arXiv subjects

Felix Fischer

Publications and source records attributed to Felix Fischer.

At least 37 records · Page 2Linked to original sources

arXiv2023

Optimal Impartial Correspondences

We study mechanisms that select a subset of the vertex set of a directed graph in order to maximize the minimum indegree of any selected vertex, subject to an impartiality constraint that the selection of a particular vertex is independent of the outgoing edges of that vertex. For graphs with maximum outdegree $d$, we give a mechanism that selects at most $d+1$ vertices and only selects vertices whose indegree is at least the maximum indegree in the graph minus one. We then show that this is best possible in the sense that no impartial mechanism can only select vertices with maximum degree, even without any restriction on the number of selected vertices. We finally obtain the following trade-off between the maximum number of vertices selected and the minimum indegree of any selected vertex: when selecting at most~$k$ vertices out of $n$, it is possible to only select vertices whose indegree is at least the maximum indegree minus $\lfloor(n-2)/(k-1)\rfloor+1$.

cs.GT↗

arXiv2022

Creating Multimodal Interactive Agents with Imitation and Self-Supervised Learning

A common vision from science fiction is that robots will one day inhabit our physical spaces, sense the world as we do, assist our physical labours, and communicate with us through natural language. Here we study how to design artificial agents that can interact naturally with humans using the simplification of a virtual environment. We show that imitation learning of human-human interactions in a simulated world, in conjunction with self-supervised learning, is sufficient to produce a multimodal interactive agent, which we call MIA, that successfully interacts with non-adversarial humans 75% of the time. We further identify architectural and algorithmic techniques that improve performance, such as hierarchical action selection. Altogether, our results demonstrate that imitation of multi-modal, real-time human behaviour may provide a straightforward and surprisingly effective means of imbuing agents with a rich behavioural prior from which agents might then be fine-tuned for specific purposes, thus laying a foundation for training capable agents for interactive robots or digital assistants. A video of MIA's behaviour may be found at https://youtu.be/ZFgRhviF7mY

cs.LG↗

arXiv2021

Prophet Inequalities for I.I.D. Random Variables from an Unknown Distribution

A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: Given a sequence of random variables $X_1,\dots,X_n$ drawn independently from a distribution $F$, the goal is to choose a stopping time $τ$ so as to maximize $α$ such that for all distributions $F$ we have $\mathbb{E}[X_τ] \geq α\cdot \mathbb{E}[\max_tX_t]$. What makes this problem challenging is that the decision whether $τ=t$ may only depend on the values of the random variables $X_1,\dots,X_t$ and on the distribution $F$. For quite some time the best known bound for the problem was $α\geq1-1/e\approx0.632$ [Hill and Kertz, 1982]. Only recently this bound was improved by Abolhassani et al. [2017], and a tight bound of $α\approx0.745$ was obtained by Correa et al. [2017]. The case where $F$ is unknown, such that the decision whether $τ=t$ may depend only on the values of the first $t$ random variables but not on $F$, is equally well motivated (e.g., [Azar et al., 2014]) but has received much less attention. A straightforward guarantee for this case of $α\geq1/e\approx0.368$ can be derived from the solution to the secretary problem. Our main result is that this bound is tight. Motivated by this impossibility result we investigate the case where the stopping time may additionally depend on a limited number of samples from~$F$. An extension of our main result shows that even with $o(n)$ samples $α\leq 1/e$, so that the interesting case is the one with $Ω(n)$ samples. Here we show that $n$ samples allow for a significant improvement over the secretary problem, while $O(n^2)$ samples are equivalent to knowledge of the distribution: specifically, with $n$ samples $α\geq1-1/e\approx0.632$ and $α\leq\ln(2)\approx0.693$, and with $O(n^2)$ samples $α\geq0.745-ε$ for any $ε>0$.

cs.DS↗

arXiv2020

Unknown I.I.D. Prophets: Better Bounds, Streaming Algorithms, and a New Impossibility

A prophet inequality states, for some $α\in[0,1]$, that the expected value achievable by a gambler who sequentially observes random variables $X_1,\dots,X_n$ 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 $βn$ samples for some $β\geq 0$. We first give improved lower bounds on $α$ for a wide range of values of $β$; specifically, $α\geq(1+β)/e$ when $β\leq 1/(e-1)$, which is tight, and $α\geq 0.648$ 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.

