A User Friendly Power Tool for Deriving Online Learning Algorithms (Invited Talk)

Author Aaron Roth

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Aaron Roth
  • University of Pennsylvania, Philadelphia, PA, USA

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Aaron Roth. A User Friendly Power Tool for Deriving Online Learning Algorithms (Invited Talk). In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


In this talk, we overview a simple and user friendly framework developed in [Noarov et al., 2021] that can be used to derive online learning algorithms in a number of settings. In the core framework, at every round, an adaptive adversary introduces a new game, consisting of an action space for the learner, an action space for the adversary, and a vector valued objective function that is concave-convex in every coordinate. The learner and the adversary then play in this game. The learner’s goal is to play so as to minimize the maximum coordinate of the cumulative vector-valued loss. The resulting one-shot game is not concave-convex, and so the minimax theorem does not apply. Nevertheless we give a simple algorithm that can compete with the setting in which the adversary must announce their action first, with optimally diminishing regret. We demonstrate the power of our simple framework by using it to derive optimal bounds and algorithms across a variety of domains. This includes no regret learning: we can recover optimal algorithms and bounds for minimizing exernal regret, internal regret, adaptive regret, multigroup regret, subsequence regret, and permutation regret in the sleeping experts setting. It also includes (multi)calibration [Hébert-Johnson et al., 2018] and related notions: we are able to recover recently derived algorithms and bounds for online adversarial multicalibration [Gupta et al., 2021], mean conditioned moment multicalibration [Jung et al., 2021], and prediction interval multivalidity [Gupta et al., 2021]. Finally we use it to derive a new variant of Blackwell’s Approachability Theorem, which we term "Fast Polytope Approachability".

Subject Classification

ACM Subject Classification
  • Theory of computation → Machine learning theory
  • Online Learning
  • Multicalibration
  • Multivalidity
  • Blackwell Approachability


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  1. Varun Gupta, Christopher Jung, Georgy Noarov, Mallesh M Pai, and Aaron Roth. Online multivalid learning: Means, moments, and prediction intervals. arXiv preprint arXiv:2101.01739, 2021. Google Scholar
  2. Ursula Hébert-Johnson, Michael Kim, Omer Reingold, and Guy Rothblum. Multicalibration: Calibration for the (computationally-identifiable) masses. In International Conference on Machine Learning, pages 1939-1948. PMLR, 2018. Google Scholar
  3. Christopher Jung, Changhwa Lee, Mallesh M Pai, Aaron Roth, and Rakesh Vohra. Moment multicalibration for uncertainty estimation. In Conference on Learning Theory. PMLR, 2021. Google Scholar
  4. Georgy Noarov, Mallesh Pai, and Aaron Roth. Online multiobjective minimax optimization and applications. Manuscript, 2021. URL: http://arxiv.org/abs/2108.03837.
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