an inference framework engineered for collaborative MoE serving across diverse GPU-equipped edge servers. By leveraging the intrinsic sparsity and input locality of MoE workloads, Prism minimizes inter-server communication and optimizes expert placement within diverse resource constraints. The framework integrates an activation-aware placement strategy that balances local request coverage with memory utilization, supplemented by a runtime migration mechanism to adapt expert distribution to dynamic workload changes. Experiments on contemporary MoE models and datasets demonstrate that Prism reduces inference latency by up to 30.6% and significantly lowers communication costs compared to state-of-the-art baselines, confirming the effectiveness of cooperative edge-based MoE serving.

Jinhang Zuo, Zhiyao Zhang, Xuchuang Wang et al.

Cooperative multi-agent multi-armed bandits (CMA2B) consider the collaborative efforts of multiple agents in a shared multi-armed bandit game. We study latent vulnerabilities exposed by this collaboration and consider adversarial attacks on a few agents with the goal of influencing the decisions of the rest. More specifically, we study adversarial attacks on CMA2B in both homogeneous settings, where agents operate with the same arm set, and heterogeneous settings, where agents have distinct arm sets. In the homogeneous setting, we propose attack strategies that, by targeting just one agent, convince all agents to select a particular target arm $T-o(T)$ times while incurring $o(T)$ attack costs in $T$ rounds. In the heterogeneous setting, we prove that a target arm attack requires linear attack costs and propose attack strategies that can force a maximum number of agents to suffer linear regrets while incurring sublinear costs and only manipulating the observations of a few target agents. Numerical experiments validate the effectiveness of our proposed attack strategies.

Manhin Poon, XiangXiang Dai, Xutong Liu et al. · uw

Large language models (LLMs) exhibit diverse response behaviors, costs, and strengths, making it challenging to select the most suitable LLM for a given user query. We study the problem of adaptive multi-LLM selection in an online setting, where the learner interacts with users through multi-step query refinement and must choose LLMs sequentially without access to offline datasets or model internals. A key challenge arises from unstructured context evolution: the prompt dynamically changes in response to previous model outputs via a black-box process, which cannot be simulated, modeled, or learned. To address this, we propose the first contextual bandit framework for sequential LLM selection under unstructured prompt dynamics. We formalize a notion of myopic regret and develop a LinUCB-based algorithm that provably achieves sublinear regret without relying on future context prediction. We further introduce budget-aware and positionally-aware (favoring early-stage satisfaction) extensions to accommodate variable query costs and user preferences for early high-quality responses. Our algorithms are theoretically grounded and require no offline fine-tuning or dataset-specific training. Experiments on diverse benchmarks demonstrate that our methods outperform existing LLM routing strategies in both accuracy and cost-efficiency, validating the power of contextual bandits for real-time, adaptive LLM selection.

Yi Hu, Jinhang Zuo, Alanis Zhao et al.

Foundation models (FMs) emerge as a promising solution to harness distributed and diverse environmental data by leveraging prior knowledge to understand the complicated temporal and spatial correlations within heterogeneous datasets. Unlike distributed learning frameworks such as federated learning, which often struggle with multimodal data, FMs can transform diverse inputs into embeddings. This process facilitates the integration of information from various modalities and the application of prior learning to new domains. However, deploying FMs in resource-constrained edge systems poses significant challenges. To this end, we introduce CoRAST, a novel learning framework that utilizes FMs for enhanced analysis of distributed, correlated heterogeneous data. Utilizing a server-based FM, CoRAST can exploit existing environment information to extract temporal, spatial, and cross-modal correlations among sensor data. This enables CoRAST to offer context-aware insights for localized client tasks through FM-powered global representation learning. Our evaluation on real-world weather dataset demonstrates CoRAST's ability to exploit correlated heterogeneous data through environmental representation learning to reduce the forecast errors by up to 50.3% compared to the baselines.

Yi Hu, Jinhang Zuo, Eddie Zhang et al.

