Corpus ID: 67855505

Optimal Algorithms for Ski Rental with Soft Machine-Learned Predictions

@article{Kodialam2019OptimalAF,
  title={Optimal Algorithms for Ski Rental with Soft Machine-Learned Predictions},
  author={Rohan Kodialam},
  journal={ArXiv},
  year={2019},
  volume={abs/1903.00092}
}
  • Rohan Kodialam
  • Published 28 February 2019
  • Computer Science, Mathematics
  • ArXiv
We consider a variant of the classic Ski Rental online algorithm with applications to machine learning. In our variant, we allow the skier access to a black-box machine-learning algorithm that provides an estimate of the probability that there will be at most a threshold number of ski-days. We derive a class of optimal randomized algorithms to determine the strategy that minimizes the worst-case expected competitive ratio for the skier given a prediction from the machine learning algorithm,and… Expand
Online Algorithms for Multi-shop Ski Rental with Machine Learned Predictions
TLDR
This work considers the MSSR problem, which is a generalization of the classical ski rental problem, and obtains both deterministic and randomized online algorithms with provably improved performance when either a single or multiple ML predictions are used to make decisions. Expand
Learning Online Algorithms with Distributional Advice
TLDR
For the broad class of log-concave distributions, it is shown that poly(1/ ) samples suffice to obtain (1 + )competitive ratio, and the sample upper bound is close to best possible, even for very simple classes of distributions. Expand
The Primal-Dual method for Learning Augmented Algorithms
TLDR
This paper extends the primal-dual method for online algorithms in order to incorporate predictions that advise the online algorithm about the next action to take and uses this framework to obtain novel algorithms for a variety of online covering problems. Expand
Data-driven Competitive Algorithms for Online Knapsack and Set Cover
TLDR
This paper develops an approach for data-driven design of online algorithms that maintain near-optimal worst-case guarantees while also performing learning in order to perform well for typical inputs. Expand
Competitive Analysis for Two-Level Ski-Rental Problem
TLDR
This paper proposes a deterministic online algorithm that can achieve 3 competitive ratio, which is optimal and tight, and proposes a randomized online algorithm, leading to a e σ eσ−1competitive ratio, where σ is the ratio between the price of a single commodity and theprice of combo purchase. Expand
(Learned) Frequency Estimation Algorithms under Zipfian Distribution
TLDR
The first error bounds for both the standard and the augmented version of Count-Sketch are provided, which show that to minimise the expected error, the number of hash functions should be a constant, strictly greater than $1$. Expand
Learning Augmented Energy Minimization via Speed Scaling
TLDR
An algorithm is proposed which incorporates predictions in a black-box manner and outperforms any online algorithm if the accuracy is high, yet maintains provable guarantees if the prediction is very inaccurate. Expand
Online Peak-Aware Energy Scheduling with Untrusted Advice
TLDR
This paper develops parameterized deterministic and randomized algorithms for the online energy scheduling problem such that the level of reliance on the advice can be adjusted by a trust parameter, and shows that the proposed randomized algorithm dominates the Pareto-optimal deterministic algorithm. Expand
Online Algorithms for Multi-shop Ski Rental with Machine Learned Advice
TLDR
This work considers the MSSR problem, which is a generalization of the classical ski rental problem, and obtains both deterministic and randomized online algorithms with provably improved performance when either a single or multiple ML predictions are used to make decisions. Expand
Learning-Assisted Competitive Algorithms for Peak-Aware Energy Scheduling
TLDR
Two deterministic and randomized algorithms are developed that are provably robust against the poor performance of learning prediction, however, achieve the optimal performance as the error of prediction goes to zero. Expand

References

SHOWING 1-9 OF 9 REFERENCES
Improving Online Algorithms via ML Predictions
In this work we study the problem of using machine-learned predictions to improve the performance of online algorithms. We consider two classical problems, ski rental and non-clairvoyant jobExpand
Competitive caching with machine learned advice
TLDR
This work develops a framework for augmenting online algorithms with a machine learned oracle to achieve competitive ratios that provably improve upon unconditional worst case lower bounds when the oracle has low error. Expand
Beyond Competitive Analysis
TLDR
This work proposes refinements of competitive analysis in two directions: the first restricts the power of the adversary by allowing only certain input distributions, while the other allows for comparisons between information regimes for online decision-making. Expand
Revenue Optimization with Approximate Bid Predictions
TLDR
This work shows how to reduce reserve price optimization to the standard setting of prediction under squared loss, a well understood problem in the learning community and further bound the gap between the expected bid and revenue in terms of the average loss of the predictor. Expand
Competitive Algorithms for Online Leasing Problem in Probabilistic Environments
We integrate probability distribution into pure competitive analysis to improve the performance measure of competitive analysis, since input sequences of the leasing problem have simple structure andExpand
Competitive randomized algorithms for nonuniform problems
TLDR
New randomized on-line algorithms for snoopy caching and the spin-block problem are presented and achieve competitive ratios approachinge/(e−1) ≈ 1.58 against an oblivious adversary, a surprising improvement over the best possible ratio in the deterministic case. Expand
Average-Case Competitive Analyses for Ski-Rental Problems
TLDR
This paper shows that the behaviors of skiers are quite reasonable by using an average- case competitive ratio and gives the result which differs from the worst-case competitive analysis and also differ from the traditional average cost analysis. Expand
Competitive snoopy caching
TLDR
This work presents new on-line algorithms to be used by the caches of snoopy cache multiprocessor systems to decide which blocks to retain and which to drop in order to minimize communication over the bus. Expand
Dynamic Noncooperative Game Theory
Preface to the classics edition Preface to the second edition 1. Introduction and motivation Part I: 2. Noncooperative Finite Games: two-person zero-aum 3. Noncooperative finite games: N-PersonExpand