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.

Quickest Change Detection with Confusing Change

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.

CoRAST: Towards Foundation Model-Powered Correlated Data Analysis in Resource-Constrained CPS and IoT

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.

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.

Intelligent Communication Planning for Constrained Environmental IoT Sensing with Reinforcement Learning

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.

Adversarial Attacks on Online Learning to Rank with Click Feedback

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.

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, we find 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.

Hierarchical Conversational Preference Elicitation with Bandit Feedback

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.

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.

Multi-layered Network Exploration via Random Walks: From Offline Optimization to Online Learning

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.