### Semiparametric Contextual Bandits

This paper studies semiparametric contextual bandits, a generalization of the linear stochastic bandit problem where the reward for an action is modeled as a linear function of known action features confounded by an non-linear action-independent term. We design new algorithms that achieve $\tilde{O}(d\sqrt{T})$ regret over $T$ rounds, when the linear function is $d$-dimensional, which matches the best known bounds for the simpler unconfounded case and improves on a recent result of Greenewald et al. (2017). Via an empirical evaluation, we show that our algorithms outperform prior approaches when there are non-linear confounding effects on the rewards. Technically, our algorithms use a new reward estimator inspired by doubly-robust approaches and our proofs require new concentration inequalities for self-normalized martingales.

### Efficient Ordered Combinatorial Semi-Bandits for Whole-Page Recommendation

Multi-Armed Bandit (MAB) framework has been successfully applied in many web applications. However, many complex real-world applications that involve multiple content recommendations cannot fit into the traditional MAB setting. To address this issue, we consider an ordered combinatorial semi-bandit problem where the learner recommends S actions from a base set of K actions, and displays the results in S (out of M ) different positions. The aim is to maximize the cumulative reward with respect to the best possible subset and positions in hindsight. By the adaptation of a minimum-cost maximum-flow network, a practical algorithm based on Thompson sampling is derived for the (contextual) combinatorial problem, thus resolving the problem of computational intractability.With its potential to work with whole-page recommendation and any probabilistic models, to illustrate the effectiveness of our method, we focus on Gaussian process optimization and a contextual setting where click-through rate is predicted using logistic regression. We demonstrate the algorithms’ performance on synthetic Gaussian process problems and on large-scale news article recommendation datasets from Yahoo! Front Page Today Module.

### Contextual Combinatorial Multi-armed Bandits with Volatile Arms and Submodular Reward

In this paper, we study the stochastic contextual combinatorial multi-armed bandit (CC-MAB) framework that is tailored for volatile arms and submodular reward functions. CC-MAB inherits properties from both contextual bandit and combinatorial bandit: it aims to select a set of arms in each round based on the side information (a.k.a. context) associated with the arms. By volatile arms'', we mean that the available arms to select from in each round may change; and by submodular rewards'', we mean that the total reward achieved by selected arms is not a simple sum of individual rewards but demonstrates a feature of diminishing returns determined by the relations between selected arms (e.g. relevance and redundancy). Volatile arms and submodular rewards are often seen in many real-world applications, e.g. recommender systems and crowdsourcing, in which multi-armed bandit (MAB) based strategies are extensively applied. Although there exist works that investigate these issues separately based on standard MAB, jointly considering all these issues in a single MAB problem requires very different algorithm design and regret analysis. Our algorithm CC-MAB provides an online decision-making policy in a contextual and combinatorial bandit setting and effectively addresses the issues raised by volatile arms and submodular reward functions. The proposed algorithm is proved to achieve $O(cT^{\frac{2\alpha+D}{3\alpha + D}}\log(T))$ regret after a span of $T$ rounds. The performance of CC-MAB is evaluated by experiments conducted on a real-world crowdsourcing dataset, and the result shows that our algorithm outperforms the prior art.

### Contextual Combinatorial Multi-armed Bandits with Volatile Arms and Submodular Reward

In this paper, we study the stochastic contextual combinatorial multi-armed bandit (CC-MAB) framework that is tailored for volatile arms and submodular reward functions. CC-MAB inherits properties from both contextual bandit and combinatorial bandit: it aims to select a set of arms in each round based on the side information (a.k.a. context) associated with the arms. By volatile arms'', we mean that the available arms to select from in each round may change; and by submodular rewards'', we mean that the total reward achieved by selected arms is not a simple sum of individual rewards but demonstrates a feature of diminishing returns determined by the relations between selected arms (e.g. relevance and redundancy). Volatile arms and submodular rewards are often seen in many real-world applications, e.g. recommender systems and crowdsourcing, in which multi-armed bandit (MAB) based strategies are extensively applied. Although there exist works that investigate these issues separately based on standard MAB, jointly considering all these issues in a single MAB problem requires very different algorithm design and regret analysis. Our algorithm CC-MAB provides an online decision-making policy in a contextual and combinatorial bandit setting and effectively addresses the issues raised by volatile arms and submodular reward functions. The proposed algorithm is proved to achieve $O(cT^{\frac{2\alpha+D}{3\alpha + D}}\log(T))$ regret after a span of $T$ rounds. The performance of CC-MAB is evaluated by experiments conducted on a real-world crowdsourcing dataset, and the result shows that our algorithm outperforms the prior art.

### Context Attentive Bandits: Contextual Bandit with Restricted Context

We consider a novel formulation of the multi-armed bandit model, which we call the contextual bandit with restricted context, where only a limited number of features can be accessed by the learner at every iteration. This novel formulation is motivated by different online problems arising in clinical trials, recommender systems and attention modeling. Herein, we adapt the standard multi-armed bandit algorithm known as Thompson Sampling to take advantage of our restricted context setting, and propose two novel algorithms, called the Thompson Sampling with Restricted Context(TSRC) and the Windows Thompson Sampling with Restricted Context(WTSRC), for handling stationary and nonstationary environments, respectively. Our empirical results demonstrate advantages of the proposed approaches on several real-life datasets