Prediction with Expert Advice: A PDE Perspective

Nadejda Drenska, Robert Kohn

Research output: Contribution to journalArticle

Abstract

This work addresses a classic problem of online prediction with expert advice. We assume an adversarial opponent, and we consider both the finite horizon and random stopping versions of this zero-sum, two-person game. Focusing on an appropriate continuum limit and using methods from optimal control, we characterize the value of the game as the viscosity solution of a certain nonlinear partial differential equation. The analysis also reveals the predictor’s and the opponent’s minimax optimal strategies. Our work provides, in particular, a continuum perspective on recent work of Gravin et al. (in: Proceedings of the twenty-seventh annual ACM-SIAM symposium on discrete algorithms, SODA ’16, (Philadelphia, PA, USA), Society for Industrial and Applied Mathematics, 2016). Our techniques are similar to those of Kohn and Serfaty (Commun Pure Appl Math 63(10):1298–1350, 2010), where scaling limits of some two-person games led to elliptic or parabolic PDEs.

Original languageEnglish (US)
JournalJournal of Nonlinear Science
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Two-person Games
Partial differential equations
Viscosity
Parabolic PDEs
Zero-sum
Elliptic PDE
Prediction
Finite Horizon
Scaling Limit
Continuum Limit
Viscosity Solutions
Optimal Strategy
Applied mathematics
Minimax
Nonlinear Partial Differential Equations
Annual
Predictors
Optimal Control
Continuum
Game

Keywords

  • Dynamic programming
  • Prediction with expert advice
  • Regret minimization
  • Two-person games
  • Viscosity solutions

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

Cite this

Prediction with Expert Advice : A PDE Perspective. / Drenska, Nadejda; Kohn, Robert.

In: Journal of Nonlinear Science, 01.01.2019.

Research output: Contribution to journalArticle

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