Shuai Li

Zhiyong Wang, Xutong Liu, Shuai Li et al. · uw

Conversational contextual bandits elicit user preferences by occasionally querying for explicit feedback on key-terms to accelerate learning. However, there are aspects of existing approaches which limit their performance. First, information gained from key-term-level conversations and arm-level recommendations is not appropriately incorporated to speed up learning. Second, it is important to ask explorative key-terms to quickly elicit the user's potential interests in various domains to accelerate the convergence of user preference estimation, which has never been considered in existing works. To tackle these issues, we first propose ``ConLinUCB", a general framework for conversational bandits with better information incorporation, combining arm-level and key-term-level feedback to estimate user preference in one step at each time. Based on this framework, we further design two bandit algorithms with explorative key-term selection strategies, ConLinUCB-BS and ConLinUCB-MCR. We prove tighter regret upper bounds of our proposed algorithms. Particularly, ConLinUCB-BS achieves a regret bound of $O(d\sqrt{T\log T})$, better than the previous result $O(d\sqrt{T}\log T)$. Extensive experiments on synthetic and real-world data show significant advantages of our algorithms in learning accuracy (up to 54\% improvement) and computational efficiency (up to 72\% improvement), compared to the classic ConUCB algorithm, showing the potential benefit to recommender systems.

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.

Fang Kong, Canzhe Zhao, Shuai Li

The linear bandit problem has been studied for many years in both stochastic and adversarial settings. Designing an algorithm that can optimize the environment without knowing the loss type attracts lots of interest. \citet{LeeLWZ021} propose an algorithm that actively detects the loss type and then switches between different algorithms specially designed for specific settings. However, such an approach requires meticulous designs to perform well in all environments. Follow-the-regularized-leader (FTRL) is another type of popular algorithm that can adapt to different environments. This algorithm is of simple design and the regret bounds are shown to be optimal in traditional multi-armed bandit problems compared with the detect-switch type. Designing an FTRL-type algorithm for linear bandits is an important question that has been open for a long time. In this paper, we prove that the FTRL algorithm with a negative entropy regularizer can achieve the best-of-three-world results for the linear bandit problem. Our regret bounds achieve the same or nearly the same order as the previous detect-switch type algorithm but with a much simpler algorithmic design.

Fang Kong, Yichi Zhou, Shuai Li

The problem of online learning with graph feedback has been extensively studied in the literature due to its generality and potential to model various learning tasks. Existing works mainly study the adversarial and stochastic feedback separately. If the prior knowledge of the feedback mechanism is unavailable or wrong, such specially designed algorithms could suffer great loss. To avoid this problem, \citet{erez2021towards} try to optimize for both environments. However, they assume the feedback graphs are undirected and each vertex has a self-loop, which compromises the generality of the framework and may not be satisfied in applications. With a general feedback graph, the observation of an arm may not be available when this arm is pulled, which makes the exploration more expensive and the algorithms more challenging to perform optimally in both environments. In this work, we overcome this difficulty by a new trade-off mechanism with a carefully-designed proportion for exploration and exploitation. We prove the proposed algorithm simultaneously achieves $\mathrm{poly} \log T$ regret in the stochastic setting and minimax-optimal regret of $\tilde{O}(T^{2/3})$ in the adversarial setting where $T$ is the horizon and $\tilde{O}$ hides parameters independent of $T$ as well as logarithmic terms. To our knowledge, this is the first best-of-both-worlds result for general feedback graphs.

Fang Kong, Junming Yin, Shuai Li

The problem of two-sided matching markets has a wide range of real-world applications and has been extensively studied in the literature. A line of recent works have focused on the problem setting where the preferences of one-side market participants are unknown \emph{a priori} and are learned by iteratively interacting with the other side of participants. All these works are based on explore-then-commit (ETC) and upper confidence bound (UCB) algorithms, two common strategies in multi-armed bandits (MAB). Thompson sampling (TS) is another popular approach, which attracts lots of attention due to its easier implementation and better empirical performances. In many problems, even when UCB and ETC-type algorithms have already been analyzed, researchers are still trying to study TS for its benefits. However, the convergence analysis of TS is much more challenging and remains open in many problem settings. In this paper, we provide the first regret analysis for TS in the new setting of iterative matching markets. Extensive experiments demonstrate the practical advantages of the TS-type algorithm over the ETC and UCB-type baselines.

