Seminar: Hadi Abbaszadehpeivasti (Tilburg) + Utku Karaca (Erasmus University), 2 PhD talks

  • When Dec 09, 2021 from 04:00 PM to 05:00 PM (Europe/Amsterdam / UTC100)
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Speaker: Hadi Abbaszadehpeivasti (Tilburg University) + Utku Karaca (Erasmus University)

Title:

Hadi Abbaszadehpeivasti: On the convergence rate of DCA

Utku Karaca : Differentially Private Resource Sharing

Zoom link: 

https://cwi-nl.zoom.us/j/84909645595?pwd=b1M4QnNKVzNMdmNSVFNaZUJmR1kvUT09
(Meeting ID: 849 0964 5595, Passcode: 772448)

Abstract of "On the convergence rate of DCA" (Hadi Abbaszadehpeivasti):

Difference-of-convex (DC) problems arise naturally in many applications. The DCA (Difference-of-Convex Algorithm) is a popular algorithm for tackling DC problems. In this talk, we study the convergence rate of the DCA, also known as the convex-concave procedure, by using Performance estimation. We derive a worst-case convergence rate of O(1/sqrt(N)) after N iterations of the objective gradient norm for certain classes of unconstrained DC problems. We give an example which shows the order of convergence cannot be improved for a certain class of DC functions. In addition, we study DC problems on a given convex set and we obtain a convergence rate O(1/N) for some termination criterion. Finally, we investigate the DCA with regularization and we get the same convergence rate.

https://arxiv.org/abs/2109.13566

Video of the talk of Hadi Abbaszadehpeivasti:



Slides of the talk of Hadi Abbaszadehpeivasti:  

Slides

Abstract of "Differentially Private Resource Sharing" (Utku Karaca):

This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange information to obtain the optimal objective function value. This information bears private data from each party in terms of coefficients used in the mathematical program. Moreover, the parties also consider the individual optimal solutions as private. In this setting, the great concern for the parties is the privacy of their data and their optimal allocations. Methodology and results: We propose a two-step approach to meet the privacy requirements of the parties. In the first step, we obtain a reformulated model that is amenable to a decomposition scheme. Although this scheme eliminates almost all data exchange, it does not provide a formal privacy guarantee. In the second step, we provide this guarantee with a differentially private algorithm at the expense of deviating slightly from the optimality. We provide bounds on this deviation and discuss the consequences of these theoretical results. The study ends with a simulation study on a planning problem that demonstrates an application of the proposed approach. Managerial implications: Our work provides a new optimization model and a solution approach for optimal allocation of a set of shared resources among multiple parties who expect privacy of their data. The proposed approach is based on the decomposition of the shared resources and the randomization of the optimization iterations. With our analysis, we show that the resulting randomized algorithm does give a guarantee for the privacy of each party's data. As we work with a general optimization model, our analysis and discussion can be used in different application areas including production planning, logistics, and network revenue management.

https://arxiv.org/abs/2102.07178

Video of the talk of Utku Karaca: 



Slides of the talk of Utku Karaca: 

Slides