Optimal Thompson Sampling strategies for support-aware CVaR bandits
Univ. Lille（里尔大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Centrale Lille（里尔中央理工学院）；CIRAD（法国农业国际合作研究发展中心）；Alliance of CIAT and Bioversity International（国际热带农业中心与国际生物多样性中心联盟）
Presented at the Thirty-eighth International Conference on Machine Learning (ICML 2021). In this version we refine Lemma 2 and correct its proof (does not change the main theorems)
In this paper we study a multi-arm bandit problem in which the quality of each arm is measured by the Conditional Value at Risk (CVaR) at some level alpha of the reward distribution. While existing works in this setting mainly focus on Upper Confidence Bound algorithms, we introduce a new Thompson Sampling approach for CVaR bandits on bounded rewards that is flexible enough to solve a variety of problems grounded on physical resources. Building on a recent work by Riou & Honda (2020), we introduce B-CVTS for continuous bounded rewards and M-CVTS for multinomial distributions. On the theoretical side, we provide a non-trivial extension of their analysis that enables to theoretically bound their CVaR regret minimization performance. Strikingly, our results show that these strategies are the first to provably achieve asymptotic optimality in CVaR bandits, matching the corresponding asymptotic lower bounds for this setting. Further, we illustrate empirically the benefit of Thompson Sampling approaches both in a realistic environment simulating a use-case in agriculture and on various synthetic examples.
The multi-armed bandit (MAB) problem is a ubiquitous decision-making problem that exemplifies the exploration-exploitation tradeoff. Standard formulations exclude risk in decision making. Risk notably complicates the basic reward-maximising objective, in part because there is no universally agreed definition of it. In this paper, we consider a popular risk measure in quantitative finance known as the Conditional Value at Risk (CVaR). We explore the performance of a Thompson Sampling-based algorithm CVaR-TS under this risk measure. We provide comprehensive comparisons between our regret bounds …
We study Thompson Sampling algorithms for stochastic multi-armed bandits in the batched setting, in which we want to minimize the regret over a sequence of arm pulls using a small number of policy changes (or, batches). We propose two algorithms and demonstrate their effectiveness by experiments on both synthetic and real datasets. We also analyze the proposed algorithms from the theoretical aspect and obtain almost tight regret-batches tradeoffs for the two-arm case.
We propose algorithms based on a multi-level Thompson sampling scheme, for the stochastic multi-armed bandit and its contextual variant with linear expected rewards, in the setting where arms are clustered. We show, both theoretically and empirically, how exploiting a given cluster structure can significantly improve the regret and computational cost compared to using standard Thompson sampling. In the case of the stochastic multi-armed bandit we give upper bounds on the expected cumulative regret showing how it depends on the quality of the clustering. Finally, we perform an empirical evaluat…
We consider the multiarm bandit problems in the timevarying dynamic system for rich structural features. For the nonlinear dynamic model, we propose the approximate inference for the posterior distributions based on Laplace Approximation. For the context bandit problems, Thompson Sampling is adopted based on the underlying posterior distributions of the parameters. More specifically, we introduce the discount decays on the previous samples impact and analyze the different decay rates with the underlying sample dynamics. Consequently, the exploration and exploitation is adaptively tradeoff acco…
Universite de Toulouse（图卢兹大学）；INRA（法国国家农业科学研究院）；Institut de Mathematiques de Toulouse（图卢兹数学研究所）；Univ. Lyon（里昂大学）；ENS de Lyon（里昂高等师范学院）
We propose and analyze StoROO, an algorithm for risk optimization on stochastic black-box functions derived from StoOO. Motivated by risk-averse decision making fields like agriculture, medicine, biology or finance, we do not focus on the mean payoff but on generic functionals of the return distribution. We provide a generic regret analysis of StoROO and illustrate its applicability with two examples: the optimization of quantiles and CVaR. Inspired by the bandit literature and black-box mean optimizers, StoROO relies on the possibility to construct confidence intervals for the targeted functi…
The literature on bandit learning and regret analysis has focused on contexts where the goal is to converge on an optimal action in a manner that limits exploration costs. One shortcoming imposed by this orientation is that it does not treat time preference in a coherent manner. Time preference plays an important role when the optimal action is costly to learn relative to near-optimal actions. This limitation has not only restricted the relevance of theoretical results but has also influenced the design of algorithms. Indeed, popular approaches such as Thompson sampling and UCB can fare poorly…
