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Prior-Independent and Subgame Optimal Online Algorithms

Authors Jason Hartline , Aleck Johnsen , Anant Shah

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ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • online algorithms
  • prior-independent algorithm design
  • zero-sum games

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Abstract

This paper develops two game-theoretic notions of beyond worst-case analysis that give better than worst-case guarantees on natural inputs. We illustrate them through the finite-horizon ski-rental problem. First, we consider prior-independent design and analysis of online algorithms where, rather than choosing a worst-case input, the adversary chooses a worst-case independent and identical distribution over inputs. Prior-independent online algorithms are generally analytically intractable; instead we give a fully polynomial-time approximation scheme to compute them. Second, we consider the worst-case design of algorithms. We define "subgame optimality" which is stronger than worst-case optimality in that it requires the algorithm to take advantage of an adversary not playing a worst-case input. Algorithms that focus only on the worst case can be far from subgame optimal. Highlighting the potential improvement from these paradigms for the finite-horizon ski-rental problem, we empirically compare worst-case, subgame optimal, and prior-independent algorithms in the prior-independent framework. Finally, we analyze the structure of their decisions across input sequences: the prior-independent algorithm exhibits more extreme adaptations to observed data, in contrast with the more conservative behavior of worst-case and subgame optimal algorithms.

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Jason Hartline, Aleck Johnsen, and Anant Shah. Prior-Independent and Subgame Optimal Online Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 75:1-75:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.75

Author Details

Jason Hartline
  • Northwestern University, Evanston, IL, USA
Aleck Johnsen
  • Geminus Research, Cambridge, MA, USA
Anant Shah
  • Northwestern University, Evanston, IL, USA

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