We propose a new sequential decision-making setting, combining key aspects of two established online learning problems with bandit feedback. The optimal action to play at any given moment is contingent on an underlying changing state which is not directly observable by the agent. Each state is associated with a context distribution, possibly corrupted, allowing the agent to identify the state. Furthermore, states evolve in a Markovian fashion, providing useful information to estimate the current state via state history. In the proposed problem setting, we tackle the challenge of deciding on which of the two sources of information the agent should base its arm selection. We present an algorithm that uses a referee to dynamically combine the policies of a contextual bandit and a multi-armed bandit. We capture the time-correlation of states through iteratively learning the action-reward transition model, allowing for efficient exploration of actions. Our setting is motivated by adaptive mobile health (mHealth) interventions. Users transition through different, time-correlated, but only partially observable internal states, determining their current needs. The side information associated with each internal state might not always be reliable, and standard approaches solely rely on the context risk of incurring high regret. Similarly, some users might exhibit weaker correlations between subsequent states, leading to approaches that solely rely on state transitions risking the same. We analyze our setting and algorithm in terms of regret lower bound and upper bounds and evaluate our method on simulated medication adherence intervention data and several real-world data sets, showing improved empirical performance compared to several popular algorithms.
We consider a novel variant of the contextual bandit problem (i.e., the multi-armed bandit with side-information, or context, available to a decision-maker) where the context used at each decision may be corrupted ("useless context"). This new problem is motivated by certain on-line settings including clinical trial and ad recommendation applications. In order to address the corrupted-context setting,we propose to combine the standard contextual bandit approach with a classical multi-armed bandit mechanism. Unlike standard contextual bandit methods, we are able to learn from all iteration, eve…
Université de Lille（里尔大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Centrale Lille（里尔中央理工学院）
We study the corrupted bandit problem, i.e. a stochastic multi-armed bandit problem with $k$ unknown reward distributions, which are heavy-tailed and corrupted by a history-independent adversary or Nature. To be specific, the reward obtained by playing an arm comes from corresponding heavy-tailed reward distribution with probability $1-\varepsilon \in (0.5,1]$ and an arbitrary corruption distribution of unbounded support with probability $\varepsilon \in [0,0.5)$. First, we provide $\textit{a problem-dependent lower bound on the regret}$ of any corrupted bandit algorithm. The lower bounds indi…
DeepMind（深度思维）；UC Berkeley（加州大学伯克利分校）；University of Massachusetts（马萨诸塞大学）
We consider model selection in stochastic bandit and reinforcement learning problems. Given a set of base learning algorithms, an effective model selection strategy adapts to the best learning algorithm in an online fashion. We show that by estimating the regret of each algorithm and playing the algorithms such that all empirical regrets are ensured to be of the same order, the overall regret balancing strategy achieves a regret that is close to the regret of the optimal base algorithm. Our strategy requires an upper bound on the optimal base regret as input, and the performance of the strateg…
Inria Lille Nord-Europe（法国国家信息与自动化研究所里尔北欧中心）；Orange Labs（Orange实验室）；CNRS（法国国家科学研究中心）；Univ. Lille（里尔大学）
We study a variant of the stochastic multi-armed bandit (MAB) problem in which the rewards are corrupted. In this framework, motivated by privacy preservation in online recommender systems, the goal is to maximize the sum of the (unobserved) rewards, based on the observation of transformation of these rewards through a stochastic corruption process with known parameters. We provide a lower bound on the expected regret of any bandit algorithm in this corrupted setting. We devise a frequentist algorithm, KLUCB-CF, and a Bayesian algorithm, TS-CF and give upper bounds on their regret. We also pro…
Contextual bandit algorithms are sensitive to the estimation method of the outcome model as well as the exploration method used, particularly in the presence of rich heterogeneity or complex outcome models, which can lead to difficult estimation problems along the path of learning. We develop algorithms for contextual bandits with linear payoffs that integrate balancing methods from the causal inference literature in their estimation to make it less prone to problems of estimation bias. We provide the first regret bound analyses for linear contextual bandits with balancing and show that our al…
Microsoft Research, NYC（微软研究院，纽约市）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔综合理工学院）