This paper tackles the risk averse multi-armed bandits problem when incurred losses are non-stationary. The conditional value-at-risk (CVaR) is used as the objective function. Two estimation methods are proposed for this objective function in the presence of non-stationary losses, one relying on a weighted empirical distribution of losses and another on the dual representation of the CVaR. Such estimates can then be embedded into classic arm selection methods such as epsilon-greedy policies. Simulation experiments assess the performance of the arm selection algorithms based on the two novel es…
University of Science and Technology of China（中国科学技术大学）；University of Chinese Academy of Sciences（中国科学院大学）；Microsoft Research（微软研究院）
Thompson sampling is one of the earliest randomized algorithms for multi-armed bandits (MAB). In this paper, we extend the Thompson sampling to Budgeted MAB, where there is random cost for pulling an arm and the total cost is constrained by a budget. We start with the case of Bernoulli bandits, in which the random rewards (costs) of an arm are independently sampled from a Bernoulli distribution. To implement the Thompson sampling algorithm in this case, at each round, we sample two numbers from the posterior distributions of the reward and cost for each arm, obtain their ratio, select the arm …
We study the asymptotic performance of the Thompson sampling algorithm in the batched multi-armed bandit setting where the time horizon $T$ is divided into batches, and the agent is not able to observe the rewards of her actions until the end of each batch. We show that in this batched setting, Thompson sampling achieves the same asymptotic performance as in the case where instantaneous feedback is available after each action, provided that the batch sizes increase subexponentially. This result implies that Thompson sampling can maintain its performance even if it receives delayed feedback in …
We study the Bayesian regret of the renowned Thompson Sampling algorithm in contextual bandits with binary losses and adversarially-selected contexts. We adapt the information-theoretic perspective of \cite{RvR16} to the contextual setting by considering a lifted version of the information ratio defined in terms of the unknown model parameter instead of the optimal action or optimal policy as done in previous works on the same setting. This allows us to bound the regret in terms of the entropy of the prior distribution through a remarkably simple proof, and with no structural assumptions on th…
Columbia University（哥伦比亚大学）；Columbia Business School（哥伦比亚商学院）
We consider a sequential subset selection problem under parameter uncertainty, where at each time step, the decision maker selects a subset of cardinality $K$ from $N$ possible items (arms), and observes a (bandit) feedback in the form of the index of one of the items in said subset, or none. Each item in the index set is ascribed a certain value (reward), and the feedback is governed by a Multinomial Logit (MNL) choice model whose parameters are a priori unknown. The objective of the decision maker is to maximize the expected cumulative rewards over a finite horizon $T$, or alternatively, min…
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…
Thompson Sampling has recently been shown to be optimal in the Bernoulli Multi-Armed Bandit setting[Kaufmann et al., 2012]. This bandit problem assumes stationary distributions for the rewards. It is often unrealistic to model the real world as a stationary distribution. In this paper we derive and evaluate algorithms using Thompson Sampling for a Switching Multi-Armed Bandit Problem. We propose a Thompson Sampling strategy equipped with a Bayesian change point mechanism to tackle this problem. We develop algorithms for a variety of cases with constant switching rate: when switching occurs all…
In algorithm optimization in reinforcement learning, how to deal with the exploration-exploitation dilemma is particularly important. Multi-armed bandit problem can optimize the proposed solutions by changing the reward distribution to realize the dynamic balance between exploration and exploitation. Thompson Sampling is a common method for solving multi-armed bandit problem and has been used to explore data that conform to various laws. In this paper, we consider the Thompson Sampling approach for multi-armed bandit problem, in which rewards conform to unknown asymmetric $α$-stable distributi…
STOR-i Centre for Doctoral Training, Lancaster University（兰卡斯特大学STOR-i博士训练中心）；Department of Mathematics and Statistics, Lancaster University（兰卡斯特大学数学与统计系）
Thompson Sampling is a well established approach to bandit and reinforcement learning problems. However its use in continuum armed bandit problems has received relatively little attention. We provide the first bounds on the regret of Thompson Sampling for continuum armed bandits under weak conditions on the function class containing the true function and sub-exponential observation noise. Our bounds are realised by analysis of the eluder dimension, a recently proposed measure of the complexity of a function class, which has been demonstrated to be useful in bounding the Bayesian regret of Thom…
