A Neural Networks Committee for the Contextual Bandit Problem

This paper presents a new contextual bandit algorithm, NeuralBandit, which does not need hypothesis on stationarity of contexts and rewards. Several neural networks are trained to modelize the value of rewards knowing the context. Two variants, based on multi-experts approach, are proposed to choose online the parameters of multi-layer perceptrons. The proposed algorithms are successfully tested on a large dataset with and without stationarity of rewards.Comment: 21st International Conference on Neural Information Processin

One Arrow, Two Kills: An Unified Framework for Achieving Optimal Regret Guarantees in Sleeping Bandits

We address the problem of \emph{`Internal Regret'} in \emph{Sleeping Bandits} in the fully adversarial setup, as well as draw connections between different existing notions of sleeping regrets in the multiarmed bandits (MAB) literature and consequently analyze the implications: Our first contribution is to propose the new notion of \emph{Internal Regret} for sleeping MAB. We then proposed an algorithm that yields sublinear regret in that measure, even for a completely adversarial sequence of losses and availabilities. We further show that a low sleeping internal regret always implies a low external regret, and as well as a low policy regret for iid sequence of losses. The main contribution of this work precisely lies in unifying different notions of existing regret in sleeping bandits and understand the implication of one to another. Finally, we also extend our results to the setting of \emph{Dueling Bandits} (DB)--a preference feedback variant of MAB, and proposed a reduction to MAB idea to design a low regret algorithm for sleeping dueling bandits with stochastic preferences and adversarial availabilities. The efficacy of our algorithms is justified through empirical evaluations

Dueling Bandits with Adversarial Sleeping

We introduce the problem of sleeping dueling bandits with stochastic preferences and adversarial availabilities (DB-SPAA). In almost all dueling bandit applications, the decision space often changes over time; eg, retail store management, online shopping, restaurant recommendation, search engine optimization, etc. Surprisingly, this `sleeping aspect' of dueling bandits has never been studied in the literature. Like dueling bandits, the goal is to compete with the best arm by sequentially querying the preference feedback of item pairs. The non-triviality however results due to the non-stationary item spaces that allow any arbitrary subsets items to go unavailable every round. The goal is to find an optimal `no-regret' policy that can identify the best available item at each round, as opposed to the standard `fixed best-arm regret objective' of dueling bandits. We first derive an instance-specific lower bound for DB-SPAA $\Omega( \sum_{i =1}^{K-1}\sum_{j=i+1}^K \frac{\log T}{\Delta(i,j)})$, where $K$ is the number of items and $\Delta(i,j)$ is the gap between items $i$ and $j$. This indicates that the sleeping problem with preference feedback is inherently more difficult than that for classical multi-armed bandits (MAB). We then propose two algorithms, with near optimal regret guarantees. Our results are corroborated empirically

Ballooning Multi-Armed Bandits

In this paper, we introduce Ballooning Multi-Armed Bandits (BL-MAB), a novel extension of the classical stochastic MAB model. In the BL-MAB model, the set of available arms grows (or balloons) over time. In contrast to the classical MAB setting where the regret is computed with respect to the best arm overall, the regret in a BL-MAB setting is computed with respect to the best available arm at each time. We first observe that the existing stochastic MAB algorithms result in linear regret for the BL-MAB model. We prove that, if the best arm is equally likely to arrive at any time instant, a sub-linear regret cannot be achieved. Next, we show that if the best arm is more likely to arrive in the early rounds, one can achieve sub-linear regret. Our proposed algorithm determines (1) the fraction of the time horizon for which the newly arriving arms should be explored and (2) the sequence of arm pulls in the exploitation phase from among the explored arms. Making reasonable assumptions on the arrival distribution of the best arm in terms of the thinness of the distribution's tail, we prove that the proposed algorithm achieves sub-linear instance-independent regret. We further quantify explicit dependence of regret on the arrival distribution parameters. We reinforce our theoretical findings with extensive simulation results. We conclude by showing that our algorithm would achieve sub-linear regret even if (a) the distributional parameters are not exactly known, but are obtained using a reasonable learning mechanism or (b) the best arm is not more likely to arrive early, but a large fraction of arms is likely to arrive relatively early.Comment: A full version of this paper is accepted in the Journal of Artificial Intelligence (AIJ) of Elsevier. A preliminary version is published as an extended abstract in AAMAS 2020. Proceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems. 202

Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems

Multi-armed bandit problems are the most basic examples of sequential decision problems with an exploration-exploitation trade-off. This is the balance between staying with the option that gave highest payoffs in the past and exploring new options that might give higher payoffs in the future. Although the study of bandit problems dates back to the Thirties, exploration-exploitation trade-offs arise in several modern applications, such as ad placement, website optimization, and packet routing. Mathematically, a multi-armed bandit is defined by the payoff process associated with each option. In this survey, we focus on two extreme cases in which the analysis of regret is particularly simple and elegant: i.i.d. payoffs and adversarial payoffs. Besides the basic setting of finitely many actions, we also analyze some of the most important variants and extensions, such as the contextual bandit model.Comment: To appear in Foundations and Trends in Machine Learnin