106 research outputs found
Optimistic No-regret Algorithms for Discrete Caching
We take a systematic look at the problem of storing whole files in a cache
with limited capacity in the context of optimistic learning, where the caching
policy has access to a prediction oracle (provided by, e.g., a Neural Network).
The successive file requests are assumed to be generated by an adversary, and
no assumption is made on the accuracy of the oracle. In this setting, we
provide a universal lower bound for prediction-assisted online caching and
proceed to design a suite of policies with a range of performance-complexity
trade-offs. All proposed policies offer sublinear regret bounds commensurate
with the accuracy of the oracle. Our results substantially improve upon all
recently-proposed online caching policies, which, being unable to exploit the
oracle predictions, offer only regret. In this pursuit, we
design, to the best of our knowledge, the first comprehensive optimistic
Follow-the-Perturbed leader policy, which generalizes beyond the caching
problem. We also study the problem of caching files with different sizes and
the bipartite network caching problem. Finally, we evaluate the efficacy of the
proposed policies through extensive numerical experiments using real-world
traces.Comment: Accepted to ACM SIGMETRICS 202
Small Extended Formulation for Knapsack Cover Inequalities from Monotone Circuits
Initially developed for the min-knapsack problem, the knapsack cover
inequalities are used in the current best relaxations for numerous
combinatorial optimization problems of covering type. In spite of their
widespread use, these inequalities yield linear programming (LP) relaxations of
exponential size, over which it is not known how to optimize exactly in
polynomial time. In this paper we address this issue and obtain LP relaxations
of quasi-polynomial size that are at least as strong as that given by the
knapsack cover inequalities.
For the min-knapsack cover problem, our main result can be stated formally as
follows: for any , there is a -size LP relaxation with an integrality gap of at most ,
where is the number of items. Prior to this work, there was no known
relaxation of subexponential size with a constant upper bound on the
integrality gap.
Our construction is inspired by a connection between extended formulations
and monotone circuit complexity via Karchmer-Wigderson games. In particular,
our LP is based on -depth monotone circuits with fan-in~ for
evaluating weighted threshold functions with inputs, as constructed by
Beimel and Weinreb. We believe that a further understanding of this connection
may lead to more positive results complementing the numerous lower bounds
recently proved for extended formulations.Comment: 21 page
- …