Factored Bandits

We introduce the factored bandits model, which is a framework for learning with limited (bandit) feedback, where actions can be decomposed into a Cartesian product of atomic actions. Factored bandits incorporate rank-1 bandits as a special case, but significantly relax the assumptions on the form of the reward function. We provide an anytime algorithm for stochastic factored bandits and up to constants matching upper and lower regret bounds for the problem. Furthermore, we show that with a slight modification the proposed algorithm can be applied to utility based dueling bandits. We obtain an improvement in the additive terms of the regret bound compared to state of the art algorithms (the additive terms are dominating up to time horizons which are exponential in the number of arms)

First-order regret bounds for combinatorial semi-bandits

We consider the problem of online combinatorial optimization under semi-bandit feedback, where a learner has to repeatedly pick actions from a combinatorial decision set in order to minimize the total losses associated with its decisions. After making each decision, the learner observes the losses associated with its action, but not other losses. For this problem, there are several learning algorithms that guarantee that the learner's expected regret grows as $\widetilde{O}(\sqrt{T})$ with the number of rounds $T$. In this paper, we propose an algorithm that improves this scaling to $\widetilde{O}(\sqrt{{L_T^*}})$, where $L_T^*$ is the total loss of the best action. Our algorithm is among the first to achieve such guarantees in a partial-feedback scheme, and the first one to do so in a combinatorial setting.Comment: To appear at COLT 201

Differentially Private Federated Combinatorial Bandits with Constraints

There is a rapid increase in the cooperative learning paradigm in online learning settings, i.e., federated learning (FL). Unlike most FL settings, there are many situations where the agents are competitive. Each agent would like to learn from others, but the part of the information it shares for others to learn from could be sensitive; thus, it desires its privacy. This work investigates a group of agents working concurrently to solve similar combinatorial bandit problems while maintaining quality constraints. Can these agents collectively learn while keeping their sensitive information confidential by employing differential privacy? We observe that communicating can reduce the regret. However, differential privacy techniques for protecting sensitive information makes the data noisy and may deteriorate than help to improve regret. Hence, we note that it is essential to decide when to communicate and what shared data to learn to strike a functional balance between regret and privacy. For such a federated combinatorial MAB setting, we propose a Privacy-preserving Federated Combinatorial Bandit algorithm, P-FCB. We illustrate the efficacy of P-FCB through simulations. We further show that our algorithm provides an improvement in terms of regret while upholding quality threshold and meaningful privacy guarantees.Comment: 12 pages, 4 Figures, A version of this paper has appeared in the Proceedings of the ECML PKDD '2

An ADMM Based Framework for AutoML Pipeline Configuration

We study the AutoML problem of automatically configuring machine learning pipelines by jointly selecting algorithms and their appropriate hyper-parameters for all steps in supervised learning pipelines. This black-box (gradient-free) optimization with mixed integer & continuous variables is a challenging problem. We propose a novel AutoML scheme by leveraging the alternating direction method of multipliers (ADMM). The proposed framework is able to (i) decompose the optimization problem into easier sub-problems that have a reduced number of variables and circumvent the challenge of mixed variable categories, and (ii) incorporate black-box constraints along-side the black-box optimization objective. We empirically evaluate the flexibility (in utilizing existing AutoML techniques), effectiveness (against open source AutoML toolkits),and unique capability (of executing AutoML with practically motivated black-box constraints) of our proposed scheme on a collection of binary classification data sets from UCI ML& OpenML repositories. We observe that on an average our framework provides significant gains in comparison to other AutoML frameworks (Auto-sklearn & TPOT), highlighting the practical advantages of this framework

An Efficient Bandit Algorithm for Realtime Multivariate Optimization

Optimization is commonly employed to determine the content of web pages, such as to maximize conversions on landing pages or click-through rates on search engine result pages. Often the layout of these pages can be decoupled into several separate decisions. For example, the composition of a landing page may involve deciding which image to show, which wording to use, what color background to display, etc. Such optimization is a combinatorial problem over an exponentially large decision space. Randomized experiments do not scale well to this setting, and therefore, in practice, one is typically limited to optimizing a single aspect of a web page at a time. This represents a missed opportunity in both the speed of experimentation and the exploitation of possible interactions between layout decisions. Here we focus on multivariate optimization of interactive web pages. We formulate an approach where the possible interactions between different components of the page are modeled explicitly. We apply bandit methodology to explore the layout space efficiently and use hill-climbing to select optimal content in realtime. Our algorithm also extends to contextualization and personalization of layout selection. Simulation results show the suitability of our approach to large decision spaces with strong interactions between content. We further apply our algorithm to optimize a message that promotes adoption of an Amazon service. After only a single week of online optimization, we saw a 21% conversion increase compared to the median layout. Our technique is currently being deployed to optimize content across several locations at Amazon.com.Comment: KDD'17 Audience Appreciation Awar