Metric-Free Individual Fairness in Online Learning

NIPS 2020, 2020.

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We study an online learning problem subject to the constraint of individual fairness, which requires that similar individuals are treated

Abstract:

We study an online learning problem subject to the constraint of individual fairness, which requires that similar individuals are treated similarly. Unlike prior work on individual fairness, we do not assume the similarity measure among individuals is known, nor do we assume that such measure takes a certain parametric form. Instead, we...More

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Introduction
  • As machine learning increasingly permeates many critical aspects of society, including education, healthcare, criminal justice, and lending, there is a vast literature that studies how to make machine learning algorithms fair.
  • They assume an auditor who can identify fairness violations in each round and provide an online learning algorithm with sublinear regret and a bounded number of fairness violations.
  • Upon seeing the deployed policy πt, the environment chooses a batch of k individuals,kτ=1 and possibly, a pair of individuals from that round on which πt will be responsible for any α-fairness violation.
Highlights
  • As machine learning increasingly permeates many critical aspects of society, including education, healthcare, criminal justice, and lending, there is a vast literature that studies how to make machine learning algorithms fair
  • The original formulation of individual fairness assumes that the algorithm designer has access to a task-specific fairness metric that captures how similar two individuals are in the context of the specific classification task at hand
  • Ilvento [2019] provides an algorithm for learning the metric by presenting human arbiters with queries concerning the distance between individuals, and Gillen et al [2018] provide an online learning algorithm that can eventually learn a Mahalanobis metric based on identified fairness violations
  • This paper studies metric-free online learning algorithms for individual fairness that rely on a weaker form of interactive human feedback and minimal assumptions on the similarity measure across individuals
  • While our algorithmic results hold under adversarial arrivals of the individuals, in the stochastic arrivals setting we show that the uniform average policy over time is probably approximate correct and fair (PACF) [Yona and Rothblum, 2018]–that is, the policy is approximately fair on almost all random pairs drawn from the distribution and nearly matches the accuracy gurantee of the best fair policy
  • We hope that relieving the metric assumption as well as the assumption regarding full access to the similarity measure, and only requiring the auditor to detect a single violation for every time interval, will be helpful in making individual fairness more achievable and easier to implement in practice
Results
  • Similar to the online fair batch classification setting, in each round t, the learner deploys a policy πt, but the environment chooses only a batch of instanceskτ=1.
  • The authors show how to achieve no regret with respect to the Lagrangian loss by reducing the problem to an online batch classification where there’s no fairness constraint.
  • This distinction between the pair chosen by the environment and the auditor is necessary as the authors need to ensure that the pair used to charge the Lagrangian loss incurs constant instantaneous regret in the rounds where there is some fairness violation.
  • During these rounds with some (α + ǫ)-fairness violation, the authors show that the instantaneous regret with respect to the Lagrangian loss must be at least 1: LC,α(πt,, ρtJ ) − LC,α(π∗,, ρtJ )
  • To provide some intuition for why this is the case, let them first attempt to upper bound the probability of running into an α′-fairness violation by the average policy on a randomly selected pair of individuals: T
  • A good intuition may arrive from considering the following thought experiment: assume worst-case compositional guarantees, and select a pair of individuals x, x′ on which the average policy has an α′′-fairness violation.
  • As the authors will see, setting α′′ to be sufficiently larger will force the number of these policies required to produce an α′′-fairness violation of the average policy on x, x′ to be high, resulting in the following improved bound: Lemma 4.8.
  • High-Level Proof Idea has the following implication: for any pair of individuals (x, x′), in order for πavg to have an α′′-fairness violation on x, x′, at least q of the policies in {π1, .
Conclusion
  • The authors will lower bound the probability of having an α′-fairness violation on a pair of individuals among those who have arrived in a single round.
  • The authors hope that relieving the metric assumption as well as the assumption regarding full access to the similarity measure, and only requiring the auditor to detect a single violation for every time interval, will be helpful in making individual fairness more achievable and easier to implement in practice.
  • As most of the literature on individual fairness is decoupling the similarity measure from the distribution over the target variable, it would be desirable to try to explore and quantify the compatibility of the two in specific instances
Summary
  • As machine learning increasingly permeates many critical aspects of society, including education, healthcare, criminal justice, and lending, there is a vast literature that studies how to make machine learning algorithms fair.
  • They assume an auditor who can identify fairness violations in each round and provide an online learning algorithm with sublinear regret and a bounded number of fairness violations.
  • Upon seeing the deployed policy πt, the environment chooses a batch of k individuals,kτ=1 and possibly, a pair of individuals from that round on which πt will be responsible for any α-fairness violation.
  • Similar to the online fair batch classification setting, in each round t, the learner deploys a policy πt, but the environment chooses only a batch of instanceskτ=1.
  • The authors show how to achieve no regret with respect to the Lagrangian loss by reducing the problem to an online batch classification where there’s no fairness constraint.
  • This distinction between the pair chosen by the environment and the auditor is necessary as the authors need to ensure that the pair used to charge the Lagrangian loss incurs constant instantaneous regret in the rounds where there is some fairness violation.
  • During these rounds with some (α + ǫ)-fairness violation, the authors show that the instantaneous regret with respect to the Lagrangian loss must be at least 1: LC,α(πt,, ρtJ ) − LC,α(π∗,, ρtJ )
  • To provide some intuition for why this is the case, let them first attempt to upper bound the probability of running into an α′-fairness violation by the average policy on a randomly selected pair of individuals: T
  • A good intuition may arrive from considering the following thought experiment: assume worst-case compositional guarantees, and select a pair of individuals x, x′ on which the average policy has an α′′-fairness violation.
  • As the authors will see, setting α′′ to be sufficiently larger will force the number of these policies required to produce an α′′-fairness violation of the average policy on x, x′ to be high, resulting in the following improved bound: Lemma 4.8.
  • High-Level Proof Idea has the following implication: for any pair of individuals (x, x′), in order for πavg to have an α′′-fairness violation on x, x′, at least q of the policies in {π1, .
  • The authors will lower bound the probability of having an α′-fairness violation on a pair of individuals among those who have arrived in a single round.
  • The authors hope that relieving the metric assumption as well as the assumption regarding full access to the similarity measure, and only requiring the auditor to detect a single violation for every time interval, will be helpful in making individual fairness more achievable and easier to implement in practice.
  • As most of the literature on individual fairness is decoupling the similarity measure from the distribution over the target variable, it would be desirable to try to explore and quantify the compatibility of the two in specific instances
Related work
  • Solving open problems in Gillen et al [2018]. The most related work to ours is Gillen et al [2018], which studies the linear contextual bandit problem subject to individual fairness with an unknown Mahalanobis metric. Similar to our work, they also assume an auditor who can identify fairness violations in each round and provide an online learning algorithm with sublinear regret and a bounded number of fairness violations. Our results resolve two main questions left open in their work. First, we assume a weaker auditor who only identifies a single fairness violation (as opposed to all of the fairness violations in their setting). Second, we remove the strong parametric assumption on the Mahalanobis metric and work with a broad class of similarity functions that need not be metric.
Funding
  • YB is supported in part by Israel Science Foundation (ISF) grant #1044/16, the United States Air Force and DARPA under contracts FA8750-16-C-0022 and FA8750-19-2-0222, and the Federmann Cyber Security Center in conjunction with the Israel national cyber directorate
  • CJ is supported in part by NSF grant AF-1763307
  • ZSW is supported in part by the NSF FAI Award #1939606, an Amazon Research Award, a Google Faculty Research Award, a J.P
  • Morgan Faculty Award, a Facebook Research Award, and a Mozilla Research Grant
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