In many fields such as digital marketing, healthcare, finance, and robotics, it is common to have a well-tested and reliable baseline policy running in production (e.g., a recommender system). Nonetheless, the baseline policy is often suboptimal. In this case, it is desirable to deploy online learning algorithms (e.g., a multi-armed bandit algorithm) that interact with the system to learn a better/optimal policy under the constraint that during the learning process the performance is almost never worse than the performance of the baseline itself. In this paper, we study the conservative learning problem in the contextual linear bandit setting and introduce a novel algorithm, the Conservative Constrained LinUCB (CLUCB2). We derive regret bounds for CLUCB2 that match existing results and empirically show that it outperforms state-of-the-art conservative bandit algorithms in a number of synthetic and real-world problems. Finally, we consider a more realistic constraint where the performance is verified only at predefined checkpoints (instead of at every step) and show how this relaxed constraint favorably impacts the regret and empirical performance of CLUCB2.
Peking University（北京大学）；University of California, Berkeley（加州大学伯克利分校）；Facebook AI Research（脸书人工智能研究院）；University of Washington（华盛顿大学）
In this paper, we present a reduction-based framework for conservative bandits and RL, in which our core technique is to calculate the necessary and sufficient budget obtained from running the baseline policy. For lower bounds, we improve the existing lower bound for conservative multi-armed bandits and obtain new lower bounds for conservative linear bandits, tabular RL and low-rank MDP, through a black-box reduction that turns a certain lower bound in the nonconservative setting into a new lower bound in the conservative setting. For upper bounds, in multi-armed bandits, linear bandits and ta…
Conservative mechanism is a desirable property in decision-making problems which balance the tradeoff between the exploration and exploitation. We propose the novel \emph{conservative contextual combinatorial cascading bandit ($C^4$-bandit)}, a cascading online learning game which incorporates the conservative mechanism. At each time step, the learning agent is given some contexts and has to recommend a list of items but not worse than the base strategy and then observes the reward by some stopping rules. We design the $C^4$-UCB algorithm to solve the problem and prove its n-step upper regret …
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,…
In this paper, we study a family of conservative bandit problems (CBPs) with sample-path reward constraints, i.e., the learner's reward performance must be at least as well as a given baseline at any time. We propose a One-Size-Fits-All solution to CBPs and present its applications to three encompassed problems, i.e. conservative multi-armed bandits (CMAB), conservative linear bandits (CLB) and conservative contextual combinatorial bandits (CCCB). Different from previous works which consider high probability constraints on the expected reward, we focus on a sample-path constraint on the actual…
Safety is a desirable property that can immensely increase the applicability of learning algorithms in real-world decision-making problems. It is much easier for a company to deploy an algorithm that is safe, i.e., guaranteed to perform at least as well as a baseline. In this paper, we study the issue of safety in contextual linear bandits that have application in many different fields including personalized ad recommendation in online marketing. We formulate a notion of safety for this class of algorithms. We develop a safe contextual linear bandit algorithm, called conservative linear UCB (C…
Institut de Mathématiques de Toulouse, Université de Toulouse（图卢兹大学图卢兹数学研究所）；IRT Saint Exupéry（圣埃克絮佩里技术研究院）
We present a new algorithm based on an gradient ascent for a general Active Exploration bandit problem in the fixed confidence setting. This problem encompasses several well studied problems such that the Best Arm Identification or Thresholding Bandits. It consists of a new sampling rule based on an online lazy mirror ascent. We prove that this algorithm is asymptotically optimal and, most importantly, computationally efficient.