We study the problem of $K$-armed dueling bandit for both stochastic and adversarial environments, where the goal of the learner is to aggregate information through relative preferences of pair of decisions points queried in an online sequential manner. We first propose a novel reduction from any (general) dueling bandits to multi-armed bandits and despite the simplicity, it allows us to improve many existing results in dueling bandits. In particular, \emph{we give the first best-of-both world result for the dueling bandits regret minimization problem} -- a unified framework that is guaranteed…
University of California, Berkeley（加州大学伯克利分校）；Google Research（谷歌研究院）
We propose a simple model selection approach for algorithms in stochastic bandit and reinforcement learning problems. As opposed to prior work that (implicitly) assumes knowledge of the optimal regret, we only require that each base algorithm comes with a candidate regret bound that may or may not hold during all rounds. In each round, our approach plays a base algorithm to keep the candidate regret bounds of all remaining base algorithms balanced, and eliminates algorithms that violate their candidate bound. We prove that the total regret of this approach is bounded by the best valid candidat…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Google Research（谷歌研究院）；The Hong Kong University of Science and Technology（香港科技大学）
We study the linear contextual bandit problem in the presence of adversarial corruption, where the reward at each round is corrupted by an adversary, and the corruption level (i.e., the sum of corruption magnitudes over the horizon) is $C\geq 0$. The best-known algorithms in this setting are limited in that they either are computationally inefficient or require a strong assumption on the corruption, or their regret is at least $C$ times worse than the regret without corruption. In this paper, to overcome these limitations, we propose a new algorithm based on the principle of optimism in the fa…
This paper addresses the problem of multiclass classification with corrupted or noisy bandit feedback. In this setting, the learner may not receive true feedback. Instead, it receives feedback that has been flipped with some non-zero probability. We propose a novel approach to deal with noisy bandit feedback based on the unbiased estimator technique. We further offer a method that can efficiently estimate the noise rates, thus providing an end-to-end framework. The proposed algorithm enjoys a mistake bound of the order of $O(\sqrt{T})$ in the high noise case and of the order of $O(T^{\nicefrac…
Reinforcement learning studies how to balance exploration and exploitation in real-world systems, optimizing interactions with the world while simultaneously learning how the world operates. One general class of algorithms for such learning is the multi-armed bandit setting. Randomized probability matching, based upon the Thompson sampling approach introduced in the 1930s, has recently been shown to perform well and to enjoy provable optimality properties. It permits generative, interpretable modeling in a Bayesian setting, where prior knowledge is incorporated, and the computed posteriors nat…
Thompson sampling, a Bayesian method for balancing exploration and exploitation in bandit problems, has theoretical guarantees and exhibits strong empirical performance in many domains. Traditional Thompson sampling, however, assumes perfect compliance, where an agent's chosen action is treated as the implemented action. This article introduces a stochastic noncompliance model that relaxes this assumption. We prove that any noncompliance in a 2-armed Bernoulli bandit increases existing regret bounds. With our noncompliance model, we derive Thompson sampling variants that explicitly handle both…
National Yang Ming Chiao Tung University（国立阳明交通大学）
The open radio access network (O-RAN) architecture offers a cost-effective and scalable solution for internet service providers to optimize their networks using machine learning algorithms. The architecture's open interfaces enable network function virtualization, with the O-RAN serving as the primary communication device for users. However, the limited frequency resources and information explosion make it difficult to achieve an optimal network experience without effective traffic control or resource allocation. To address this, we consider mobility-aware load balancing to evenly distribute l…
Royal Institute of Technology (KTH)（皇家理工学院（KTH））；Ericsson Research（爱立信研究院）
We introduce and study a new class of stochastic bandit problems, referred to as predictive bandits. In each round, the decision maker first decides whether to gather information about the rewards of particular arms (so that their rewards in this round can be predicted). These measurements are costly, and may be corrupted by noise. The decision maker then selects an arm to be actually played in the round. Predictive bandits find applications in many areas; e.g. they can be applied to channel selection problems in radio communication systems. In this paper, we provide the first theoretical resu…
Contextual bandit algorithms are sensitive to the estimation method of the outcome model as well as the exploration method used, particularly in the presence of rich heterogeneity or complex outcome models, which can lead to difficult estimation problems along the path of learning. We study a consideration for the exploration vs. exploitation framework that does not arise in multi-armed bandits but is crucial in contextual bandits; the way exploration and exploitation is conducted in the present affects the bias and variance in the potential outcome model estimation in subsequent stages of lea…
