Competitive ratio versus regret minimization: achieving the best of both worlds
This work addresses a foundational challenge in online algorithms for researchers and practitioners, offering a novel integration of two key performance criteria, though it builds incrementally on existing regret minimization methods.
The paper tackles the problem of designing online algorithms that simultaneously achieve both competitive ratio and regret minimization guarantees, demonstrating a unified methodology that matches the best known competitive ratio while providing low regret over any time interval, with an efficient polynomial-time algorithm for the paging problem.
We consider online algorithms under both the competitive ratio criteria and the regret minimization one. Our main goal is to build a unified methodology that would be able to guarantee both criteria simultaneously. For a general class of online algorithms, namely any Metrical Task System (MTS), we show that one can simultaneously guarantee the best known competitive ratio and a natural regret bound. For the paging problem we further show an efficient online algorithm (polynomial in the number of pages) with this guarantee. To this end, we extend an existing regret minimization algorithm (specifically, Kapralov and Panigrahy) to handle movement cost (the cost of switching between states of the online system). We then show how to use the extended regret minimization algorithm to combine multiple online algorithms. Our end result is an online algorithm that can combine a "base" online algorithm, having a guaranteed competitive ratio, with a range of online algorithms that guarantee a small regret over any interval of time. The combined algorithm guarantees both that the competitive ratio matches that of the base algorithm and a low regret over any time interval. As a by product, we obtain an expert algorithm with close to optimal regret bound on every time interval, even in the presence of switching costs. This result is of independent interest.