University of Maryland（马里兰大学）；Microsoft Research（微软研究院）
We describe MELEE, a meta-learning algorithm for learning a good exploration policy in the interactive contextual bandit setting. Here, an algorithm must take actions based on contexts, and learn based only on a reward signal from the action taken, thereby generating an exploration/exploitation trade-off. MELEE addresses this trade-off by learning a good exploration strategy for offline tasks based on synthetic data, on which it can simulate the contextual bandit setting. Based on these simulations, MELEE uses an imitation learning strategy to learn a good exploration policy that can then be a…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
In this paper, we propose a novel neural exploration strategy in contextual bandits, EE-Net, distinct from the standard UCB-based and TS-based approaches. Contextual multi-armed bandits have been studied for decades with various applications. To solve the exploitation-exploration tradeoff in bandits, there are three main techniques: epsilon-greedy, Thompson Sampling (TS), and Upper Confidence Bound (UCB). In recent literature, linear contextual bandits have adopted ridge regression to estimate the reward function and combine it with TS or UCB strategies for exploration. However, this line of w…
University of California, Los Angeles（加州大学洛杉矶分校）；Purdue University（普渡大学）
We propose a new bootstrap-based online algorithm for stochastic linear bandit problems. The key idea is to adopt residual bootstrap exploration, in which the agent estimates the next step reward by re-sampling the residuals of mean reward estimate. Our algorithm, residual bootstrap exploration for stochastic linear bandit (\texttt{LinReBoot}), estimates the linear reward from its re-sampling distribution and pulls the arm with the highest reward estimate. In particular, we contribute a theoretical framework to demystify residual bootstrap-based exploration mechanisms in stochastic linear band…
Department of Statistics, Purdue University（普渡大学统计系）；Department of Electrical Engineering, Princeton University（普林斯顿大学电气工程系）；Purdue University（普渡大学）；Princeton University（普林斯顿大学）
In this paper, we propose a novel perturbation-based exploration method in bandit algorithms with bounded or unbounded rewards, called residual bootstrap exploration (\texttt{ReBoot}). The \texttt{ReBoot} enforces exploration by injecting data-driven randomness through a residual-based perturbation mechanism. This novel mechanism captures the underlying distributional properties of fitting errors, and more importantly boosts exploration to escape from suboptimal solutions (for small sample sizes) by inflating variance level in an \textit{unconventional} way. In theory, with appropriate varianc…
IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Strasbourg University（斯特拉斯堡大学）；CNRS（法国国家科学研究中心）
We study here the problem of learning the exploration exploitation trade-off in the contextual bandit problem with linear reward function setting. In the traditional algorithms that solve the contextual bandit problem, the exploration is a parameter that is tuned by the user. However, our proposed algorithm learn to choose the right exploration parameters in an online manner based on the observed context, and the immediate reward received for the chosen action. We have presented here two algorithms that uses a bandit to find the optimal exploration of the contextual bandit algorithm, which we …
Wharton School（沃顿商学院）；Stanford Graduate School of Business（斯坦福商学院）；Stanford University（斯坦福大学）
The contextual bandit literature has traditionally focused on algorithms that address the exploration-exploitation tradeoff. In particular, greedy algorithms that exploit current estimates without any exploration may be sub-optimal in general. However, exploration-free greedy algorithms are desirable in practical settings where exploration may be costly or unethical (e.g., clinical trials). Surprisingly, we find that a simple greedy algorithm can be rate optimal (achieves asymptotically optimal regret) if there is sufficient randomness in the observed contexts (covariates). We prove that this …
We study a novel multi-armed bandit problem that models the challenge faced by a company wishing to explore new strategies to maximize revenue whilst simultaneously maintaining their revenue above a fixed baseline, uniformly over time. While previous work addressed the problem under the weaker requirement of maintaining the revenue constraint only at a given fixed time in the future, the algorithms previously proposed are unsuitable due to their design under the more stringent constraints. We consider both the stochastic and the adversarial settings, where we propose, natural, yet novel strate…
