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.

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.

Fed-CVLC: Compressing Federated Learning Communications with Variable-Length Codes

In Federated Learning (FL) paradigm, a parameter server (PS) concurrently communicates with distributed participating clients for model collection, update aggregation, and model distribution over multiple rounds, without touching private data owned by individual clients. FL is appealing in preserving data privacy; yet the communication between the PS and scattered clients can be a severe bottleneck. Model compression algorithms, such as quantization and sparsification, have been suggested but they generally assume a fixed code length, which does not reflect the heterogeneity and variability of model updates. In this paper, through both analysis and experiments, we show strong evidences that variable-length is beneficial for compression in FL. We accordingly present Fed-CVLC (Federated Learning Compression with Variable-Length Codes), which fine-tunes the code length in response of the dynamics of model updates. We develop optimal tuning strategy that minimizes the loss function (equivalent to maximizing the model utility) subject to the budget for communication. We further demonstrate that Fed-CVLC is indeed a general compression design that bridges quantization and sparsification, with greater flexibility. Extensive experiments have been conducted with public datasets to demonstrate that Fed-CVLC remarkably outperforms state-of-the-art baselines, improving model utility by 1.50%-5.44%, or shrinking communication traffic by 16.67%-41.61%.

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.

Online Clustering of Bandits with Misspecified User Models

The contextual linear bandit is an important online learning problem where given arm features, a learning agent selects an arm at each round to maximize the cumulative rewards in the long run. A line of works, called the clustering of bandits (CB), utilize the collaborative effect over user preferences and have shown significant improvements over classic linear bandit algorithms. However, existing CB algorithms require well-specified linear user models and can fail when this critical assumption does not hold. Whether robust CB algorithms can be designed for more practical scenarios with misspecified user models remains an open problem. In this paper, we are the first to present the important problem of clustering of bandits with misspecified user models (CBMUM), where the expected rewards in user models can be perturbed away from perfect linear models. We devise two robust CB algorithms, RCLUMB and RSCLUMB (representing the learned clustering structure with dynamic graph and sets, respectively), that can accommodate the inaccurate user preference estimations and erroneous clustering caused by model misspecifications. We prove regret upper bounds of $O(\epsilon_*T\sqrt{md\log T} + d\sqrt{mT}\log T)$ for our algorithms under milder assumptions than previous CB works (notably, we move past a restrictive technical assumption on the distribution of the arms), which match the lower bound asymptotically in $T$ up to logarithmic factors, and also match the state-of-the-art results in several degenerate cases. The techniques in proving the regret caused by misclustering users are quite general and may be of independent interest. Experiments on both synthetic and real-world data show our outperformance over previous algorithms.

Online Corrupted User Detection and Regret Minimization

In real-world online web systems, multiple users usually arrive sequentially into the system. For applications like click fraud and fake reviews, some users can maliciously perform corrupted (disrupted) behaviors to trick the system. Therefore, it is crucial to design efficient online learning algorithms to robustly learn from potentially corrupted user behaviors and accurately identify the corrupted users in an online manner. Existing works propose bandit algorithms robust to adversarial corruption. However, these algorithms are designed for a single user, and cannot leverage the implicit social relations among multiple users for more efficient learning. Moreover, none of them consider how to detect corrupted users online in the multiple-user scenario. In this paper, we present an important online learning problem named LOCUD to learn and utilize unknown user relations from disrupted behaviors to speed up learning, and identify the corrupted users in an online setting. To robustly learn and utilize the unknown relations among potentially corrupted users, we propose a novel bandit algorithm RCLUB-WCU. To detect the corrupted users, we devise a novel online detection algorithm OCCUD based on RCLUB-WCU's inferred user relations. We prove a regret upper bound for RCLUB-WCU, which asymptotically matches the lower bound with respect to $T$ up to logarithmic factors, and matches the state-of-the-art results in degenerate cases. We also give a theoretical guarantee for the detection accuracy of OCCUD. With extensive experiments, our methods achieve superior performance over previous bandit algorithms and high corrupted user detection accuracy.

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 $\Lambda$.

A Survey of Federated Evaluation in Federated Learning

In traditional machine learning, it is trivial to conduct model evaluation since all data samples are managed centrally by a server. However, model evaluation becomes a challenging problem in federated learning (FL), which is called federated evaluation in this work. This is because clients do not expose their original data to preserve data privacy. Federated evaluation plays a vital role in client selection, incentive mechanism design, malicious attack detection, etc. In this paper, we provide the first comprehensive survey of existing federated evaluation methods. Moreover, we explore various applications of federated evaluation for enhancing FL performance and finally present future research directions by envisioning some challenges.