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Approximating the min–max (regret) selecting items problem

Adam Kasperski, Adam Kurpisz, Paweł Zieliński
2013 Information Processing Letters  
It is shown that both min-max and min-max regret problems are not approximable within any constant factor unless P=NP, which strengthens the results known up to date.  ...  In this paper the problem of selecting p items out of n available to minimize the total cost is discussed.  ...  Approximation algorithm for Min-max Selecting Items In this section, we construct a deterministic approximation algorithm for the Min-max Selecting Items problem, whose performance ratio is O(ln K).  ... 
doi:10.1016/j.ipl.2012.10.001 fatcat:avffmx3ohzchpiroowdtjdyoxe

Robust approach to restricted items selection problem

Maciej Drwal
2020 Optimization Letters  
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations.  ...  Next, we consider the robust version in which we aim at minimizing the maximum regret of the solution under interval parameter uncertainty.  ...  ,r i x i j ∈ {0, 1}. (4) Let us now define the version of the problem with uncertain data, which we call Interval Min-Max Regret Restricted Items Selection Problem (abbreviated IRIS).  ... 
doi:10.1007/s11590-020-01626-8 fatcat:diurjb3v65feraxtyyj2qpjgkm

Randomized Minmax Regret for Combinatorial Optimization Under Uncertainty [article]

Andrew Mastin, Patrick Jaillet, Sang Chin
2014 arXiv   pre-print
and the adversary selects costs with the intention of maximizing the regret of the player.  ...  The minmax regret problem for combinatorial optimization under uncertainty can be viewed as a zero-sum game played between an optimizing player and an adversary, where the optimizing player selects a solution  ...  He looked at the minmax regret version of the simple problem of selecting k items out of n total items where the cost of each item is uncertain, and the goal is to select the set of items with minimum  ... 
arXiv:1401.7043v2 fatcat:n4cmjrwlvrahborepvarbltsoy

Combinatorial Optimization Problems with Balanced Regret [article]

Marc Goerigk, Michael Hartisch
2021 arXiv   pre-print
We then consider a type of selection problem in more detail and show that, while the classic regret setting with budgeted uncertainty sets can be solved in polynomial time, the balanced regret problem  ...  For decision making under uncertainty, min-max regret has been established as a popular methodology to find robust solutions.  ...  Selection problems play a major role in the analysis of robust discrete optimization, as they tend to lie on the boundary between NP-hard and polynomially solvable problems; the min-max regret selection  ... 
arXiv:2111.12470v1 fatcat:jjl4ep5c3vfb3ezgxxxpyvamuu

Randomized Minmax Regret for Combinatorial Optimization Under Uncertainty [chapter]

Andrew Mastin, Patrick Jaillet, Sang Chin
2015 Lecture Notes in Computer Science  
and the adversary selects costs with the intention of maximizing the regret of the player.  ...  The minmax regret problem for combinatorial optimization under uncertainty can be viewed as a zero-sum game played between an optimizing player and an adversary, where the optimizing player selects a solution  ...  The minmax expected regret problem, which we refer to as the randomized minmax regret problem, is Z R := min y∈Y R max (y) = min y∈Y max c∈C T ∈F y T (F (T, c) − F * (c)) , (11) where we have replaced  ... 
doi:10.1007/978-3-662-48971-0_42 fatcat:qyfsxivjrncx7mozkvjfercuuq

Regret in Online Recommendation Systems [article]

Kaito Ariu, Narae Ryu, Se-Young Yun, Alexandre Proutière
2020 arXiv   pre-print
The decision-maker observes the user and selects an item from a catalogue of n items. Importantly, an item cannot be recommended twice to the same user.  ...  Interestingly, our analysis reveals the relative weights of the different components of regret: the component due to the constraint of not presenting the same item twice to the same user, that due to learning  ...  From Lemma 18, we deduce that (the rank-K approximation of A) is approximately the same as E[A].  ... 
arXiv:2010.12363v1 fatcat:4lo46h3razgexkd3kc75ifasj4

RRR: Rank-Regret Representative [article]

Abolfazl Asudeh and Azade Nazi and Nan Zhang and Gautam Das and H. V. Jagadish
2018 arXiv   pre-print
Selecting the best items in a dataset is a common task in data exploration.  ...  the problem.  ...  (v − min(A))/(max(A) − min(A)) and for each lower-preferred attribute A, we do it as (max(A) − v)/(max(A) − min(A)).  ... 
arXiv:1802.10303v2 fatcat:intbu4utwngt7dcnznb7filslu

Batch-Size Independent Regret Bounds for the Combinatorial Multi-Armed Bandit Problem [article]

Nadav Merlis, Shie Mannor
2020 arXiv   pre-print
The reward that the agent aims to maximize is a function of the selected arms and their expectations.  ...  We consider the combinatorial multi-armed bandit (CMAB) problem, where the reward function is nonlinear.  ...  Acknowledgments The authors thank Asaf Cassel and Esther Derman for their helpful comments on the manuscript.  ... 
arXiv:1905.03125v4 fatcat:dqwkyiztjje6bgdcz7sp3rlrga

