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Documents authored by Fischer, Felix

Document
Extended Abstract
DOI: 10.4230/LIPIcs.ITCS.2021.86
Unknown I.I.D. Prophets: Better Bounds, Streaming Algorithms, and a New Impossibility (Extended Abstract)

Authors: José Correa, Paul Dütting, Felix Fischer, Kevin Schewior, and Bruno Ziliotto

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
A prophet inequality states, for some α ∈ [0,1], that the expected value achievable by a gambler who sequentially observes random variables X_1,… ,X_n and selects one of them is at least an α fraction of the maximum value in the sequence. We obtain three distinct improvements for a setting that was first studied by Correa et al. (EC, 2019) and is particularly relevant to modern applications in algorithmic pricing. In this setting, the random variables are i.i.d. from an unknown distribution and the gambler has access to an additional β n samples for some β ≥ 0. We first give improved lower bounds on α for a wide range of values of β; specifically, α ≥ (1+β)/e when β ≤ 1/(e-1), which is tight, and α ≥ 0.648 when β = 1, which improves on a bound of around 0.635 due to Correa et al. (SODA, 2020). Adding to their practical appeal, specifically in the context of algorithmic pricing, we then show that the new bounds can be obtained even in a streaming model of computation and thus in situations where the use of relevant data is complicated by the sheer amount of data available. We finally establish that the upper bound of 1/e for the case without samples is robust to additional information about the distribution, and applies also to sequences of i.i.d. random variables whose distribution is itself drawn, according to a known distribution, from a finite set of known candidate distributions. This implies a tight prophet inequality for exchangeable sequences of random variables, answering a question of Hill and Kertz (Contemporary Mathematics, 1992), but leaves open the possibility of better guarantees when the number of candidate distributions is small, a setting we believe is of strong interest to applications.
Cite as

José Correa, Paul Dütting, Felix Fischer, Kevin Schewior, and Bruno Ziliotto. Unknown I.I.D. Prophets: Better Bounds, Streaming Algorithms, and a New Impossibility (Extended Abstract). In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, p. 86:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{correa_et_al:LIPIcs.ITCS.2021.86,
  author =	{Correa, Jos\'{e} and D\"{u}tting, Paul and Fischer, Felix and Schewior, Kevin and Ziliotto, Bruno},
  title =	{{Unknown I.I.D. Prophets: Better Bounds, Streaming Algorithms, and a New Impossibility}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{86:1--86:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.86},
  URN =		{urn:nbn:de:0030-drops-136255},
  doi =		{10.4230/LIPIcs.ITCS.2021.86},
  annote =	{Keywords: Prophet Inequalities, Stopping Theory, Unknown Distributions}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2448
On Iterated Dominance, Matrix Elimination, and Matched Paths

Authors: Felix Brandt, Felix Fischer, and Markus Holzer

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated weak dominance. The two-action case can be reformulated as a natural elimination problem on a matrix, the complexity of which turns out to be surprisingly difficult to characterize and ultimately remains open. We however establish connections to a matching problem along paths in a directed graph, which is computationally hard in general but can also be used to identify tractable cases of matrix elimination. We finally identify different classes of anonymous games where iterated dominance is in P and NP-complete, respectively.
Cite as

Felix Brandt, Felix Fischer, and Markus Holzer. On Iterated Dominance, Matrix Elimination, and Matched Paths. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 107-118, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{brandt_et_al:LIPIcs.STACS.2010.2448,
  author =	{Brandt, Felix and Fischer, Felix and Holzer, Markus},
  title =	{{On Iterated Dominance, Matrix Elimination, and Matched Paths}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{107--118},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2448},
  URN =		{urn:nbn:de:0030-drops-24485},
  doi =		{10.4230/LIPIcs.STACS.2010.2448},
  annote =	{Keywords: Algorithmic Game Theory, Computational Complexity, Iterated Dominance, Matching}
}
Document
DOI: 10.4230/DagSemProc.07271.6
Incentive Compatible Regression Learning

Authors: Ofer Dekel, Felix Fischer, and Ariel D. Procaccia

Published in: Dagstuhl Seminar Proceedings, Volume 7271, Computational Social Systems and the Internet (2007)

Abstract
We initiate the study of incentives in a general machine learning framework. We focus on a game theoretic regression learning setting where private information is elicited from multiple agents, which are interested in different distributions over the sample space. This conflict potentially gives rise to untruthfulness on the part of the agents. In the restricted but important case when distributions are degenerate, and under mild assumptions, we show that agents are motivated to tell the truth. In a more general setting, we study the power and limitations of mechanisms without payments. We finally establish that, in the general setting, the VCG mechanism goes a long way in guaranteeing truthfulness and efficiency.
Cite as

Ofer Dekel, Felix Fischer, and Ariel D. Procaccia. Incentive Compatible Regression Learning. In Computational Social Systems and the Internet. Dagstuhl Seminar Proceedings, Volume 7271, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{dekel_et_al:DagSemProc.07271.6,
  author =	{Dekel, Ofer and Fischer, Felix and Procaccia, Ariel D.},
  title =	{{Incentive Compatible Regression Learning}},
  booktitle =	{Computational Social Systems and the Internet},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7271},
  editor =	{Peter Cramton and Rudolf M\"{u}ller and Eva Tardos and Moshe Tennenholtz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07271.6},
  URN =		{urn:nbn:de:0030-drops-11622},
  doi =		{10.4230/DagSemProc.07271.6},
  annote =	{Keywords: Machine learning, regression, mechanism design}
}
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