Cheng Chen, Canzhe Zhao, Shuai Li

Online learning to rank (OLTR) interactively learns to choose lists of items from a large collection based on certain click models that describe users' click behaviors. Most recent works for this problem focus on the stochastic environment where the item attractiveness is assumed to be invariant during the learning process. In many real-world scenarios, however, the environment could be dynamic or even arbitrarily changing. This work studies the OLTR problem in both stochastic and adversarial environments under the position-based model (PBM). We propose a method based on the follow-the-regularized-leader (FTRL) framework with Tsallis entropy and develop a new self-bounding constraint especially designed for PBM. We prove the proposed algorithm simultaneously achieves $O(\log{T})$ regret in the stochastic environment and $O(m\sqrt{nT})$ regret in the adversarial environment, where $T$ is the number of rounds, $n$ is the number of items and $m$ is the number of positions. We also provide a lower bound of order $Ω(m\sqrt{nT})$ for adversarial PBM, which matches our upper bound and improves over the state-of-the-art lower bound. The experiments show that our algorithm could simultaneously learn in both stochastic and adversarial environments and is competitive compared to existing methods that are designed for a single environment.

Zichun Ye, Runqi Wang, Xutong Liu et al.

The combinatorial multi-armed bandit (CMAB) is a cornerstone of sequential decision-making framework, dominated by two algorithmic families: UCB-based and adversarial methods such as follow the regularized leader (FTRL) and online mirror descent (OMD). However, prominent UCB-based approaches like CUCB suffer from additional regret factor $\log T$ that is detrimental over long horizons, while adversarial methods such as EXP3.M and HYBRID impose significant computational overhead. To resolve this trade-off, we introduce the Combinatorial Minimax Optimal Strategy in the Stochastic setting (CMOSS). CMOSS is a computationally efficient algorithm that achieves an instance-independent regret of $O\big( (\log k)^2\sqrt{kmT}\big )$ under semi-bandit feedback, where $m$ is the number of arms and $k$ is the maximum cardinality of a feasible action. Crucially, this result eliminates the dependency on $\log T$ and matches the established $Ω\big( \sqrt{kmT}\big)$ lower bound up to $O\big((\log k)^2\big)$. We then extend our analysis to show that CMOSS is also applicable to cascading feedback. Experiments on synthetic and real-world datasets validate that CMOSS consistently outperforms benchmark algorithms in both regret and runtime efficiency.

Fang Kong, Yueran Yang, Wei Chen et al.

Thompson sampling (TS) has attracted a lot of interest in the bandit area. It was introduced in the 1930s but has not been theoretically proven until recent years. All of its analysis in the combinatorial multi-armed bandit (CMAB) setting requires an exact oracle to provide optimal solutions with any input. However, such an oracle is usually not feasible since many combinatorial optimization problems are NP-hard and only approximation oracles are available. An example (Wang and Chen, 2018) has shown the failure of TS to learn with an approximation oracle. However, this oracle is uncommon and is designed only for a specific problem instance. It is still an open question whether the convergence analysis of TS can be extended beyond the exact oracle in CMAB. In this paper, we study this question under the greedy oracle, which is a common (approximation) oracle with theoretical guarantees to solve many (offline) combinatorial optimization problems. We provide a problem-dependent regret lower bound of order $Ω(\log T/Δ^2)$ to quantify the hardness of TS to solve CMAB problems with greedy oracle, where $T$ is the time horizon and $Δ$ is some reward gap. We also provide an almost matching regret upper bound. These are the first theoretical results for TS to solve CMAB with a common approximation oracle and break the misconception that TS cannot work with approximation oracles.

Anirban Santara, Claudio Gentile, Gaurav Aggarwal et al.

