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1. Online Learning with an Unknown Fairness Metric

   Gillen, S ; Jung, C ; Kearns, M ; Roth, A ( January 2019 , Neural information Processing Systems (NeurIPS))

   We consider the problem of online learning in the linear contextual bandits setting, but in which there are also strong individual fairness constraints governed by an unknown similarity metric. These constraints demand that we select similar actions or individuals with approximately equal probability, which may be at odds with optimizing reward, thus modeling settings where profit and social policy are in tension. We assume we learn about an unknown Mahalanobis similarity metric from only weak feedback that identifies fairness violations, but does not quantify their extent. This is intended to represent the interventions of a regulator who “knows unfairness when he sees it” but nevertheless cannot enunciate a quantitative fairness metric over individuals. Our main result is an algorithm in the adversarial context setting that has a number of fairness violations that depends only logarithmically on T, while obtaining an optimal O(√T) regret bound to the best fair policy. 

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2. Fairness of Exposure in Stochastic Bandits

   Wang, Lequn ; Bai, Yiwei ; Sun, Wen ; Joachims, Thorsten ( January 2021 , International Conference on Machine Learning)

   Contextual bandit algorithms have become widely used for recommendation in online systems (e.g. marketplaces, music streaming, news), where they now wield substantial influence on which items get shown to users. This raises questions of fairness to the items — and to the sellers, artists, and writers that benefit from this exposure. We argue that the conventional bandit formulation can lead to an undesirable and unfair winner-takes-all allocation of exposure. To remedy this problem, we propose a new bandit objective that guarantees merit-based fairness of exposure to the items while optimizing utility to the users. We formulate fairness regret and reward regret in this setting and present algorithms for both stochastic multi-armed bandits and stochastic linear bandits. We prove that the algorithms achieve sublinear fairness regret and reward regret. Beyond the theoretical analysis, we also provide empirical evidence that these algorithms can allocate exposure to different arms effectively. 

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3. More Adaptive Algorithms for Adversarial Bandits.

   Wei, Chen-Yu ; Luo, Haipeng ( July 2018 , Proceedings of Machine Learning Research)

   We develop a novel and generic algorithm for the adversarial multi-armed bandit problem (or more generally the combinatorial semi-bandit problem). When instantiated differently, our algorithm achieves various new data-dependent regret bounds improving previous work. Examples include: 1) a regret bound depending on the variance of only the best arm; 2) a regret bound depending on the first-order path-length of only the best arm; 3) a regret bound depending on the sum of the first-order path-lengths of all arms as well as an important negative term, which together lead to faster convergence rates for some normal form games with partial feedback; 4) a regret bound that simultaneously implies small regret when the best arm has small loss {\it and} logarithmic regret when there exists an arm whose expected loss is always smaller than those of other arms by a fixed gap (e.g. the classic i.i.d. setting). In some cases, such as the last two results, our algorithm is completely parameter-free. The main idea of our algorithm is to apply the optimism and adaptivity techniques to the well-known Online Mirror Descent framework with a special log-barrier regularizer. The challenges are to come up with appropriate optimistic predictions and correction terms in this framework. Some of our results also crucially rely on using a sophisticated increasing learning rate schedule. 

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4. Online Multivalid Learning: Means, Moments, and Prediction Intervals

   Varun Gupta ; Christopher Jung ; Georgy Noarov ; Mallesh M. Pai ; Aaron Roth ( January 2022 , Innovations in Theoretical Computer Science (ITCS))

   We present a general, efficient technique for providing contextual predictions that are "multivalid" in various senses, against an online sequence of adversarially chosen examples (x,y). This means that the resulting estimates correctly predict various statistics of the labels y not just marginally --- as averaged over the sequence of examples --- but also conditionally on x in G for any G belonging to an arbitrary intersecting collection of groups. We provide three instantiations of this framework. The first is mean prediction, which corresponds to an online algorithm satisfying the notion of multicalibration from Hebert-Johnson et al. The second is variance and higher moment prediction, which corresponds to an online algorithm satisfying the notion of mean-conditioned moment multicalibration from Jung et al. Finally, we define a new notion of prediction interval multivalidity, and give an algorithm for finding prediction intervals which satisfy it. Because our algorithms handle adversarially chosen examples, they can equally well be used to predict statistics of the residuals of arbitrary point prediction methods, giving rise to very general techniques for quantifying the uncertainty of predictions of black box algorithms, even in an online adversarial setting. When instantiated for prediction intervals, this solves a similar problem as conformal prediction, but in an adversarial environment and with multivalidity guarantees stronger than simple marginal coverage guarantees. 

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5. Stochastic Multi-Player Bandit Learning from Player-Dependent Feedback

   Wang, Z. ; Singh, M.K. ; Zhang, C. ; Riek, L.D. ; Chaudhuri, K. ( January 2020 , ICML Workshop on Real World Experiment Design and Active Learning)

   We investigate robust data aggregation in a multi-agent online learning setting. In reality, multiple online learning agents are often deployed to perform similar tasks and receive similar feedback. We study how agents can improve their collective performance by sharing information among each other. In this paper, we formulate the ε-multi-player multi-armed bandit problem, in which a set of M players that have similar reward distributions for each arm play concurrently. We develop an upper confidence bound-based algorithm that adaptively aggregates rewards collected by different players. To our best knowledge, we are the first to develop such a scheme in a multi-player bandit learning setting. We show that under the assumption that pairwise distances between the means of the player-dependent distributions for each arm are small, we improve the (collective) regret bound by nearly a factor of M , in comparison with a baseline algorithm in which the players learn individually using the UCB-1 algorithm (Auer et al., 2002). Our algorithm also exhibits a fallback guarantee, namely, if our task similarity assumption fails to hold, our algorithm still has a performance guarantee that cannot be worse than the baseline by a constant factor. Empirically, we validate our algorithm on synthetic data. 

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