University California San Diego（加州大学圣地亚哥分校）；Shanghai Jiao Tong University（上海交通大学）；Nanjing University of Posts and Telecommunications（南京邮电大学）
We study the problem of stochastic bandits with adversarial corruptions in the cooperative multi-agent setting, where $V$ agents interact with a common $K$-armed bandit problem, and each pair of agents can communicate with each other to expedite the learning process. In the problem, the rewards are independently sampled from distributions across all agents and rounds, but they may be corrupted by an adversary. Our goal is to minimize both the overall regret and communication cost across all agents. We first show that an additive term of corruption is unavoidable for any algorithm in this probl…
Indiana University - Purdue University Indianapolis（印第安纳大学-普渡大学印第安纳波利斯分校）
We propose a novel framework for integrating Hawkes processes with multi-armed bandit algorithms to solve spatio-temporal event forecasting and detection problems when data may be undersampled or spatially biased. In particular, we introduce an upper confidence bound algorithm using Bayesian spatial Hawkes process estimation for balancing the tradeoff between exploiting geographic regions where data has been collected and exploring geographic regions where data is unobserved. We first validate our model using simulated data and then apply it to the problem of disaster search and rescue using c…
The Chinese University of Hong Kong（香港中文大学）；Shanghai Jiao Tong University（上海交通大学）；Tencent（腾讯）
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,…
Princeton University（普林斯顿大学）；Massachusetts Institute of Technology（麻省理工学院）
The cooperative bandit problem is increasingly becoming relevant due to its applications in large-scale decision-making. However, most research for this problem focuses exclusively on the setting with perfect communication, whereas in most real-world distributed settings, communication is often over stochastic networks, with arbitrary corruptions and delays. In this paper, we study cooperative bandit learning under three typical real-world communication scenarios, namely, (a) message-passing over stochastic time-varying networks, (b) instantaneous reward-sharing over a network with random dela…
The multi-armed bandit problem is a classical decision-making problem where an agent has to learn an optimal action balancing exploration and exploitation. Properly managing this trade-off requires a correct assessment of uncertainty; in multi-armed bandits, as in other machine learning applications, it is important to distinguish between stochasticity that is inherent to the system (aleatoric uncertainty) and stochasticity that derives from the limited knowledge of the agent (epistemic uncertainty). In this paper we consider the formalism of subjective logic, a concise and expressive framewor…
In this paper we propose a novel experimental design-based algorithm to minimize regret in online stochastic linear and combinatorial bandits. While existing literature tends to focus on optimism-based algorithms--which have been shown to be suboptimal in many cases--our approach carefully plans which action to take by balancing the tradeoff between information gain and reward, overcoming the failures of optimism. In addition, we leverage tools from the theory of suprema of empirical processes to obtain regret guarantees that scale with the Gaussian width of the action set, avoiding wasteful u…
For marketing, we sometimes need to recommend content for multiple pages in sequence. Different from general sequential decision making process, the use cases have a simpler flow where customers per seeing recommended content on each page can only return feedback as moving forward in the process or dropping from it until a termination state. We refer to this type of problems as sequential decision making in linear--flow. We propose to formulate the problem as an MDP with Bandits where Bandits are employed to model the transition probability matrix. At recommendation time, we use Thompson sampl…
We study model selection in linear bandits, where the learner must adapt to the dimension (denoted by $d_\star$) of the smallest hypothesis class containing the true linear model while balancing exploration and exploitation. Previous papers provide various guarantees for this model selection problem, but have limitations; i.e., the analysis requires favorable conditions that allow for inexpensive statistical testing to locate the right hypothesis class or are based on the idea of "corralling" multiple base algorithms, which often performs relatively poorly in practice. These works also mainly …
Multi-armed bandits are a quintessential machine learning problem requiring the balancing of exploration and exploitation. While there has been progress in developing algorithms with strong theoretical guarantees, there has been less focus on practical near-optimal finite-time performance. In this paper, we propose an algorithm for Bayesian multi-armed bandits that utilizes value-function-driven online planning techniques. Building on previous work on UCB and Gittins index, we introduce linearly-separable value functions that take both the expected return and the benefit of exploration into co…