Recent advancements in machine learning (ML) have enabled its deployment on resource-constrained edge devices, fostering innovative applications such as intelligent environmental sensing. However, these devices, particularly microcontrollers (MCUs), face substantial challenges due to limited memory, computing capabilities, and the absence of dedicated floating-point units (FPUs). These constraints hinder the deployment of complex ML models, especially those requiring lifelong learning capabilities. To address these challenges, we propose Tin-Tin, an integer-based on-device training framework designed specifically for low-power MCUs. Tin-Tin introduces novel integer rescaling techniques to efficiently manage dynamic ranges and facilitate efficient weight updates using integer data types. Unlike existing methods optimized for devices with FPUs, GPUs, or FPGAs, Tin-Tin addresses the unique demands of tiny MCUs, prioritizing energy efficiency and optimized memory utilization. We validate the effectiveness of Tin-Tin through end-to-end application examples on real-world tiny devices, demonstrating its potential to support energy-efficient and sustainable ML applications on edge platforms.

Amirmahdi Mirfakhar, Xuchuang Wang, Jinhang Zuo et al.

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 $O(M^4K)$ regret with $O(MK\log T)$ 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 $O(M^3K^2)$ regret with $O(M^3K\log T)$ 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.

Xutong Liu, Xiangxiang Dai, Jinhang Zuo et al. · uw

The combinatorial multi-armed bandit (CMAB) is a fundamental sequential decision-making framework, extensively studied over the past decade. However, existing work primarily focuses on the online setting, overlooking the substantial costs of online interactions and the readily available offline datasets. To overcome these limitations, we introduce Off-CMAB, the first offline learning framework for CMAB. Central to our framework is the combinatorial lower confidence bound (CLCB) algorithm, which combines pessimistic reward estimations with combinatorial solvers. To characterize the quality of offline datasets, we propose two novel data coverage conditions and prove that, under these conditions, CLCB achieves a near-optimal suboptimality gap, matching the theoretical lower bound up to a logarithmic factor. We validate Off-CMAB through practical applications, including learning to rank, large language model (LLM) caching, and social influence maximization, showing its ability to handle nonlinear reward functions, general feedback models, and out-of-distribution action samples that excludes optimal or even feasible actions. Extensive experiments on synthetic and real-world datasets further highlight the superior performance of CLCB.

Fatemeh Ghaffari, Xuchuang Wang, Jinhang Zuo et al.

We study the problem of multi-agent multi-armed bandits with adversarial corruption in a heterogeneous setting, where each agent accesses a subset of arms. The adversary can corrupt the reward observations for all agents. Agents share these corrupted rewards with each other, and the objective is to maximize the cumulative total reward of all agents (and not be misled by the adversary). We propose a multi-agent cooperative learning algorithm that is robust to adversarial corruptions. For this newly devised algorithm, we demonstrate that an adversary with an unknown corruption budget $C$ only incurs an additive $O((L / L_{\min}) C)$ term to the standard regret of the model in non-corruption settings, where $L$ is the total number of agents, and $L_{\min}$ is the minimum number of agents with mutual access to an arm. As a side-product, our algorithm also improves the state-of-the-art regret bounds when reducing to both the single-agent and homogeneous multi-agent scenarios, tightening multiplicative $K$ (the number of arms) and $L$ (the number of agents) factors, respectively.

Xutong Liu, Baran Atalar, Xiangxiang Dai et al. · uw

Large Language Models (LLMs) are revolutionizing how users interact with information systems, yet their high inference cost poses serious scalability and sustainability challenges. Caching inference responses, allowing them to be retrieved without another forward pass through the LLM, has emerged as one possible solution. Traditional exact-match caching, however, overlooks the semantic similarity between queries, leading to unnecessary recomputation. Semantic caching addresses this by retrieving responses based on semantic similarity, but introduces a fundamentally different cache eviction problem: one must account for mismatch costs between incoming queries and cached responses. Moreover, key system parameters, such as query arrival probabilities and serving costs, are often unknown and must be learned over time. Existing semantic caching methods are largely ad-hoc, lacking theoretical foundations and unable to adapt to real-world uncertainty. In this paper, we present a principled, learning-based framework for semantic cache eviction under unknown query and cost distributions. We formulate both offline optimization and online learning variants of the problem, and develop provably efficient algorithms with state-of-the-art guarantees. We also evaluate our framework on a synthetic dataset, showing that our proposed algorithms perform matching or superior performance compared with baselines.