Contextual multi-armed bandits are classical models in reinforcement learning for sequential decision-making associated with individual information. A widely-used policy for bandits is Thompson Sampling, where samples from a data-driven probabilistic belief about unknown parameters are used to select the control actions. For this computationally fast algorithm, performance analyses are available under full context-observations. However, little is known for problems that contexts are not fully observed. We propose a Thompson Sampling algorithm for partially observable contextual multi-armed ban…
In this paper, we propose a Double Thompson Sampling (D-TS) algorithm for dueling bandit problems. As indicated by its name, D-TS selects both the first and the second candidates according to Thompson Sampling. Specifically, D-TS maintains a posterior distribution for the preference matrix, and chooses the pair of arms for comparison by sampling twice from the posterior distribution. This simple algorithm applies to general Copeland dueling bandits, including Condorcet dueling bandits as its special case. For general Copeland dueling bandits, we show that D-TS achieves $O(K^2 \log T)$ regret. …
The multi-armed bandit (MAB) problem is a ubiquitous decision-making problem that exemplifies exploration-exploitation tradeoff. Standard formulations exclude risk in decision making. Risknotably complicates the basic reward-maximising objectives, in part because there is no universally agreed definition of it. In this paper, we consider an entropic risk (ER) measure and explore the performance of a Thompson sampling-based algorithm ERTS under this risk measure by providing regret bounds for ERTS and corresponding instance dependent lower bounds.
IBM（国际商业机器公司）；Orange（奥兰治公司）；IBM Research AI（IBM研究院人工智能部门）；Mila（米拉魁北克人工智能研究所）
In this paper, we analyze and extend an online learning framework known as Context-Attentive Bandit, motivated by various practical applications, from medical diagnosis to dialog systems, where due to observation costs only a small subset of a potentially large number of context variables can be observed at each iteration;however, the agent has a freedom to choose which variables to observe. We derive a novel algorithm, called Context-Attentive Thompson Sampling (CATS), which builds upon the Linear Thompson Sampling approach, adapting it to Context-Attentive Bandit setting. We provide a theore…
Lewis-Sigler Institute（刘易斯-西格勒研究所）；Princeton University（普林斯顿大学）；Department of Computer Science（计算机科学系）；Center for Statistics and Machine Learning（统计与机器学习中心）
We address the problem of regret minimization in logistic contextual bandits, where a learner decides among sequential actions or arms given their respective contexts to maximize binary rewards. Using a fast inference procedure with Polya-Gamma distributed augmentation variables, we propose an improved version of Thompson Sampling, a Bayesian formulation of contextual bandits with near-optimal performance. Our approach, Polya-Gamma augmented Thompson Sampling (PG-TS), achieves state-of-the-art performance on simulated and real data. PG-TS explores the action space efficiently and exploits high…
ENS Paris-Saclay（巴黎萨克雷高等师范学院）；CNRS（法国国家科学研究中心）；Université de Lille（里尔大学）；Inria（法国国家信息与自动化研究所）；DeepMind（深度思维）；CentraleSupélec（中央理工-高等电力学院）
Stochastic Rank-One Bandits (Katarya et al, (2017a,b)) are a simple framework for regret minimization problems over rank-one matrices of arms. The initially proposed algorithms are proved to have logarithmic regret, but do not match the existing lower bound for this problem. We close this gap by first proving that rank-one bandits are a particular instance of unimodal bandits, and then providing a new analysis of Unimodal Thompson Sampling (UTS), initially proposed by Paladino et al (2017). We prove an asymptotically optimal regret bound on the frequentist regret of UTS and we support our clai…
Thompson Sampling provides an efficient technique to introduce prior knowledge in the multi-armed bandit problem, along with providing remarkable empirical performance. In this paper, we revisit the Thompson Sampling algorithm under rewards drawn from symmetric $α$-stable distributions, which are a class of heavy-tailed probability distributions utilized in finance and economics, in problems such as modeling stock prices and human behavior. We present an efficient framework for posterior inference, which leads to two algorithms for Thompson Sampling in this setting. We prove finite-time regret…
