Heterogeneous Multi-Agent Bandits with Parsimonious Hints

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.

Heterogeneous Multi-agent Multi-armed Bandits on Stochastic Block Models

We study a novel heterogeneous multi-agent multi-armed bandit problem with a cluster structure induced by stochastic block models, influencing not only graph topology, but also reward heterogeneity. Specifically, agents are distributed on random graphs based on stochastic block models - a generalized Erdos-Renyi model with heterogeneous edge probabilities: agents are grouped into clusters (known or unknown); edge probabilities for agents within the same cluster differ from those across clusters. In addition, the cluster structure in stochastic block model also determines our heterogeneous rewards. Rewards distributions of the same arm vary across agents in different clusters but remain consistent within a cluster, unifying homogeneous and heterogeneous settings and varying degree of heterogeneity, and rewards are independent samples from these distributions. The objective is to minimize system-wide regret across all agents. To address this, we propose a novel algorithm applicable to both known and unknown cluster settings. The algorithm combines an averaging-based consensus approach with a newly introduced information aggregation and weighting technique, resulting in a UCB-type strategy. It accounts for graph randomness, leverages both intra-cluster (homogeneous) and inter-cluster (heterogeneous) information from rewards and graphs, and incorporates cluster detection for unknown cluster settings. We derive optimal instance-dependent regret upper bounds of order $\log{T}$ under sub-Gaussian rewards. Importantly, our regret bounds capture the degree of heterogeneity in the system (an additional layer of complexity), exhibit smaller constants, scale better for large systems, and impose significantly relaxed assumptions on edge probabilities. In contrast, prior works have not accounted for this refined problem complexity, rely on more stringent assumptions, and exhibit limited scalability.

Multi-Agent Conversational Online Learning for Adaptive LLM Response Identification

The remarkable generative capability of large language models (LLMs) has sparked a growing interest in automatically generating responses for different applications. Given the dynamic nature of user preferences and the uncertainty of LLM response performance, it is crucial to design efficient online learning algorithms to identify optimal LLM responses (i.e., high-quality responses that also meet user preferences). Most existing online algorithms adopt a centralized approach and fail to leverage explicit user preferences for more efficient and personalized LLM response identification. In contrast, this paper introduces \textit{MACO} (\underline{M}ulti-\underline{A}gent \underline{C}onversational \underline{O}nline Learning for Adaptive LLM Response Identification): 1) The online LLM response identification process is accelerated by multiple local agents (such as smartphones), while enhancing data privacy; 2) A novel conversational mechanism is proposed to adaptively conduct conversations for soliciting user preferences (e.g., a preference for a humorous tone over a serious one in generated responses), so to minimize uncertainty in preference estimation. Our theoretical analysis demonstrates that \cadi\ is near-optimal regarding cumulative regret. Additionally, \cadi\ offers reduced communication costs and computational complexity by eliminating the traditional, computing-intensive ``G-optimal design" found in previous works. Extensive experiments with the open LLM \textit{Llama}, coupled with two different embedding models from Google and OpenAI for text vector representation, demonstrate that \cadi\ significantly outperforms the current state-of-the-art in online LLM response identification.

Multi-Agent Stochastic Bandits Robust to Adversarial Corruptions

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.

Combinatorial Logistic Bandits

We introduce a novel framework called combinatorial logistic bandits (CLogB), where in each round, a subset of base arms (called the super arm) is selected, with the outcome of each base arm being binary and its expectation following a logistic parametric model. The feedback is governed by a general arm triggering process. Our study covers CLogB with reward functions satisfying two smoothness conditions, capturing application scenarios such as online content delivery, online learning to rank, and dynamic channel allocation. We first propose a simple yet efficient algorithm, CLogUCB, utilizing a variance-agnostic exploration bonus. Under the 1-norm triggering probability modulated (TPM) smoothness condition, CLogUCB achieves a regret bound of $\tilde{O}(d\sqrt{\kappa KT})$, where $\tilde{O}$ ignores logarithmic factors, $d$ is the dimension of the feature vector, $\kappa$ represents the nonlinearity of the logistic model, and $K$ is the maximum number of base arms a super arm can trigger. This result improves on prior work by a factor of $\tilde{O}(\sqrt{\kappa})$. We then enhance CLogUCB with a variance-adaptive version, VA-CLogUCB, which attains a regret bound of $\tilde{O}(d\sqrt{KT})$ under the same 1-norm TPM condition, improving another $\tilde{O}(\sqrt{\kappa})$ factor. VA-CLogUCB shows even greater promise under the stronger triggering probability and variance modulated (TPVM) condition, achieving a leading $\tilde{O}(d\sqrt{T})$ regret, thus removing the additional dependency on the action-size $K$. Furthermore, we enhance the computational efficiency of VA-CLogUCB by eliminating the nonconvex optimization process when the context feature map is time-invariant while maintaining the tight $\tilde{O}(d\sqrt{T})$ regret. Finally, experiments on synthetic and real-world datasets demonstrate the superior performance of our algorithms compared to benchmark algorithms.

Combinatorial Multivariant Multi-Armed Bandits with Applications to Episodic Reinforcement Learning and Beyond

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.

Adversarial Attacks on Cooperative Multi-agent Bandits

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.

Cooperative Multi-agent Bandits: Distributed Algorithms with Optimal Individual Regret and Constant Communication Costs

Recently, there has been extensive study of cooperative multi-agent multi-armed bandits where a set of distributed agents cooperatively play the same multi-armed bandit game. The goal is to develop bandit algorithms with the optimal group and individual regrets and low communication between agents. The prior work tackled this problem using two paradigms: leader-follower and fully distributed algorithms. Prior algorithms in both paradigms achieve the optimal group regret. The leader-follower algorithms achieve constant communication costs but fail to achieve optimal individual regrets. The state-of-the-art fully distributed algorithms achieve optimal individual regrets but fail to achieve constant communication costs. This paper presents a simple yet effective communication policy and integrates it into a learning algorithm for cooperative bandits. Our algorithm achieves the best of both paradigms: optimal individual regret and constant communication costs.

Multi-Fidelity Multi-Armed Bandits Revisited

We study the multi-fidelity multi-armed bandit (MF-MAB), an extension of the canonical multi-armed bandit (MAB) problem. 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 (BAI) and the regret minimization objectives. For 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 MF-MAB, one can recover the standard sample complexity bounds of the classic (single-fidelity) MAB. For regret minimization of 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 $\Lambda$.

On-Demand Communication for Asynchronous Multi-Agent Bandits

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.