We investigate an active pure-exploration setting, that includes best-arm identification, in the context of linear stochastic bandits. While asymptotically optimal algorithms exist for standard multi-arm bandits, the existence of such algorithms for the best-arm identification in linear bandits has been elusive despite several attempts to address it. First, we provide a thorough comparison and new insight over different notions of optimality in the linear case, including G-optimality, transductive optimality from optimal experimental design and asymptotic optimality. Second, we design the firs…
Contextual multi-armed bandit problems arise frequently in important industrial applications. Existing solutions model the context either linearly, which enables uncertainty driven (principled) exploration, or non-linearly, by using epsilon-greedy exploration policies. Here we present a deep learning framework for contextual multi-armed bandits that is both non-linear and enables principled exploration at the same time. We tackle the exploration vs. exploitation trade-off through Thompson sampling by exploiting the connection between inference time dropout and sampling from the posterior over …
University of Colorado, Boulder（科罗拉多大学博尔德分校）；University of Virginia（弗吉尼亚大学）；Clemson University（克莱姆森大学）
We study incentivized exploration for the multi-armed bandit (MAB) problem where the players receive compensation for exploring arms other than the greedy choice and may provide biased feedback on reward. We seek to understand the impact of this drifted reward feedback by analyzing the performance of three instantiations of the incentivized MAB algorithm: UCB, $\varepsilon$-Greedy, and Thompson Sampling. Our results show that they all achieve $\mathcal{O}(\log T)$ regret and compensation under the drifted reward, and are therefore effective in incentivizing exploration. Numerical examples are …
University of Virginia（弗吉尼亚大学）；Google Research（谷歌研究院）
We propose a bandit algorithm that explores purely by randomizing its past observations. In particular, the sufficient optimism in the mean reward estimates is achieved by exploiting the variance in the past observed rewards. We name the algorithm Capitalizing On Rewards (CORe). The algorithm is general and can be easily applied to different bandit settings. The main benefit of CORe is that its exploration is fully data-dependent. It does not rely on any external noise and adapts to different problems without parameter tuning. We derive a $\tilde O(d\sqrt{n\log K})$ gap-free bound on the $n$-r…
Carnegie Mellon University（卡内基梅隆大学）；H. John Heinz III College, Carnegie Mellon University（卡内基梅隆大学H.约翰·海因茨三世学院）；School of Computer Science, Carnegie Mellon University（卡内基梅隆大学计算机科学学院）
Contextual bandit learning is an increasingly popular approach to optimizing recommender systems via user feedback, but can be slow to converge in practice due to the need for exploring a large feature space. In this paper, we propose a coarse-to-fine hierarchical approach for encoding prior knowledge that drastically reduces the amount of exploration required. Intuitively, user preferences can be reasonably embedded in a coarse low-dimensional feature space that can be explored efficiently, requiring exploration in the high-dimensional space only as necessary. We introduce a bandit algorithm …
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Google Research（谷歌研究院）
We study the stochastic contextual bandit problem, where the reward is generated from an unknown function with additive noise. No assumption is made about the reward function other than boundedness. We propose a new algorithm, NeuralUCB, which leverages the representation power of deep neural networks and uses a neural network-based random feature mapping to construct an upper confidence bound (UCB) of reward for efficient exploration. We prove that, under standard assumptions, NeuralUCB achieves $\tilde O(\sqrt{T})$ regret, where $T$ is the number of rounds. To the best of our knowledge, it i…
UC San Diego（加州大学圣地亚哥分校）；West Virginia University（西弗吉尼亚大学）
We propose a novel modification of the standard upper confidence bound (UCB) method for the stochastic multi-armed bandit (MAB) problem which tunes the confidence bound of a given bandit based on its distance to others. Our UCB distance tuning (UCB-DT) formulation enables improved performance as measured by expected regret by preventing the MAB algorithm from focusing on non-optimal bandits which is a well-known deficiency of standard UCB. "Distance tuning" of the standard UCB is done using a proposed distance measure, which we call bandit distance, that is parameterizable and which therefore …
University of California, Los Angeles（加州大学洛杉矶分校）；DeepMind（深度思考（DeepMind））；Adobe Research（Adobe研究院）
