Calibrated Fairness in Bandits

Liu, Yang; Radanovic, Goran; Dimitrakakis, Christos; Mandal, Debmalya; Parkes, David C.

doi:10.48550/arxiv.1707.01875

Cited by 54 publications

(50 citation statements)

References 5 publications

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“…Their regret bound is O( K 3 T ln T K δ ), with a higher cubic dependence on K, which is the price they pay to give equal probability to all the arms in the set. More generally, Liu et al (2017) considers a fairness through awareness. An algorithm is said to be (ǫ 1 , ǫ 2 , δ)-smooth fair 5 , if for any pair of arms a, a ′ and any t, with a probability at least…”

Section: Fairnessmentioning

confidence: 99%

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Bandit Algorithms for Precision Medicine

Lu,

Xu,

Tewari

2021

Preprint

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Section: Fairnessmentioning

confidence: 99%

“…Note thatLiu et al (2017) considers a general divergence function for the distribution of action selection and rewards, we introduce a special case here for a cleaner form.…”

mentioning

confidence: 99%

Bandit Algorithms for Precision Medicine

Lu,

Xu,

Tewari

2021

Preprint

View full text Add to dashboard Cite

“…Sub-linear fairness regret and reward regret are also guaranteed in this setting. Similarly, Liu et al (2017) study the stochastic bandit with a smoothness constraint that if two arms have a similar quality distribution, the probability of selecting each arm should be similar. Patil et al (2020) and Chen et al (2020) study stochastic and contextual bandit problem with fairness requirement that there is a minimum rate that each arm must been pulled.…”

Section: Related Workmentioning

confidence: 99%

Fairer LP-based Online Allocation via Analytic Center

Chen¹,

Li²,

Ye³

2021

Preprint

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In this paper, we consider a Linear Program (LP)-based online resource allocation problem where a decision maker accepts or rejects incoming customer requests irrevocably in order to maximize expected revenue given limited resources. At each time, a new order/customer/bid is revealed with a request of some resource(s) and a reward. We consider a stochastic setting where all the orders are i.i.d. sampled from an unknown distribution. Such formulation gives rise to many classic applications such as the canonical (quantity-based) network revenue management problem and the Adwords problem. Instead of focusing only on regret minimization, this paper aims to provide fairness guarantees while maintaining low regret. Our definition of fairness is that a fair online algorithm should treat similar agents/customers similarly and the decision made for similar individuals should be consistent over time. We define the fair offline solution as the analytic center of the offline optimal solution set, and define cumulative unfairness as the cumulative deviation from the online solutions to the fair offline solution. We propose a fair algorithm that uses an interior-point LP solver and dynamically detects unfair resource spending. Our algorithm can control cumulative unfairness on the scale of order O(log(T )), while maintaining the regret to be bounded without dependency on T . Moreover, we partially remove the nondegeneracy assumptions used in early results in the literature. This paper only requires the nondegeneracy condition for the binding constraints, and allows the existence of multiple optimal solutions.

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“…There have also been a handful of papers (Joseph et al 2016, Liu et al 2017, Gillen et al 2018, Patil et al 2020) that study 'fairness in bandits' in a completely different context. These works enforce a fairness criterion between arms, which is relevant in settings where a 'pull' represents some resource that is allocated to that arm, and these pulls should be distributed between arms in a fair manner.…”

Section: Related Literaturementioning

confidence: 99%

Fair Exploration via Axiomatic Bargaining

Baek

Farias

2021

Preprint

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Motivated by the consideration of fairly sharing the cost of exploration between multiple groups in learning problems, we develop the Nash bargaining solution in the context of multiarmed bandits. Specifically, the 'grouped' bandit associated with any multi-armed bandit problem associates, with each time step, a single group from some finite set of groups. The utility gained by a given group under some learning policy is naturally viewed as the reduction in that group's regret relative to the regret that group would have incurred 'on its own'. We derive policies that yield the Nash bargaining solution relative to the set of incremental utilities possible under any policy. We show that on the one hand, the 'price of fairness' under such policies is limited, while on the other hand, regret optimal policies are arbitrarily unfair under generic conditions. Our theoretical development is complemented by a case study on contextual bandits for warfarin dosing where we are concerned with the cost of exploration across multiple races and age groups.

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Calibrated Fairness in Bandits

Cited by 54 publications

References 5 publications

Bandit Algorithms for Precision Medicine

Bandit Algorithms for Precision Medicine

Fairer LP-based Online Allocation via Analytic Center

Fair Exploration via Axiomatic Bargaining

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