cs.DS↗

arXiv2019

Modeling of GERDA Phase II data

The GERmanium Detector Array (GERDA) experiment at the Gran Sasso underground laboratory (LNGS) of INFN is searching for neutrinoless double-beta ($0νββ$) decay of $^{76}$Ge. The technological challenge of GERDA is to operate in a "background-free" regime in the region of interest (ROI) after analysis cuts for the full 100$\,$kg$\cdot$yr target exposure of the experiment. A careful modeling and decomposition of the full-range energy spectrum is essential to predict the shape and composition of events in the ROI around $Q_{ββ}$ for the $0νββ$ search, to extract a precise measurement of the half-life of the double-beta decay mode with neutrinos ($2νββ$) and in order to identify the location of residual impurities. The latter will permit future experiments to build strategies in order to further lower the background and achieve even better sensitivities. In this article the background decomposition prior to analysis cuts is presented for GERDA Phase II. The background model fit yields a flat spectrum in the ROI with a background index (BI) of $16.04^{+0.78}_{-0.85} \cdot 10^{-3}\,$cts/(kg$\cdot$keV$\cdot$yr) for the enriched BEGe data set and $14.68^{+0.47}_{-0.52} \cdot 10^{-3}\,$cts/(kg$\cdot$keV$\cdot$yr) for the enriched coaxial data set. These values are similar to the one of Gerda Phase I despite a much larger number of detectors and hence radioactive hardware components.

nucl-ex↗

arXiv2019

Revenue Gaps for Static and Dynamic Posted Pricing of Homogeneous Goods

We consider the problem of maximizing the expected revenue from selling $k$ homogeneous goods to $n$ unit-demand buyers who arrive sequentially with independent and identically distributed valuations. In this setting the optimal posted prices are dynamic in the sense that they depend on the remaining numbers of goods and buyers. We investigate how much revenue is lost when a single static price is used instead for all buyers and goods, and prove upper bounds on the ratio between the maximum revenue from dynamic prices and that from static prices. These bounds are tight for all values of $k$ and $n$ and vary depending on a regularity property of the underlying distribution. For general distributions we obtain a ratio of $2-k/n$, for regular distributions a ratio that increases in $n$ and is bounded from above by $1/(1-k^k/(e^{k}k!))$, which is roughly $1/(1-1/(\sqrt{2πk}))$. The lower bounds hold for the revenue gap between dynamic and static prices. The upper bounds are obtained via an ex-ante relaxation of the revenue maximization problem, as a consequence the tight bounds of $2-k/n$ in the general case and of $1/(1-1/(\sqrt{2πk}))$ in the regular case apply also to the potentially larger revenue gap between the optimal incentive-compatible mechanism and the optimal static price. Our results imply that for regular distributions the benefit of dynamic prices vanishes while for non-regular distributions dynamic prices may achieve up to twice the revenue of static prices.

cs.GT↗

arXiv2019

How Reliable is the Crowdsourced Knowledge of Security Implementation?

Stack Overflow (SO) is the most popular online Q&A site for developers to share their expertise in solving programming issues. Given multiple answers to certain questions, developers may take the accepted answer, the answer from a person with high reputation, or the one frequently suggested. However, researchers recently observed exploitable security vulnerabilities in popular SO answers. This observation inspires us to explore the following questions: How much can we trust the security implementation suggestions on SO? If suggested answers are vulnerable, can developers rely on the community's dynamics to infer the vulnerability and identify a secure counterpart? To answer these highly important questions, we conducted a study on SO posts by contrasting secure and insecure advices with the community-given content evaluation. We investigated whether SO incentive mechanism is effective in improving security properties of distributed code examples. Moreover, we also traced duplicated answers to assess whether the community behavior facilitates propagation of secure and insecure code suggestions. We compiled 953 different groups of similar security-related code examples and labeled their security, identifying 785 secure answer posts and 644 insecure ones. Compared with secure suggestions, insecure ones had higher view counts (36,508 vs. 18,713), received a higher score (14 vs. 5), and had significantly more duplicates (3.8 vs. 3.0) on average. 34% of the posts provided by highly reputable so-called trusted users were insecure. Our findings show that there are lots of insecure snippets on SO, while the community-given feedback does not allow differentiating secure from insecure choices. Moreover, the reputation mechanism fails in indicating trustworthy users with respect to security questions, ultimately leaving other users wandering around alone in a software security minefield.

cs.SE↗

arXiv2018

Non-Truthful Position Auctions Are More Robust to Misspecification

In the standard single-dimensional model of position auctions, bidders agree on the relative values of the positions and each of them submits a single bid that is interpreted in terms of these values. Motivated by current practice in sponsored search we consider a situation where the auctioneer uses estimates of the relative values, which may be imprecise, and show that under both complete and incomplete information a non-truthful mechanism is able to support an efficient outcome in equilibrium for a wider range of these estimates than the VCG mechanism. We thus exhibit a property of the VCG mechanism that may help explain the surprising rarity with which it is used even in settings with unit demand, a relative lack of robustness to misspecification of the bidding language. The result for complete information concerns the generalized second-price mechanism and lends additional theoretical support to the use of this mechanism in practice. Particularly interesting from a technical perspective is the result for incomplete information, which is driven by a surprising connection between equilibrium bids in the VCG mechanism and the generalized first-price mechanism.

