We initiate the study of learning in contextual bandits with the help of loss predictors. The main question we address is whether one can improve over the minimax regret $\mathcal{O}(\sqrt{T})$ for learning over $T$ rounds, when the total error of the predictor $\mathcal{E} \leq T$ is relatively small. We provide a complete answer to this question, including upper and lower bounds for various settings: adversarial versus stochastic environments, known versus unknown $\mathcal{E}$, and single versus multiple predictors. We show several surprising results, such as 1) the optimal regret is $\mathcal{O}(\min\{\sqrt{T}, \sqrt{\mathcal{E}}T^\frac{1}{4}\})$ when $\mathcal{E}$ is known, a sharp contrast to the standard and better bound $\mathcal{O}(\sqrt{\mathcal{E}})$ for non-contextual problems (such as multi-armed bandits); 2) the same bound cannot be achieved if $\mathcal{E}$ is unknown, but as a remedy, $\mathcal{O}(\sqrt{\mathcal{E}}T^\frac{1}{3})$ is achievable; 3) with $M$ predictors, a linear dependence on $M$ is necessary, even if logarithmic dependence is possible for non-contextual problems.
We also develop several novel algorithmic techniques to achieve matching upper bounds, including 1) a key action remapping technique for optimal regret with known $\mathcal{E}$, 2) implementing Catoni's robust mean estimator efficiently via an ERM oracle leading to an efficient algorithm in the stochastic setting with optimal regret, 3) constructing an underestimator for $\mathcal{E}$ via estimating the histogram with bins of exponentially increasing size for the stochastic setting with unknown $\mathcal{E}$, and 4) a self-referential scheme for learning with multiple predictors, all of which might be of independent interest.
We study the setting of optimizing with bandit feedback with additional prior knowledge provided to the learner in the form of an initial hint of the optimal action. We present a novel algorithm for stochastic linear bandits that uses this hint to improve its regret to $\tilde O(\sqrt{T})$ when the hint is accurate, while maintaining a minimax-optimal $\tilde O(d\sqrt{T})$ regret independent of the quality of the hint. Furthermore, we provide a Pareto frontier of tight tradeoffs between best-case and worst-case regret, with matching lower bounds. Perhaps surprisingly, our work shows that lever…
University of Trento（特伦托大学）；Aarhus University（奥胡斯大学）
We introduce Explearn, an online algorithm that learns to jointly output predictions and explanations for those predictions. Explearn leverages Gaussian Processes (GP)-based contextual bandits. This brings two key benefits. First, GPs naturally capture different kinds of explanations and enable the system designer to control how explanations generalize across the space by virtue of choosing a suitable kernel. Second, Explearn builds on recent results in contextual bandits which guarantee convergence with high probability. Our initial experiments hint at the promise of the approach.
