# Online Computation with Untrusted Advice

## TL;DR

This paper explores online algorithms that operate with advice from an untrusted source, analyzing their robustness and efficiency across four problems, and establishing bounds on advice and competitiveness tradeoffs.

## Contribution

It introduces a model for untrusted advice in online algorithms, providing algorithms and lower bounds for tradeoffs between advice bits and competitiveness.

## Key findings

- Algorithms that are Pareto-optimal for ski rental and online bidding.
- Tradeoff bounds between advice bits and competitiveness for bin packing and list update.
- Lower bounds on advice-competitiveness tradeoffs in the untrusted advice model.

## 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.