The multi-armed bandit problem is a popular model for studying exploration/exploitation trade-off in sequential decision problems. Many algorithms are now available for this well-studied problem. One of the earliest algorithms, given by W. R. Thompson, dates back to 1933. This algorithm, referred to as Thompson Sampling, is a natural Bayesian algorithm. The basic idea is to choose an arm to play according to its probability of being the best arm. Thompson Sampling algorithm has experimentally been shown to be close to optimal. In addition, it is efficient to implement and exhibits several desi…
Carnegie Mellon University（卡内基梅隆大学）；Google Research（谷歌研究院）；DeepMind；Duke University（杜克大学）；Norwegian University of Science and Technology（挪威科技大学）
We propose a novel framework for structured bandits, which we call an influence diagram bandit. Our framework captures complex statistical dependencies between actions, latent variables, and observations; and thus unifies and extends many existing models, such as combinatorial semi-bandits, cascading bandits, and low-rank bandits. We develop novel online learning algorithms that learn to act efficiently in our models. The key idea is to track a structured posterior distribution of model parameters, either exactly or approximately. To act, we sample model parameters from their posterior and the…
In this paper, we propose a Thompson Sampling algorithm for \emph{unimodal} bandits, where the expected reward is unimodal over the partially ordered arms. To exploit the unimodal structure better, at each step, instead of exploration from the entire decision space, our algorithm makes decision according to posterior distribution only in the neighborhood of the arm that has the highest empirical mean estimate. We theoretically prove that, for Bernoulli rewards, the regret of our algorithm reaches the lower bound of unimodal bandits, thus it is asymptotically optimal. For Gaussian rewards, the …
We consider Thompson sampling for linear bandit problems with finitely many independent arms, where rewards are sampled from normal distributions that are linearly dependent on unknown parameter vectors and with unknown variance. Specifically, with a Bayesian formulation we consider multivariate normal-gamma priors to represent environment uncertainty for all involved parameters. We show that our chosen sampling prior is a conjugate prior to the reward model and derive a Bayesian regret bound for Thompson sampling under the condition that the 5/2-moment of the variance distribution exist.
We analyze the regret of combinatorial Thompson sampling (CTS) for the combinatorial multi-armed bandit with probabilistically triggered arms under the semi-bandit feedback setting. We assume that the learner has access to an exact optimization oracle but does not know the expected base arm outcomes beforehand. When the expected reward function is Lipschitz continuous in the expected base arm outcomes, we derive $O(\sum_{i =1}^m \log T / (p_i Δ_i))$ regret bound for CTS, where $m$ denotes the number of base arms, $p_i$ denotes the minimum non-zero triggering probability of base arm $i$ and $Δ_…
Tsinghua University（清华大学）；Microsoft Research Asia（微软亚洲研究院）
In this paper, we study the application of the Thompson sampling (TS) methodology to the stochastic combinatorial multi-armed bandit (CMAB) framework. We first analyze the standard TS algorithm for the general CMAB model when the outcome distributions of all the base arms are independent, and obtain a distribution-dependent regret bound of $O(m\log K_{\max}\log T / Δ_{\min})$, where $m$ is the number of base arms, $K_{\max}$ is the size of the largest super arm, $T$ is the time horizon, and $Δ_{\min}$ is the minimum gap between the expected reward of the optimal solution and any non-optimal so…
Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games. However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved. Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model. At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical. Thus, it is attractive to consider a…
Thompson Sampling, one of the oldest heuristics for solving multi-armed bandits, has recently been shown to demonstrate state-of-the-art performance. The empirical success has led to great interests in theoretical understanding of this heuristic. In this paper, we approach this problem in a way very different from existing efforts. In particular, motivated by the connection between Thompson Sampling and exponentiated updates, we propose a new family of algorithms called Generalized Thompson Sampling in the expert-learning framework, which includes Thompson Sampling as a special case. Similar t…
In this paper, we study the stochastic combinatorial multi-armed bandit problem under semi-bandit feedback. While much work has been done on algorithms that optimize the expected reward for linear as well as some general reward functions, we study a variant of the problem, where the objective is to be risk-aware. More specifically, we consider the problem of maximizing the Conditional Value-at-Risk (CVaR), a risk measure that takes into account only the worst-case rewards. We propose new algorithms that maximize the CVaR of the rewards obtained from the super arms of the combinatorial bandit f…