Xiangxiang Dai, Xiaowei Sun, Jinhang Zuo et al. · uw

Co-branding has become a vital strategy for businesses aiming to expand market reach within recommendation systems. However, identifying effective cross-industry partnerships remains challenging due to resource imbalances, uncertain brand willingness, and ever-changing market conditions. In this paper, we provide the first systematic study of this problem and propose a unified online-offline framework to enable co-branding recommendations. Our approach begins by constructing a bipartite graph linking ``initiating'' and ``target'' brands to quantify co-branding probabilities and assess market benefits. During the online learning phase, we dynamically update the graph in response to market feedback, while striking a balance between exploring new collaborations for long-term gains and exploiting established partnerships for immediate benefits. To address the high initial co-branding costs, our framework mitigates redundant exploration, thereby enhancing short-term performance while ensuring sustainable strategic growth. In the offline optimization phase, our framework consolidates the interests of multiple sub-brands under the same parent brand to maximize overall returns, avoid excessive investment in single sub-brands, and reduce unnecessary costs associated with over-prioritizing a single sub-brand. We present a theoretical analysis of our approach, establishing a highly nontrivial sublinear regret bound for online learning in the complex co-branding problem, and enhancing the approximation guarantee for the NP-hard offline budget allocation optimization. Experiments on both synthetic and real-world co-branding datasets demonstrate the practical effectiveness of our framework, with at least 12\% improvement.

Qirun Zeng, Eric He, Richard Hoffmann et al.

Adversarial attacks on stochastic bandits have traditionally relied on some unrealistic assumptions, such as per-round reward manipulation and unbounded perturbations, limiting their relevance to real-world systems. We propose a more practical threat model, Fake Data Injection, which reflects realistic adversarial constraints: the attacker can inject only a limited number of bounded fake feedback samples into the learner's history, simulating legitimate interactions. We design efficient attack strategies under this model, explicitly addressing both magnitude constraints (on reward values) and temporal constraints (on when and how often data can be injected). Our theoretical analysis shows that these attacks can mislead both Upper Confidence Bound (UCB) and Thompson Sampling algorithms into selecting a target arm in nearly all rounds while incurring only sublinear attack cost. Experiments on synthetic and real-world datasets validate the effectiveness of our strategies, revealing significant vulnerabilities in widely used stochastic bandit algorithms under practical adversarial scenarios.

Xuchuang Wang, Qirun Zeng, Jinhang Zuo et al.

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.

Xutong Liu, Siwei Wang, Jinhang Zuo et al.

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.

Yu-Zhen Janice Chen, Jinhang Zuo, Venugopal V. Veeravalli et al.

In the problem of quickest change detection (QCD), a change occurs at some unknown time in the distribution of a sequence of independent observations. This work studies a QCD problem where the change is either a bad change, which we aim to detect, or a confusing change, which is not of our interest. Our objective is to detect a bad change as quickly as possible while avoiding raising a false alarm for pre-change or a confusing change. We identify a specific set of pre-change, bad change, and confusing change distributions that pose challenges beyond the capabilities of standard Cumulative Sum (CuSum) procedures. Proposing novel CuSum-based detection procedures, S-CuSum and J-CuSum, leveraging two CuSum statistics, we offer solutions applicable across all kinds of pre-change, bad change, and confusing change distributions. For both S-CuSum and J-CuSum, we provide analytical performance guarantees and validate them by numerical results. Furthermore, both procedures are computationally efficient as they only require simple recursive updates.

Jinhang Zuo, Zhiyao Zhang, Zhiyong Wang et al.

Online learning to rank (OLTR) is a sequential decision-making problem where a learning agent selects an ordered list of items and receives feedback through user clicks. Although potential attacks against OLTR algorithms may cause serious losses in real-world applications, little is known about adversarial attacks on OLTR. This paper studies attack strategies against multiple variants of OLTR. Our first result provides an attack strategy against the UCB algorithm on classical stochastic bandits with binary feedback, which solves the key issues caused by bounded and discrete feedback that previous works can not handle. Building on this result, we design attack algorithms against UCB-based OLTR algorithms in position-based and cascade models. Finally, we propose a general attack strategy against any algorithm under the general click model. Each attack algorithm manipulates the learning agent into choosing the target attack item $T-o(T)$ times, incurring a cumulative cost of $o(T)$. Experiments on synthetic and real data further validate the effectiveness of our proposed attack algorithms.