We study a general class of contextual bandits, where each context-action pair is associated with a raw feature vector, but the reward generating function is unknown. We propose a novel learning algorithm that transforms the raw feature vector using the last hidden layer of a deep ReLU neural network (deep representation learning), and uses an upper confidence bound (UCB) approach to explore in the last linear layer (shallow exploration). We prove that under standard assumptions, our proposed algorithm achieves $\tilde{O}(\sqrt{T})$ finite-time regret, where $T$ is the learning time horizon. C…
Twitter Inc.（推特公司）；University of California, Davis（加州大学戴维斯分校）
In this paper, we propose and study opportunistic bandits - a new variant of bandits where the regret of pulling a suboptimal arm varies under different environmental conditions, such as network load or produce price. When the load/price is low, so is the cost/regret of pulling a suboptimal arm (e.g., trying a suboptimal network configuration). Therefore, intuitively, we could explore more when the load/price is low and exploit more when the load/price is high. Inspired by this intuition, we propose an Adaptive Upper-Confidence-Bound (AdaUCB) algorithm to adaptively balance the exploration-exp…
CREST（法国经济与统计研究中心）；ENSAE Paris（巴黎国立统计与经济管理学院）；London School of Economics（伦敦政治经济学院）；Criteo AI Lab（Criteo人工智能实验室）
Finding an optimal matching in a weighted graph is a standard combinatorial problem. We consider its semi-bandit version where either a pair or a full matching is sampled sequentially. We prove that it is possible to leverage a rank-1 assumption on the adjacency matrix to reduce the sample complexity and the regret of off-the-shelf algorithms up to reaching a linear dependency in the number of vertices (up to poly log terms).
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（中央理工学院里尔分校）；UMR 9198-CRIStAL（UMR 9198-CRIStAL研究所）；F-59000 Lille France（法国里尔59000）
In this paper we propose the first multi-armed bandit algorithm based on re-sampling that achieves asymptotically optimal regret simultaneously for different families of arms (namely Bernoulli, Gaussian and Poisson distributions). Unlike Thompson Sampling which requires to specify a different prior to be optimal in each case, our proposal RB-SDA does not need any distribution-dependent tuning. RB-SDA belongs to the family of Sub-sampling Duelling Algorithms (SDA) which combines the sub-sampling idea first used by the BESA [1] and SSMC [2] algorithms with different sub-sampling schemes. In part…
University of California, Davis（加州大学戴维斯分校）；University of California, Los Angeles（加州大学洛杉矶分校）
The stochastic contextual bandit problem, which models the trade-off between exploration and exploitation, has many real applications, including recommender systems, online advertising and clinical trials. As many other machine learning algorithms, contextual bandit algorithms often have one or more hyper-parameters. As an example, in most optimal stochastic contextual bandit algorithms, there is an unknown exploration parameter which controls the trade-off between exploration and exploitation. A proper choice of the hyper-parameters is essential for contextual bandit algorithms to perform wel…
Mortal bandits have proven to be extremely useful for providing news article recommendations, running automated online advertising campaigns, and for other applications where the set of available options changes over time. Previous work on this problem showed how to regulate exploration of new arms when they have recently appeared, but they do not adapt when the arms are about to disappear. Since in most applications we can determine either exactly or approximately when arms will disappear, we can leverage this information to improve performance: we should not be exploring arms that are about …
Designing efficient exploration is central to Reinforcement Learning due to the fundamental problem posed by the exploration-exploitation dilemma. Bayesian exploration strategies like Thompson Sampling resolve this trade-off in a principled way by modeling and updating the distribution of the parameters of the action-value function, the outcome model of the environment. However, this technique becomes infeasible for complex environments due to the computational intractability of maintaining probability distributions over parameters of outcome models of corresponding complexity. Moreover, the a…
We introduce the model selection problem in pure exploration linear bandits, where the learner needs to adapt to the instance-dependent complexity measure of the smallest hypothesis class containing the true model. We design algorithms in both fixed confidence and fixed budget settings with near instance optimal guarantees. The core of our algorithms is a new optimization problem based on experimental design that leverages the geometry of the action set to identify a near-optimal hypothesis class. Our fixed budget algorithm is developed based on a novel selection-validation procedure, which pr…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of California, Los Angeles（加州大学洛杉矶分校）；University of Chicago（芝加哥大学）