Inria Lille（里尔法国国家信息与自动化研究所）；ENS Paris-Saclay（巴黎萨克雷高等师范学院）；ENSAE（法国国家统计与经济管理学院）；Criteo AI Lab（Criteo人工智能实验室）；DeepMind Paris（巴黎DeepMind）
We investigate stochastic combinatorial multi-armed bandit with semi-bandit feedback (CMAB). In CMAB, the question of the existence of an efficient policy with an optimal asymptotic regret (up to a factor poly-logarithmic with the action size) is still open for many families of distributions, including mutually independent outcomes, and more generally the multivariate sub-Gaussian family. We propose to answer the above question for these two families by analyzing variants of the Combinatorial Thompson Sampling policy (CTS). For mutually independent outcomes in $[0,1]$, we propose a tight analy…
National University of Singapore（新加坡国立大学）；California Institute of Technology（加州理工学院）
We study the regret of Thompson sampling (TS) algorithms for exponential family bandits, where the reward distribution is from a one-dimensional exponential family, which covers many common reward distributions including Bernoulli, Gaussian, Gamma, Exponential, etc. We propose a Thompson sampling algorithm, termed ExpTS, which uses a novel sampling distribution to avoid the under-estimation of the optimal arm. We provide a tight regret analysis for ExpTS, which simultaneously yields both the finite-time regret bound as well as the asymptotic regret bound. In particular, for a $K$-armed bandit …
Google Research（谷歌研究院）；Hong Kong University of Science and Technology（香港科技大学）
Thompson Sampling has been widely used for contextual bandit problems due to the flexibility of its modeling power. However, a general theory for this class of methods in the frequentist setting is still lacking. In this paper, we present a theoretical analysis of Thompson Sampling, with a focus on frequentist regret bounds. In this setting, we show that the standard Thompson Sampling is not aggressive enough in exploring new actions, leading to suboptimality in some pessimistic situations. A simple modification called Feel-Good Thompson Sampling, which favors high reward models more aggressiv…
University of Michigan（密歇根大学）；Criteo AI Lab（科韬人工智能实验室）
Restless bandit problems assume time-varying reward distributions of the arms, which adds flexibility to the model but makes the analysis more challenging. We study learning algorithms over the unknown reward distributions and prove a sub-linear, $O(\sqrt{T}\log T)$, regret bound for a variant of Thompson sampling. Our analysis applies in the infinite time horizon setting, resolving the open question raised by Jung and Tewari (2019) whose analysis is limited to the episodic case. We adopt their policy mapping framework, which allows our algorithm to be efficient and simultaneously keeps the re…
We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterio…
Louis Vuitton（路易威登）；Univ. Rennes（雷恩大学）；Ensai（雷恩高等统计与信息分析学院）；CNRS（法国国家科学研究中心）；CREST；Université de Rennes 1（雷恩第一大学）；IRISA；INRIA（法国国家信息与自动化研究所）；IUF（法国大学研究院）
Multiple-play bandits aim at displaying relevant items at relevant positions on a web page. We introduce a new bandit-based algorithm, PB-MHB, for online recommender systems which uses the Thompson sampling framework. This algorithm handles a display setting governed by the position-based model. Our sampling method does not require as input the probability of a user to look at a given position in the web page which is, in practice, very difficult to obtain. Experiments on simulated and real datasets show that our method, with fewer prior information, deliver better recommendations than state-o…
Thompson sampling provides a solution to bandit problems in which new observations are allocated to arms with the posterior probability that an arm is optimal. While sometimes easy to implement and asymptotically optimal, Thompson sampling can be computationally demanding in large scale bandit problems, and its performance is dependent on the model fit to the observed data. We introduce bootstrap Thompson sampling (BTS), a heuristic method for solving bandit problems which modifies Thompson sampling by replacing the posterior distribution used in Thompson sampling by a bootstrap distribution. …
We study the logistic bandit, in which rewards are binary with success probability $\exp(βa^\top θ) / (1 + \exp(βa^\top θ))$ and actions $a$ and coefficients $θ$ are within the $d$-dimensional unit ball. While prior regret bounds for algorithms that address the logistic bandit exhibit exponential dependence on the slope parameter $β$, we establish a regret bound for Thompson sampling that is independent of $β$. Specifically, we establish that, when the set of feasible actions is identical to the set of possible coefficient vectors, the Bayesian regret of Thompson sampling is $\tilde{O}(d\sqrt{…