Motivated by problems of learning to rank long item sequences, we introduce a variant of the cascading bandit model that considers flexible length sequences with varying rewards and losses. We formulate two generative models for this problem within the generalized linear setting, and design and analyze upper confidence algorithms for it. Our analysis delivers tight regret bounds which, when specialized to vanilla cascading bandits, results in sharper guarantees than previously available in the literature. We evaluate our algorithms on a number of real-world datasets, and show significantly improved empirical performance as compared to known cascading bandit baselines.

Houshuang Chen, Zengfeng Huang, Shuai Li et al.

The bandit problem with graph feedback, proposed in [Mannor and Shamir, NeurIPS 2011], is modeled by a directed graph $G=(V,E)$ where $V$ is the collection of bandit arms, and once an arm is triggered, all its incident arms are observed. A fundamental question is how the structure of the graph affects the min-max regret. We propose the notions of the fractional weak domination number $δ^*$ and the $k$-packing independence number capturing upper bound and lower bound for the regret respectively. We show that the two notions are inherently connected via aligning them with the linear program of the weakly dominating set and its dual -- the fractional vertex packing set respectively. Based on this connection, we utilize the strong duality theorem to prove a general regret upper bound $O\left(\left( δ^*\log |V|\right)^{\frac{1}{3}}T^{\frac{2}{3}}\right)$ and a lower bound $Ω\left(\left(δ^*/α\right)^{\frac{1}{3}}T^{\frac{2}{3}}\right)$ where $α$ is the integrality gap of the dual linear program. Therefore, our bounds are tight up to a $\left(\log |V|\right)^{\frac{1}{3}}$ factor on graphs with bounded integrality gap for the vertex packing problem including trees and graphs with bounded degree. Moreover, we show that for several special families of graphs, we can get rid of the $\left(\log |V|\right)^{\frac{1}{3}}$ factor and establish optimal regret.

Xiaojin Zhang, Shuai Li, Weiwen Liu et al.

The problem of multi-armed bandits (MAB) asks to make sequential decisions while balancing between exploitation and exploration, and have been successfully applied to a wide range of practical scenarios. Various algorithms have been designed to achieve a high reward in a long term. However, its short-term performance might be rather low, which is injurious in risk sensitive applications. Building on previous work of conservative bandits, we bring up a framework of contextual combinatorial conservative bandits. An algorithm is presented and a regret bound of $\tilde O(d^2+d\sqrt{T})$ is proven, where $d$ is the dimension of the feature vectors, and $T$ is the total number of time steps. We further provide an algorithm as well as regret analysis for the case when the conservative reward is unknown. Experiments are conducted, and the results validate the effectiveness of our algorithm.

Shuai Li, Wei Chen, Shuai Li et al.

We generalize the setting of online clustering of bandits by allowing non-uniform distribution over user frequencies. A more efficient algorithm is proposed with simple set structures to represent clusters. We prove a regret bound for the new algorithm which is free of the minimal frequency over users. The experiments on both synthetic and real datasets consistently show the advantage of the new algorithm over existing methods.

Shuai Li, Tor Lattimore, Csaba Szepesvári

We introduce a new model for online ranking in which the click probability factors into an examination and attractiveness function and the attractiveness function is a linear function of a feature vector and an unknown parameter. Only relatively mild assumptions are made on the examination function. A novel algorithm for this setup is analysed, showing that the dependence on the number of items is replaced by a dependence on the dimension, allowing the new algorithm to handle a large number of items. When reduced to the orthogonal case, the regret of the algorithm improves on the state-of-the-art.

Shuai Li

We consider a new setting of online clustering of contextual cascading bandits, an online learning problem where the underlying cluster structure over users is unknown and needs to be learned from a random prefix feedback. More precisely, a learning agent recommends an ordered list of items to a user, who checks the list and stops at the first satisfactory item, if any. We propose an algorithm of CLUB-cascade for this setting and prove a $T$-step regret bound of order $\tilde{O}(\sqrt{T})$. Previous work corresponds to the degenerate case of only one cluster, and our general regret bound in this special case also significantly improves theirs. We conduct experiments on both synthetic and real data, and demonstrate the effectiveness of our algorithm and the advantage of incorporating online clustering method.

