Online Computation with Untrusted Advice
Spyros Angelopoulos, Christoph Dürr, Shendan Jin, Shahin Kamali, Marc Renault
TL;DR
This work introduces a model of online computation with untrusted advice, formalizing a two-dimensional competitiveness measure $(r,w)$ that captures performance when advice is trusted versus adversarially corrupted. It develops Pareto-optimal strategies for ski rental and online bidding, and robust, tunable algorithms for bin packing and list update that trade off trust in the advice against competitive performance. The paper provides both upper and lower bounds linking the size of the advice to achievable competitiveness, and extends the framework to randomized online algorithms to reveal nuanced interactions between randomness and untrusted advice. Together, these results illuminate how to design online algorithms that remain efficient under potentially faulty guidance and inform practical guidance for advice-based optimization under uncertainty.
Abstract
We study a generalization of the advice complexity model of online computation in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms that are robust if the advice is adversarial, and efficient is the advice is foolproof. We focus on four well-studied online problems, namely ski rental, online bidding, bin packing and list update. For ski rental and online bidding, we show how to obtain algorithms that are Pareto-optimal with respect to the competitive ratios achieved, whereas for bin packing and list update, we give online algorithms with worst-case tradeoffs in their competitiveness, depending on whether the advice is trusted or adversarial. More importantly, we demonstrate how to prove lower bounds, within this model, on the tradeoff between the number of advice bits and the competitiveness of any online algorithm.