Motivated by the pressing need for efficient optimization in online recommender systems, we revisit the cascading bandit model proposed by Kveton et al. (2015). While Thompson sampling (TS) algorithms have been shown to be empirically superior to Upper Confidence Bound (UCB) algorithms for cascading bandits, theoretical guarantees are only known for the latter. In this paper, we first provide a problem-dependent upper bound on the regret of a TS algorithm with Beta-Bernoulli updates; this upper bound is tighter than a recent derivation under a more general setting by Huyuk and Tekin (2019). Ne…
The Ohio State University（俄亥俄州立大学）；Tulane University（杜兰大学）
We study multi-armed bandit problems with graph feedback, in which the decision maker is allowed to observe the neighboring actions of the chosen action, in a setting where the graph may vary over time and is never fully revealed to the decision maker. We show that when the feedback graphs are undirected, the original Thompson Sampling achieves the optimal (within logarithmic factors) regret $\tilde{O}\left(\sqrt{β_0(G)T}\right)$ over time horizon $T$, where $β_0(G)$ is the average independence number of the latent graphs. To the best of our knowledge, this is the first result showing that the…
Chalmers University of Technology（查尔姆斯理工大学）；University of Lille（里尔大学）；Harvard University（哈佛大学）
We present a novel extension of Thompson Sampling for stochastic sequential decision problems with graph feedback, even when the graph structure itself is unknown and/or changing. We provide theoretical guarantees on the Bayesian regret of the algorithm, linking its performance to the underlying properties of the graph. Thompson Sampling has the advantage of being applicable without the need to construct complicated upper confidence bounds for different problems. We illustrate its performance through extensive experimental results on real and simulated networks with graph feedback. More specif…
We discuss a multiple-play multi-armed bandit (MAB) problem in which several arms are selected at each round. Recently, Thompson sampling (TS), a randomized algorithm with a Bayesian spirit, has attracted much attention for its empirically excellent performance, and it is revealed to have an optimal regret bound in the standard single-play MAB problem. In this paper, we propose the multiple-play Thompson sampling (MP-TS) algorithm, an extension of TS to the multiple-play MAB problem, and discuss its regret analysis. We prove that MP-TS for binary rewards has the optimal regret upper bound that…
Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better empirical performance compared to the state-of-the-art methods. However, many questions regarding its theoretical performance remained open. In this paper, we design and analyze a generalization of Thompson Sampling algorithm for the stochastic contextual multi-armed bandit problem with linear payoff functions, when the contexts are provided by an adaptive adv…
VITS : Variational Inference Thompson Sampling for contextual bandits
CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris（法国综合理工学院CMAP、法国国家科学研究中心、巴黎综合理工学院、巴黎理工学院）；Inria Paris（法国国家信息与自动化研究所巴黎分部）；Centre de Recherche des Cordeliers, INSERM, Universite de Paris, Sorbonne Universite（科尔德里耶研究中心、法国国家健康与医学研究院、巴黎大学、索邦大学）
Columbia University（哥伦比亚大学）；Stanford University（斯坦福大学）
Much of the recent literature on bandit learning focuses on algorithms that aim to converge on an optimal action. One shortcoming is that this orientation does not account for time sensitivity, which can play a crucial role when learning an optimal action requires much more information than near-optimal ones. Indeed, popular approaches such as upper-confidence-bound methods and Thompson sampling can fare poorly in such situations. We consider instead learning a satisficing action, which is near-optimal while requiring less information, and propose satisficing Thompson sampling, an algorithm th…
KTH Royal Institute of Technology（KTH皇家理工学院）；University of California Berkeley（加州大学伯克利分校）
We address multi-armed bandits (MAB) where the objective is to maximize the cumulative reward under a probabilistic linear constraint. For a few real-world instances of this problem, constrained extensions of the well-known Thompson Sampling (TS) heuristic have recently been proposed. However, finite-time analysis of constrained TS is challenging; as a result, only O(\sqrt{T}) bounds on the cumulative reward loss (i.e., the regret) are available. In this paper, we describe LinConTS, a TS-based algorithm for bandits that place a linear constraint on the probability of earning a reward in every …
Recent advances in contextual bandit optimization and reinforcement learning have garnered interest in applying these methods to real-world sequential decision making problems. Real-world applications frequently have constraints with respect to a currently deployed policy. Many of the existing constraint-aware algorithms consider problems with a single objective (the reward) and a constraint on the reward with respect to a baseline policy. However, many important applications involve multiple competing objectives and auxiliary constraints. In this paper, we propose a novel Thompson sampling al…