We investigate the sample complexity of learning the optimal arm for multi-task bandit problems. Arms consist of two components: one that is shared across tasks (that we call representation) and one that is task-specific (that we call predictor). The objective is to learn the optimal (representation, predictor)-pair for each task, under the assumption that the optimal representation is common to all tasks. Within this framework, efficient learning algorithms should transfer knowledge across tasks. We consider the best-arm identification problem for a fixed confidence, where, in each round, the…
Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）；University of Chicago（芝加哥大学）
We present a family $\{\hatπ\}_{p\ge 1}$ of pessimistic learning rules for offline learning of linear contextual bandits, relying on confidence sets with respect to different $\ell_p$ norms, where $\hatπ_2$ corresponds to Bellman-consistent pessimism (BCP), while $\hatπ_\infty$ is a novel generalization of lower confidence bound (LCB) to the linear setting. We show that the novel $\hatπ_\infty$ learning rule is, in a sense, adaptively optimal, as it achieves the minimax performance (up to log factors) against all $\ell_q$-constrained problems, and as such it strictly dominates all other predic…
Carnegie Mellon University（卡内基梅隆大学）；Université de Montréal（蒙特利尔大学）；Adobe Research（Adobe研究院）
Most recommender systems recommend a list of items. The user examines the list, from the first item to the last, and often chooses the first attractive item and does not examine the rest. This type of user behavior can be modeled by the cascade model. In this work, we study cascading bandits, an online learning variant of the cascade model where the goal is to recommend $K$ most attractive items from a large set of $L$ candidate items. We propose two algorithms for solving this problem, which are based on the idea of linear generalization. The key idea in our solutions is that we learn a predi…
In a multi-armed bandit (MAB) problem, an online algorithm makes a sequence of choices. In each round it chooses from a time-invariant set of alternatives and receives the payoff associated with this alternative. While the case of small strategy sets is by now well-understood, a lot of recent work has focused on MAB problems with exponentially or infinitely large strategy sets, where one needs to assume extra structure in order to make the problem tractable. In particular, recent literature considered information on similarity between arms. We consider similarity information in the setting of …
Focusing on Random Forests, we propose a multi-armed contextual bandit recommendation framework for feature-based selection of a single shallow tree of the learned ensemble. The trained system, which works on top of the Random Forest, dynamically identifies a base predictor that is responsible for providing the final output. In this way, we obtain local interpretations by observing the rules of the recommended tree. The carried out experiments reveal that our dynamic method is superior to an independent fitted CART decision tree and comparable to the whole black-box Random Forest in terms of p…
University of Twente（特文特大学）；University of Oxford（牛津大学）；Bocconi University（博科尼大学）；Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；IN2P3 Computing Center / CNRS（法国国家核物理与粒子物理研究所计算中心/法国国家科学研究中心）
Thompson sampling is a heuristic algorithm for the multi-armed bandit problem which has a long tradition in machine learning. The algorithm has a Bayesian spirit in the sense that it selects arms based on posterior samples of reward probabilities of each arm. By forging a connection between combinatorial binary bandits and spike-and-slab variable selection, we propose a stochastic optimization approach to subset selection called Thompson Variable Selection (TVS). TVS is a framework for interpretable machine learning which does not rely on the underlying model to be linear. TVS brings together …
Adapter-Augmented Bandits for Online Multi-Constrained Multi-Modal Inference Scheduling
School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510006, China.（中山大学计算机科学与工程学院）；School of Computing, Macquarie University, NSW 2109, Australia（麦考瑞大学计算机学院）
University of Utah（犹他大学）；Google Research（谷歌研究院）；Duke University（杜克大学）
We consider the classic online learning and stochastic multi-armed bandit (MAB) problems, when at each step, the online policy can probe and find out which of a small number ($k$) of choices has better reward (or loss) before making its choice. In this model, we derive algorithms whose regret bounds have exponentially better dependence on the time horizon compared to the classic regret bounds. In particular, we show that probing with $k=2$ suffices to achieve time-independent regret bounds for online linear and convex optimization. The same number of probes improve the regret bound of stochast…
Cornell University（康奈尔大学）；Google Research（谷歌研究院）；University of Southern California（南加州大学）；New York University（纽约大学）
Learning linear predictors with the logistic loss---both in stochastic and online settings---is a fundamental task in machine learning and statistics, with direct connections to classification and boosting. Existing "fast rates" for this setting exhibit exponential dependence on the predictor norm, and Hazan et al. (2014) showed that this is unfortunately unimprovable. Starting with the simple observation that the logistic loss is $1$-mixable, we design a new efficient improper learning algorithm for online logistic regression that circumvents the aforementioned lower bound with a regret bound…
This paper considers a variant of the online paging problem, where the online algorithm has access to multiple predictors, each producing a sequence of predictions for the page arrival times. The predictors may have occasional prediction errors and it is assumed that at least one of them makes a sublinear number of prediction errors in total. Our main result states that this assumption suffices for the design of a randomized online algorithm whose time-average regret with respect to the optimal offline algorithm tends to zero as the time tends to infinity. This holds (with different regret bou…