Learning in Auctions: Regret is Hard, Envy is Easy [article]

Constantinos Daskalakis, Vasilis Syrgkanis
2016 arXiv   pre-print
No-envy learning outcomes are a relaxation of no-regret outcomes, which maintain their approximate welfare optimality while endowing them with computational tractability.  ...  Unfortunately, off-the-shelf no-regret algorithms for these auctions are computationally inefficient as the number of actions is exponential.  ...  step takes the closed form: Π j P (y) = max{0, min{1, y j }} (72) and thereby is efficiently computable.  ... 
arXiv:1511.01411v6 fatcat:i3sb2c5xl5fo5nsmjb7zc7hrxa

LeadCache: Regret-Optimal Caching in Networks [article]

Debjit Paria, Abhishek Sinha
2021 arXiv   pre-print
Finally, we derive an approximately tight regret lower bound using results from graph coloring.  ...  The problem is non-trivial due to the non-convex and non-smooth nature of the objective function.  ...  This work was partially supported by the grant IND-417880 from Qualcomm, USA, and a research grant from the Govt. of India under the IoE initiative.  ... 
arXiv:2009.08228v4 fatcat:uzrixodeh5aw5iajutovggsjvq

Interactive regret minimization

Danupon Nanongkai, Ashwin Lall, Atish Das Sarma, Kazuhisa Makino
2012 Proceedings of the 2012 international conference on Management of Data - SIGMOD '12  
In this paper, we study the problem of minimizing regret ratio when the system is enhanced with interaction.  ...  Under this assumption, we develop the problem of interactive regret minimization where we fix the number of questions and tuples per question that we can display, and aim at minimizing the regret ratio  ...  Acknowledgement: The authors would like to thank Bobby Kleinberg for his guidance towards the proofs presented in the lower bounds section. We also thank anonymous referees for many useful comments.  ... 
doi:10.1145/2213836.2213850 dblp:conf/sigmod/NanongkaiLSM12 fatcat:fiegdpofbnfzreumq4v22kpsnq

On Regret with Multiple Best Arms [article]

Yinglun Zhu, Robert Nowak
2020 arXiv   pre-print
We study a regret minimization problem with the existence of multiple best/near-optimal arms in the multi-armed bandit setting.  ...  Our goal is to design algorithms that can automatically adapt to the unknown hardness of the problem, i.e., the number of best arms.  ...  ) R T ≤ 231 (log 2 T ) 5/2 · T min{max{β,1+α−β},1} = O T min{max{β,1+α−β},1} t=Ti−1+1 X t ] the expected cumulative regret at iteration i.  ... 
arXiv:2006.14785v2 fatcat:spxpxwyzm5fe3jotom3mtplu6u

Min–max and min–max (relative) regret approaches to representatives selection problem

Alexandre Dolgui, Sergey Kovalev
2012 4OR  
The arising min-max, min-max regret and min-max relative regret optimization problems are shown to be polynomially solvable for interval scenarios.  ...  The uncertainty is modeled by discrete and interval scenarios, and the min-max and min-max (relative) regret approaches are used for making a selection decision.  ...  Acknowledgments We would like to thank two anonymous reviewers and Associate Editor for the useful suggestions and pointing us to the fact that the representatives selection problem is a special case of  ... 
doi:10.1007/s10288-012-0202-3 fatcat:e35y34c4cvbjzhujij5ahvrxje

Combinatorial two-stage minmax regret problems under interval uncertainty [article]

Marc Goerigk, Adam Kasperski, Pawel Zielinski
2020 arXiv   pre-print
Some general properties of the problem are established and results for two particular problems, namely the shortest path and the selection problem, are shown.  ...  In order to choose a solution, the minmax regret criterion is used.  ...  Acknowledgements The second and third author were supported by the National Science Centre, Poland, grant 2017/25/B/ST6/00486.  ... 
arXiv:2005.10610v1 fatcat:xbvgrn7ey5e5bavecr52d633te

Approximating Regret Minimizing Sets: A Happiness Perspective [article]

Phoomraphee Luenam, Yau Pun Chen, Raymond Chi-Wing Wong
2022 arXiv   pre-print
In this paper, we study the k-Regret Minimizing Sets (k-RMS) and Average Regret Minimizing Sets (ARMS) problems. k-RMS selects r records from a database such that the maximum regret ratio between the k-th  ...  We then provide approximation algorithms for approximating the happiness of ARMS with better approximation ratios and time complexities than known algorithms for approximating the regret.  ...  DMM works similarly to HittingSet but instead formulates the problem as a matrix min-max problem. 𝜀-Kernel [12] computes an 𝜀-kernel on the original dataset to use as the input to the hitting set formulation  ... 
arXiv:2102.03578v3 fatcat:hdlvnqkwa5dihhvyj7ofuvm7nu
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