On Kernelized Multi-armed Bandits

We consider the stochastic bandit problem with a continuous set of arms, with the expected reward function over the arms assumed to be fixed but unknown. We provide two new Gaussian process-based algorithms for continuous bandit optimization-Improved GP-UCB (IGP-UCB) and GP-Thomson sampling (GP-TS), and derive corresponding regret bounds. Specifically, the bounds hold when the expected reward function belongs to the reproducing kernel Hilbert space (RKHS) that naturally corresponds to a Gaussian process kernel used as input by the algorithms. Along the way, we derive a new self-normalized concentration inequality for vector- valued martingales of arbitrary, possibly infinite, dimension. Finally, experimental evaluation and comparisons to existing algorithms on synthetic and real-world environments are carried out that highlight the favorable gains of the proposed strategies in many cases

QoS-Aware Multi-Armed Bandits

Motivated by runtime verification of QoS requirements in self-adaptive and self-organizing systems that are able to reconfigure their structure and behavior in response to runtime data, we propose a QoS-aware variant of Thompson sampling for multi-armed bandits. It is applicable in settings where QoS satisfaction of an arm has to be ensured with high confidence efficiently, rather than finding the optimal arm while minimizing regret. Preliminary experimental results encourage further research in the field of QoS-aware decision making.Comment: Accepted at IEEE Workshop on Quality Assurance for Self-adaptive Self-organising Systems, FAS* 201

Distributed Exploration in Multi-Armed Bandits

We study exploration in Multi-Armed Bandits in a setting where $k$ players collaborate in order to identify an $\epsilon$-optimal arm. Our motivation comes from recent employment of bandit algorithms in computationally intensive, large-scale applications. Our results demonstrate a non-trivial tradeoff between the number of arm pulls required by each of the players, and the amount of communication between them. In particular, our main result shows that by allowing the $k$ players to communicate only once, they are able to learn $\sqrt{k}$ times faster than a single player. That is, distributing learning to $k$ players gives rise to a factor $\sqrt{k}$ parallel speed-up. We complement this result with a lower bound showing this is in general the best possible. On the other extreme, we present an algorithm that achieves the ideal factor $k$ speed-up in learning performance, with communication only logarithmic in $1/\epsilon$

Decentralized Exploration in Multi-Armed Bandits

We consider the decentralized exploration problem: a set of players collaborate to identify the best arm by asynchronously interacting with the same stochastic environment. The objective is to insure privacy in the best arm identification problem between asynchronous, collaborative, and thrifty players. In the context of a digital service, we advocate that this decentralized approach allows a good balance between the interests of users and those of service providers: the providers optimize their services, while protecting the privacy of the users and saving resources. We define the privacy level as the amount of information an adversary could infer by intercepting the messages concerning a single user. We provide a generic algorithm Decentralized Elimination, which uses any best arm identification algorithm as a subroutine. We prove that this algorithm insures privacy, with a low communication cost, and that in comparison to the lower bound of the best arm identification problem, its sample complexity suffers from a penalty depending on the inverse of the probability of the most frequent players. Then, thanks to the genericity of the approach, we extend the proposed algorithm to the non-stationary bandits. Finally, experiments illustrate and complete the analysis