Claudio Gentile, Shuai Li, Purushottam Kar et al.

We investigate a novel cluster-of-bandit algorithm CAB for collaborative recommendation tasks that implements the underlying feedback sharing mechanism by estimating the neighborhood of users in a context-dependent manner. CAB makes sharp departures from the state of the art by incorporating collaborative effects into inference as well as learning processes in a manner that seamlessly interleaving explore-exploit tradeoffs and collaborative steps. We prove regret bounds under various assumptions on the data, which exhibit a crisp dependence on the expected number of clusters over the users, a natural measure of the statistical difficulty of the learning task. Experiments on production and real-world datasets show that CAB offers significantly increased prediction performance against a representative pool of state-of-the-art methods.

Shuai Li, Claudio Gentile, Alexandros Karatzoglou

We investigate an efficient context-dependent clustering technique for recommender systems based on exploration-exploitation strategies through multi-armed bandits over multiple users. Our algorithm dynamically groups users based on their observed behavioral similarity during a sequence of logged activities. In doing so, the algorithm reacts to the currently served user by shaping clusters around him/her but, at the same time, it explores the generation of clusters over users which are not currently engaged. We motivate the effectiveness of this clustering policy, and provide an extensive empirical analysis on real-world datasets, showing scalability and improved prediction performance over state-of-the-art methods for sequential clustering of users in multi-armed bandit scenarios.

Nathan Korda, Balazs Szorenyi, Shuai Li

We provide two distributed confidence ball algorithms for solving linear bandit problems in peer to peer networks with limited communication capabilities. For the first, we assume that all the peers are solving the same linear bandit problem, and prove that our algorithm achieves the optimal asymptotic regret rate of any centralised algorithm that can instantly communicate information between the peers. For the second, we assume that there are clusters of peers solving the same bandit problem within each cluster, and we prove that our algorithm discovers these clusters, while achieving the optimal asymptotic regret rate within each one. Through experiments on several real-world datasets, we demonstrate the performance of proposed algorithms compared to the state-of-the-art.

Shuai Li, Purushottam Kar

We propose an efficient Context-Aware clustering of Bandits (CAB) algorithm, which can capture collaborative effects. CAB can be easily deployed in a real-world recommendation system, where multi-armed bandits have been shown to perform well in particular with respect to the cold-start problem. CAB utilizes a context-aware clustering augmented by exploration-exploitation strategies. CAB dynamically clusters the users based on the content universe under consideration. We give a theoretical analysis in the standard stochastic multi-armed bandits setting. We show the efficiency of our approach on production and real-world datasets, demonstrate the scalability, and, more importantly, the significant increased prediction performance against several state-of-the-art methods.

Shuai Li, Alexandros Karatzoglou, Claudio Gentile

Classical collaborative filtering, and content-based filtering methods try to learn a static recommendation model given training data. These approaches are far from ideal in highly dynamic recommendation domains such as news recommendation and computational advertisement, where the set of items and users is very fluid. In this work, we investigate an adaptive clustering technique for content recommendation based on exploration-exploitation strategies in contextual multi-armed bandit settings. Our algorithm takes into account the collaborative effects that arise due to the interaction of the users with the items, by dynamically grouping users based on the items under consideration and, at the same time, grouping items based on the similarity of the clusterings induced over the users. The resulting algorithm thus takes advantage of preference patterns in the data in a way akin to collaborative filtering methods. We provide an empirical analysis on medium-size real-world datasets, showing scalability and increased prediction performance (as measured by click-through rate) over state-of-the-art methods for clustering bandits. We also provide a regret analysis within a standard linear stochastic noise setting.

Claudio Gentile, Shuai Li, Giovanni Zappella

We introduce a novel algorithmic approach to content recommendation based on adaptive clustering of exploration-exploitation ("bandit") strategies. We provide a sharp regret analysis of this algorithm in a standard stochastic noise setting, demonstrate its scalability properties, and prove its effectiveness on a number of artificial and real-world datasets. Our experiments show a significant increase in prediction performance over state-of-the-art methods for bandit problems.