The Primal-Dual method for Learning Augmented Algorithms

The extension of classical online algorithms when provided with predictions is a new and active research area. In this paper, we extend the primal-dual method for online algorithms in order to incorporate predictions that advise the online algorithm about the next action to take. We use this framework to obtain novel algorithms for a variety of online covering problems. We compare our algorithms to the cost of the true and predicted offline optimal solutions and show that these algorithms outperform any online algorithm when the prediction is accurate while maintaining good guarantees when the prediction is misleading.

[1]  Silvio Lattanzi,et al.  Online Scheduling via Learned Weights , 2020, SODA.

[2]  Michael Mitzenmacher,et al.  Dynamic Models for File Sizes and Double Pareto Distributions , 2004, Internet Math..

[3]  Claire Mathieu,et al.  Dynamic TCP acknowledgement and other stories about e/(e-1) , 2001, STOC '01.

[4]  Joseph Naor,et al.  Online Primal-Dual Algorithms for Maximizing Ad-Auctions Revenue , 2007, ESA.

[5]  Google,et al.  Improving Online Algorithms via ML Predictions , 2024, NeurIPS.

[6]  Shiqiang Wang,et al.  Online Algorithms for Multi-shop Ski Rental with Machine Learned Predictions , 2020, AAMAS.

[7]  Michael Wilson,et al.  A Historical View of Network Traffic Models , 2006 .

[8]  Joseph Naor,et al.  The Design of Competitive Online Algorithms via a Primal-Dual Approach , 2009, Found. Trends Theor. Comput. Sci..

[9]  Piotr Indyk,et al.  Learning-Based Frequency Estimation Algorithms , 2018, ICLR.

[10]  Sergei Vassilvitskii,et al.  Revenue Optimization with Approximate Bid Predictions , 2017, NIPS.

[11]  Joseph Naor,et al.  A primal-dual randomized algorithm for weighted paging , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[12]  Dhruv Rohatgi,et al.  Near-Optimal Bounds for Online Caching with Machine Learned Advice , 2019, SODA.

[13]  Rohan Kodialam,et al.  Optimal Algorithms for Ski Rental with Soft Machine-Learned Predictions , 2019, ArXiv.

[14]  Vishal Misra,et al.  On the tails of web file size distributions , 2001 .

[15]  Sally A. Goldman,et al.  TCP dynamic acknowledgment delay (extended abstract): theory and practice , 1998, STOC '98.

[16]  Michael Mitzenmacher,et al.  Scheduling with Predictions and the Price of Misprediction , 2019, ITCS.

[17]  Sergei Vassilvitskii,et al.  Competitive caching with machine learned advice , 2018, ICML.

[18]  Steven S. Seiden,et al.  A guessing game and randomized online algorithms , 2000, STOC '00.

[19]  Anna R. Karlin,et al.  Competitive snoopy caching , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[20]  Rudolf Fleischer.  On The Bahncard Problem , 1998, COCOON.

[21]  Jure Leskovec,et al.  Friendship and mobility: user movement in location-based social networks , 2011, KDD.

[22]  Jian Li,et al.  Learning-Assisted Competitive Algorithms for Peak-Aware Energy Scheduling , 2019, ArXiv.

[23]  Noga Alon,et al.  The online set cover problem , 2003, STOC '03.

[24]  Christian Coester,et al.  Online Metric Algorithms with Untrusted Predictions , 2020, ICML.

[25]  Anna R. Karlin,et al.  Competitive randomized algorithms for non-uniform problems , 1990, SODA '90.

[26]  Sreenivas Gollapudi,et al.  Online Algorithms for Rent-Or-Buy with Expert Advice , 2019, ICML.

[27]  Piotr Indyk,et al.  Learning Space Partitions for Nearest Neighbor Search , 2019, ICLR.

[28]  Michael Mitzenmacher,et al.  A Model for Learned Bloom Filters and Optimizing by Sandwiching , 2018, NeurIPS.