Subgame Optimal and Prior-Independent Online Algorithms
Jason Hartline, Aleck Johnsen, Anant Shah
TL;DR
The paper advances beyond-worst-case analysis for online algorithms by introducing subgame optimality and prior-independence, illustrating their value with the finite-horizon ski-rental problem. It develops a game-theoretic framework that connects worst-case, subgame-optimal, and prior-independent perspectives, and provides both analytic characterizations and computational schemes. A key contribution is showing how to compute near-optimal prior-independent algorithms via a four-property framework (Small-Cover, Efficient Best Response, Efficient Utility Computation, Bounded Best Response Utility), yielding a polynomial-time approximation scheme. Empirical results demonstrate that subgame-optimal and prior-independent algorithms can outperform traditional worst-case methods in realistic, non-worst-case inputs. The work offers a cohesive methodology for robust online algorithm design with practical implications for systems where inputs are uncertain yet exhibit structure beyond pure worst-case behavior.
Abstract
This paper takes a game theoretic approach to the design and analysis of online algorithms and illustrates the approach on the finite-horizon ski-rental problem. This approach allows beyond worst-case analysis of online algorithms. First, 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 only focusing on the worst case can be far from subgame optimal. Second, 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. 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.