University of Southern California（南加州大学）；The Chinese University of Hong Kong（香港中文大学）
In this work, we develop linear bandit algorithms that automatically adapt to different environments. By plugging a novel loss estimator into the optimization problem that characterizes the instance-optimal strategy, our first algorithm not only achieves nearly instance-optimal regret in stochastic environments, but also works in corrupted environments with additional regret being the amount of corruption, while the state-of-the-art (Li et al., 2019) achieves neither instance-optimality nor the optimal dependence on the corruption amount. Moreover, by equipping this algorithm with an adversari…
We consider a general multi-armed bandit problem with correlated (and simple contextual and restless) elements, as a relaxed control problem. By introducing an entropy regularisation, we obtain a smooth asymptotic approximation to the value function. This yields a novel semi-index approximation of the optimal decision process. This semi-index can be interpreted as explicitly balancing an exploration-exploitation trade-off as in the optimistic (UCB) principle where the learning premium explicitly describes asymmetry of information available in the environment and non-linearity in the reward fun…
Exploration in reinforcement learning (RL) suffers from the curse of dimensionality when the state-action space is large. A common practice is to parameterize the high-dimensional value and policy functions using given features. However existing methods either have no theoretical guarantee or suffer a regret that is exponential in the planning horizon $H$. In this paper, we propose an online RL algorithm, namely the MatrixRL, that leverages ideas from linear bandit to learn a low-dimensional representation of the probability transition model while carefully balancing the exploitation-explorati…
Revisiting Matrix Sketching in Linear Bandits: Achieving Sublinear Regret via Dyadic Block Sketching
Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学人工智能学院）；National Key Laboratory for Novel Software Technology, Nanjing University（南京大学新型软件技术国家重点实验室）
Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, including personalized medicine and online advertising. We derive a novel $Ω(n^{2/3})$ dimension-free minimax regret lower bound for sparse linear bandits in the data-poor regime where the horizon is smaller than the ambient dimension and where the feature vectors admit a well-conditioned exploration distribution. This is complemented by a nearly matching upper bound for an explore-then-commit algorithm showing that that $Θ(n^{2/3})$ is the optimal rate in the data-poor regime. The r…
We study the stochastic multi-player multi-armed bandit problem. In this problem, $m$ players cooperate to maximize their total reward from $K > m$ arms. However the players cannot communicate and are penalized (e.g. receive no reward) if they pull the same arm at the same time. We ask whether it is possible to obtain optimal instance-dependent regret $\tilde{O}(1/Δ)$ where $Δ$ is the gap between the $m$-th and $m+1$-st best arms. Such guarantees were recently achieved in a model allowing the players to implicitly communicate through intentional collisions. Surprisingly, we show that with no c…
Classical multi-armed bandit problems use the expected value of an arm as a metric to evaluate its goodness. However, the expected value is a risk-neutral metric. In many applications like finance, one is interested in balancing the expected return of an arm (or portfolio) with the risk associated with that return. In this paper, we consider the problem of selecting the arm that optimizes a linear combination of the expected reward and the associated Conditional Value at Risk (CVaR) in a fixed budget best-arm identification framework. We allow the reward distributions to be unbounded or even h…
Dynamic treatment regimes (DTRs) are personalized, adaptive, multi-stage treatment plans that adapt treatment decisions both to an individual's initial features and to intermediate outcomes and features at each subsequent stage, which are affected by decisions in prior stages. Examples include personalized first- and second-line treatments of chronic conditions like diabetes, cancer, and depression, which adapt to patient response to first-line treatment, disease progression, and individual characteristics. While existing literature mostly focuses on estimating the optimal DTR from offline dat…
Cascading Bandits Robust to Adversarial Corruptions
Hong Kong University of Science and Technology（香港科技大学）；East China Normal University（华东师范大学）；The Chinese University of Hong Kong（香港中文大学）；Shanghai Jiao Tong University（上海交通大学）
This work studies the problem of learning episodic Markov Decision Processes with known transition and bandit feedback. We develop the first algorithm with a ``best-of-both-worlds'' guarantee: it achieves $\mathcal{O}(log T)$ regret when the losses are stochastic, and simultaneously enjoys worst-case robustness with $\tilde{\mathcal{O}}(\sqrt{T})$ regret even when the losses are adversarial, where $T$ is the number of episodes. More generally, it achieves $\tilde{\mathcal{O}}(\sqrt{C})$ regret in an intermediate setting where the losses are corrupted by a total amount of $C$. Our algorithm is …