We study pure exploration in bandits, where the dimension of the feature representation can be much larger than the number of arms. To overcome the curse of dimensionality, we propose to adaptively embed the feature representation of each arm into a lower-dimensional space and carefully deal with the induced model misspecification. Our approach is conceptually very different from existing works that can either only handle low-dimensional linear bandits or passively deal with model misspecification. We showcase the application of our approach to two pure exploration settings that were previousl…
Google Research（谷歌研究院）；DeepMind（深度思维）；University of Alberta（阿尔伯塔大学）
Exploration policies in Bayesian bandits maximize the average reward over problem instances drawn from some distribution $\mathcal{P}$. In this work, we learn such policies for an unknown distribution $\mathcal{P}$ using samples from $\mathcal{P}$. Our approach is a form of meta-learning and exploits properties of $\mathcal{P}$ without making strong assumptions about its form. To do this, we parameterize our policies in a differentiable way and optimize them by policy gradients, an approach that is general and easy to implement. We derive effective gradient estimators and introduce novel varia…
Combinatorial bandits with semi-bandit feedback generalize multi-armed bandits, where the agent chooses sets of arms and observes a noisy reward for each arm contained in the chosen set. The action set satisfies a given structure such as forming a base of a matroid or a path in a graph. We focus on the pure-exploration problem of identifying the best arm with fixed confidence, as well as a more general setting, where the structure of the answer set differs from the one of the action set. Using the recently popularized game framework, we interpret this problem as a sequential zero-sum game and …
Contextual bandits can solve a huge range of real-world problems. However, current popular algorithms to solve them either rely on linear models, or unreliable uncertainty estimation in non-linear models, which are required to deal with the exploration-exploitation trade-off. Inspired by theories of human cognition, we introduce novel techniques that use maximum entropy exploration, relying on neural networks to find optimal policies in settings with both continuous and discrete action spaces. We present two classes of models, one with neural networks as reward estimators, and the other with e…
Google Research（谷歌研究院）；DeepMind（深度思考）；University of Alberta（阿尔伯塔大学）；Facebook AI Research（脸书人工智能研究院）
We propose an online algorithm for cumulative regret minimization in a stochastic multi-armed bandit. The algorithm adds $O(t)$ i.i.d. pseudo-rewards to its history in round $t$ and then pulls the arm with the highest average reward in its perturbed history. Therefore, we call it perturbed-history exploration (PHE). The pseudo-rewards are carefully designed to offset potentially underestimated mean rewards of arms with a high probability. We derive near-optimal gap-dependent and gap-free bounds on the $n$-round regret of PHE. The key step in our analysis is a novel argument that shows that ran…
Northeastern University（东北大学）；CNRS & CRIStAL, UMR 9189, Université de Lille（法国国家科学研究中心与里尔大学晶体实验室（UMR 9189））；Inria Lille, SequeL team（法国国家信息与自动化研究所里尔分所序列团队）
We consider the problem of near-optimal arm identification in the fixed confidence setting of the infinitely armed bandit problem when nothing is known about the arm reservoir distribution. We (1) introduce a PAC-like framework within which to derive and cast results; (2) derive a sample complexity lower bound for near-optimal arm identification; (3) propose an algorithm that identifies a nearly-optimal arm with high probability and derive an upper bound on its sample complexity which is within a log factor of our lower bound; and (4) discuss whether our log^2(1/delta) dependence is inescapabl…
Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE -- a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential family, we show that RBMLE yields an index policy. To choose the bias-growth rate $α(t)$ in RBMLE, we reveal the nontrivial interplay between $α(t)$ and the regret bound that generally applies in both the Exponential Family as well as the sub-Gaussian/Exponential family bandits. T…
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…
Google Research（谷歌研究院）；DeepMind（深度思维）；University of Alberta（阿尔伯塔大学）；Mila, University of Montreal（蒙特利尔大学米拉研究所）；Adobe Research（奥多比研究院）；Facebook AI Research（脸书人工智能研究院）
We propose a bandit algorithm that explores by randomizing its history of rewards. Specifically, it pulls the arm with the highest mean reward in a non-parametric bootstrap sample of its history with pseudo rewards. We design the pseudo rewards such that the bootstrap mean is optimistic with a sufficiently high probability. We call our algorithm Giro, which stands for garbage in, reward out. We analyze Giro in a Bernoulli bandit and derive a $O(K Δ^{-1} \log n)$ bound on its $n$-round regret, where $Δ$ is the difference in the expected rewards of the optimal and the best suboptimal arms, and $…
