First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper studies the multi-armed bandit problem where they have a set of relevant features; and the expected reward of an action is a Lipschitz continuous of relevant features. This is also a feature selection problem where you have a set of features but only r of them are relevant (the target function only depends on r of these features): here each arm has only one relevant feature, meaning the function representing the arm payoff depending on only one feature and we do not know which one. They propose an algorithm and get the bound for such adaptive case; but their regret is higher than what you would get if someone tells you the relevant type. Q2: Please summarize your review in 1-2 sentences This paper makes a small step towards understanding the problem of having a subset of features being relevant for a given arm which itself is certainly an interesting problem: they study the bandit problem only for one relevant feature per arm and did not give the optimal rate. Potentially, they could go with all arbitrary number of relevant features and figure out the optimal regret.

In this paper we consider the problem of learning online what is the information to consider when making sequential decisions. We formalize this as a contextual multi-armed bandit problem where a high dimensional (D-dimensional) context vector arrives to a learner which needs to select an action to maximize its expected reward at each time step. Each dimension of the context vector is called a type. We assume that there exists an unknown relation between actions and types, called the relevance relation, such that the reward of an action only depends on the contexts of the relevant types. When the relation is a function, i.e., the reward of an action only depends on the context of a single type, and the expected reward of an action is Lipschitz continuous in the context of its relevant type, we propose an algorithm that achieves Õ(T

In this paper we consider the problem of learning online what is the information to consider when making sequential decisions. We formalize this as a contextual multi-armed bandit problem where a high dimensional (D-dimensional) context vector arrives to a learner which needs to select an action to maximize its expected reward at each time step. Each dimension of the context vector is called a type. We assume that there exists an unknown relation between actions and types, called the relevance relation, such that the reward of an action only depends on the contexts of the relevant types. When the relation is a function, i.e., the reward of an action only depends on the context of a single type, and the expected reward of an action is Lipschitz continuous in the context of its relevant type, we propose an algorithm that achieves Õ(T

Recommender systems, medical diagnosis, network security, etc., require on-going learning and decision-making in real time. These -- and many others -- represent perfect examples of the opportunities and difficulties presented by Big Data: the available information often arrives from a variety of sources and has diverse features so that learning from all the sources may be valuable but integrating what is learned is subject to the curse of dimensionality. This paper develops and analyzes algorithms that allow efficient learning and decision-making while avoiding the curse of dimensionality. We formalize the information available to the learner/decision-maker at a particular time as a context vector which the learner should consider when taking actions. In general the context vector is very high dimensional, but in many settings, the most relevant information is embedded into only a few relevant dimensions. If these relevant dimensions were known in advance, the problem would be simple -- but they are not. Moreover, the relevant dimensions may be different for different actions. Our algorithm learns the relevant dimensions for each action, and makes decisions based in what it has learned. Formally, we build on the structure of a contextual multi-armed bandit by adding and exploiting a relevance relation. We prove a general regret bound for our algorithm whose time order depends only on the maximum number of relevant dimensions among all the actions, which in the special case where the relevance relation is single-valued (a function), reduces to $\tilde{O}(T^{2(\sqrt{2}-1)})$; in the absence of a relevance relation, the best known contextual bandit algorithms achieve regret $\tilde{O}(T^{(D+1)/(D+2)})$, where $D$ is the full dimension of the context vector.

In this paper we consider the problem of learning online what is the information to consider when making sequential decisions. We formalize this as a contextual multi-armed bandit problem where a high dimensional ($D$-dimensional) context vector arrives to a learner which needs to select an action to maximize its expected reward at each time step. Each dimension of the context vector is called a type. We assume that there exists an unknown relation between actions and types, called the relevance relation, such that the reward of an action only depends on the contexts of the relevant types. When the relation is a function, i.e., the reward of an action only depends on the context of a single type, and the expected reward of an action is Lipschitz continuous in the context of its relevant type, we propose an algorithm that achieves $\tilde{O}(T^{\gamma})$ regret with a high probability, where $\gamma=2/(1+\sqrt{2})$. Our algorithm achieves this by learning the unknown relevance relation, whereas prior contextual bandit algorithms that do not exploit the existence of a relevance relation will have $\tilde{O}(T^{(D+1)/(D+2)})$ regret. Our algorithm alternates between exploring and exploiting, it does not require reward observations in exploitations, and it guarantees with a high probability that actions with suboptimality greater than $\epsilon$ are never selected in exploitations. Our proposed method can be applied to a variety of learning applications including medical diagnosis, recommender systems, popularity prediction from social networks, network security etc., where at each instance of time vast amounts of different types of information are available to the decision maker, but the effect of an action depends only on a single type.