Xutong Liu, Jinhang Zuo, Xiaowei Chen et al.

Multi-layered network exploration (MuLaNE) problem is an important problem abstracted from many applications. In MuLaNE, there are multiple network layers where each node has an importance weight and each layer is explored by a random walk. The MuLaNE task is to allocate total random walk budget $B$ into each network layer so that the total weights of the unique nodes visited by random walks are maximized. We systematically study this problem from offline optimization to online learning. For the offline optimization setting where the network structure and node weights are known, we provide greedy based constant-ratio approximation algorithms for overlapping networks, and greedy or dynamic-programming based optimal solutions for non-overlapping networks. For the online learning setting, neither the network structure nor the node weights are known initially. We adapt the combinatorial multi-armed bandit framework and design algorithms to learn random walk related parameters and node weights while optimizing the budget allocation in multiple rounds, and prove that they achieve logarithmic regret bounds. Finally, we conduct experiments on a real-world social network dataset to validate our theoretical results.

Jinhang Zuo, Carlee Joe-Wong

We study the sequential resource allocation problem where a decision maker repeatedly allocates budgets between resources. Motivating examples include allocating limited computing time or wireless spectrum bands to multiple users (i.e., resources). At each timestep, the decision maker should distribute its available budgets among different resources to maximize the expected reward, or equivalently to minimize the cumulative regret. In doing so, the decision maker should learn the value of the resources allocated for each user from feedback on each user's received reward. For example, users may send messages of different urgency over wireless spectrum bands; the reward generated by allocating spectrum to a user then depends on the message's urgency. We assume each user's reward follows a random process that is initially unknown. We design combinatorial multi-armed bandit algorithms to solve this problem with discrete or continuous budgets. We prove the proposed algorithms achieve logarithmic regrets under semi-bandit feedback.

Jinhang Zuo, Xutong Liu, Carlee Joe-Wong et al.

Online influence maximization has attracted much attention as a way to maximize influence spread through a social network while learning the values of unknown network parameters. Most previous works focus on single-item diffusion. In this paper, we introduce a new Online Competitive Influence Maximization (OCIM) problem, where two competing items (e.g., products, news stories) propagate in the same network and influence probabilities on edges are unknown. We adopt a combinatorial multi-armed bandit (CMAB) framework for OCIM, but unlike the non-competitive setting, the important monotonicity property (influence spread increases when influence probabilities on edges increase) no longer holds due to the competitive nature of propagation, which brings a significant new challenge to the problem. We provide a nontrivial proof showing that the Triggering Probability Modulated (TPM) condition for CMAB still holds in OCIM, which is instrumental for our proposed algorithms OCIM-TS and OCIM-OFU to achieve sublinear Bayesian and frequentist regret, respectively. We also design an OCIM-ETC algorithm that requires less feedback and easier offline computation, at the expense of a worse frequentist regret bound. Experimental evaluations demonstrate the effectiveness of our algorithms.

Jinhang Zuo, Xiaoxi Zhang, Carlee Joe-Wong

We consider the stochastic multi-armed bandit (MAB) problem in a setting where a player can pay to pre-observe arm rewards before playing an arm in each round. Apart from the usual trade-off between exploring new arms to find the best one and exploiting the arm believed to offer the highest reward, we encounter an additional dilemma: pre-observing more arms gives a higher chance to play the best one, but incurs a larger cost. For the single-player setting, we design an Observe-Before-Play Upper Confidence Bound (OBP-UCB) algorithm for $K$ arms with Bernoulli rewards, and prove a $T$-round regret upper bound $O(K^2\log T)$. In the multi-player setting, collisions will occur when players select the same arm to play in the same round. We design a centralized algorithm, C-MP-OBP, and prove its $T$-round regret relative to an offline greedy strategy is upper bounded in $O(\frac{K^4}{M^2}\log T)$ for $K$ arms and $M$ players. We also propose distributed versions of the C-MP-OBP policy, called D-MP-OBP and D-MP-Adapt-OBP, achieving logarithmic regret with respect to collision-free target policies. Experiments on synthetic data and wireless channel traces show that C-MP-OBP and D-MP-OBP outperform random heuristics and offline optimal policies that do not allow pre-observations.