In this paper, we propose and study opportunistic contextual bandits - a special case of contextual bandits where the exploration cost varies under different environmental conditions, such as network load or return variation in recommendations. When the exploration cost is low, so is the actual regret of pulling a sub-optimal arm (e.g., trying a suboptimal recommendation). Therefore, intuitively, we could explore more when the exploration cost is relatively low and exploit more when the exploration cost is relatively high. Inspired by this intuition, for opportunistic contextual bandits with L…
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…
University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）
We study stage-wise conservative linear stochastic bandits: an instance of bandit optimization, which accounts for (unknown) safety constraints that appear in applications such as online advertising and medical trials. At each stage, the learner must choose actions that not only maximize cumulative reward across the entire time horizon but further satisfy a linear baseline constraint that takes the form of a lower bound on the instantaneous reward. For this problem, we present two novel algorithms, stage-wise conservative linear Thompson Sampling (SCLTS) and stage-wise conservative linear UCB …
Many physical systems have underlying safety considerations that require that the strategy deployed ensures the satisfaction of a set of constraints. Further, often we have only partial information on the state of the system. We study the problem of safe real-time decision making under uncertainty. In this paper, we formulate a conservative stochastic contextual bandit formulation for real-time decision making when an adversary chooses a distribution on the set of possible contexts and the learner is subject to certain safety/performance constraints. The learner observes only the context distr…
Motivated by real-world applications such as fast fashion retailing and online advertising, the Multinomial Logit Bandit (MNL-bandit) is a popular model in online learning and operations research, and has attracted much attention in the past decade. However, it is a bit surprising that pure exploration, a basic problem in bandit theory, has not been well studied in MNL-bandit so far. In this paper we give efficient algorithms for pure exploration in MNL-bandit. Our algorithms achieve instance-sensitive pull complexities. We also complement the upper bounds by an almost matching lower bound.
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Princeton University（普林斯顿大学）
The paper proposes a novel upper confidence bound (UCB) procedure for identifying the arm with the largest mean in a multi-armed bandit game in the fixed confidence setting using a small number of total samples. The procedure cannot be improved in the sense that the number of samples required to identify the best arm is within a constant factor of a lower bound based on the law of the iterated logarithm (LIL). Inspired by the LIL, we construct our confidence bounds to explicitly account for the infinite time horizon of the algorithm. In addition, by using a novel stopping time for the algorith…
Stanford University（斯坦福大学）；University of Pennsylvania（宾夕法尼亚大学）
A key challenge to deploying reinforcement learning in practice is avoiding excessive (harmful) exploration in individual episodes. We propose a natural constraint on exploration -- \textit{uniformly} outperforming a conservative policy (adaptively estimated from all data observed thus far), up to a per-episode exploration budget. We design a novel algorithm that uses a UCB reinforcement learning policy for exploration, but overrides it as needed to satisfy our exploration constraint with high probability. Importantly, to ensure unbiased exploration across the state space, our algorithm adapti…
Pure Exploration in Asynchronous Federated Bandits
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Yale University（耶鲁大学）；Oregon State University（俄勒冈州立大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
While learning in an unknown Markov Decision Process (MDP), an agent should trade off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward. Although the agent will eventually learn a good or optimal policy, there is no guarantee on the quality of the intermediate policies. This lack of control is undesired in real-world applications where a minimum requirement is that the executed policies are guaranteed to perform at least as well as an existing baseline. In this paper, we introduce the notion of conservative exploration for a…
