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A PDE approach for regret bounds under partial monitoring

arXiv 2209.01256 ↗First posted 2 Sep 2022math.PR cs.LG math.OCcited by 0

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Abstract (arXiv)

In this paper, we study a learning problem in which a forecaster only observes partial information. By properly rescaling the problem, we heuristically derive a limiting PDE on Wasserstein space which characterizes the asymptotic behavior of the regret of the forecaster. Using a verification type argument, we show that the problem of obtaining regret bounds and efficient algorithms can be tackled by finding appropriate smooth sub/supersolutions of this parabolic PDE.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 16 of its 29 references that are in the map. First posted on arXiv 2 Sep 2022.

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References · 16

  1. 2022PDE-Based Optimal Strategy for Unconstrained Online Learningcited by 27
  2. 2019Prediction with Expert Advice: a PDE Perspectivecited by 16
  3. 2020Optimal anytime regret with two expertscited by 16
  4. 2019New Potential-Based Bounds for Prediction with Expert Advicecited by 15
  5. 2019Finite-Time 4-Expert Prediction Problemcited by 13
  6. 2014Towards Optimal Algorithms for Prediction with Expert Advicecited by 12
  7. 2015Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advicecited by 10
  8. 2019On the asymptotic optimality of the comb strategy for prediction with expert advicecited by 9
  9. 2016Tight Lower Bounds for Multiplicative Weights Algorithmic Familiescited by 8
  10. 2020A PDE Approach to the Prediction of a Binary Sequence with Advice from Two History-Dependent Expertscited by 6
  11. 2020Malicious Experts versus the multiplicative weights algorithm in online predictioncited by 5
  12. 2022Efficient and Optimal Fixed-Time Regret with Two Expertscited by 5
4 more
  1. 2022A PDE-Based Analysis of the Symmetric Two-Armed Bernoulli Banditcited by 3
  2. 2021Master Bellman equation in the Wasserstein space: Uniqueness of viscosity solutionscited by 2
  3. 2016Randomized filtering and Bellman equation in Wasserstein space for partial observation control problemcited by 1
  4. 2019Viscosity solutions for controlled McKean--Vlasov jump-diffusionscited by 1

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