cs.GT↗

arXiv2017

Stack Overflow Considered Harmful? The Impact of Copy&Paste on Android Application Security

Online programming discussion platforms such as Stack Overflow serve as a rich source of information for software developers. Available information include vibrant discussions and oftentimes ready-to-use code snippets. Anecdotes report that software developers copy and paste code snippets from those information sources for convenience reasons. Such behavior results in a constant flow of community-provided code snippets into production software. To date, the impact of this behaviour on code security is unknown. We answer this highly important question by quantifying the proliferation of security-related code snippets from Stack Overflow in Android applications available on Google Play. Access to the rich source of information available on Stack Overflow including ready-to-use code snippets provides huge benefits for software developers. However, when it comes to code security there are some caveats to bear in mind: Due to the complex nature of code security, it is very difficult to provide ready-to-use and secure solutions for every problem. Hence, integrating a security-related code snippet from Stack Overflow into production software requires caution and expertise. Unsurprisingly, we observed insecure code snippets being copied into Android applications millions of users install from Google Play every day. To quantitatively evaluate the extent of this observation, we scanned Stack Overflow for code snippets and evaluated their security score using a stochastic gradient descent classifier. In order to identify code reuse in Android applications, we applied state-of-the-art static analysis. Our results are alarming: 15.4% of the 1.3 million Android applications we analyzed, contained security-related code snippets from Stack Overflow. Out of these 97.9% contain at least one insecure code snippet.

cs.CR↗

arXiv2017

Short-Channel Field Effect Transistors with 9-Atom and 13-Atom wide Graphene Nanoribbons

Bottom-up synthesized GNRs and GNR heterostructures have promising electronic properties for high performance field effect transistors (FETs) and ultra-low power devices such as tunnelling FETs. However, the short length and wide band gap of these GNRs have prevented the fabrication of devices with the desired performance and switching behaviour. Here, by fabricating short channel (Lch ~20 nm) devices with a thin, high-k gate dielectric and a 9-atom wide (0.95 nm) armchair GNR as the channel material, we demonstrate FETs with high on-current (Ion >1 uA at Vd = -1 V) and high Ion/Ioff ~10^5 at room temperature. We find that the performance of these devices is limited by tunnelling through the Schottky barrier (SB) at the contacts and we observe an increase in the transparency of the barrier by increasing the gate field near the contacts. Our results thus demonstrate successful fabrication of high performance short-channel FETs with bottom-up synthesized armchair GNRs.

cond-mat.mes-hall↗

arXiv2013

Optimal Impartial Selection

We study the problem of selecting a member of a set of agents based on impartial nominations by agents from that set. The problem was studied previously by Alon et al. and Holzman and Moulin and has important applications in situations where representatives are selected from within a group or where publishing or funding decisions are made based on a process of peer review. Our main result concerns a randomized mechanism that in expectation awards the prize to an agent with at least half the maximum number of nominations. Subject to impartiality, this is best possible.

cs.GT↗

arXiv2013

Expressiveness and Robustness of First-Price Position Auctions

Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments.

cs.GT↗

arXiv2012

Payment Rules through Discriminant-Based Classifiers

In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex post regret, we are able to adapt statistical machine learning techniques to the design of payment rules. This computational approach to mechanism design is applicable to domains with multi-dimensional types and situations where computational efficiency is a concern. Specifically, given an outcome rule and access to a type distribution, we train a support vector machine with a special discriminant function structure such that it implicitly establishes a payment rule with desirable incentive properties. We discuss applications to a multi-minded combinatorial auction with a greedy winner-determination algorithm and to an assignment problem with egalitarian outcome rule. Experimental results demonstrate both that the construction produces payment rules with low ex post regret, and that penalizing classification errors is effective in preventing failures of ex post individual rationality.

cs.GT↗

arXiv2011

Simplicity-Expressiveness Tradeoffs in Mechanism Design

A fundamental result in mechanism design theory, the so-called revelation principle, asserts that for many questions concerning the existence of mechanisms with a given outcome one can restrict attention to truthful direct revelation-mechanisms. In practice, however, many mechanism use a restricted message space. This motivates the study of the tradeoffs involved in choosing simplified mechanisms, which can sometimes bring benefits in precluding bad or promoting good equilibria, and other times impose costs on welfare and revenue. We study the simplicity-expressiveness tradeoff in two representative settings, sponsored search auctions and combinatorial auctions, each being a canonical example for complete information and incomplete information analysis, respectively. We observe that the amount of information available to the agents plays an important role for the tradeoff between simplicity and expressiveness.

cs.GT↗

arXiv2010

Mix and Match

Consider a matching problem on a graph where disjoint sets of vertices are privately owned by self-interested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to maximize the number of matches despite self-interest, with agents that each want to maximize the number of their own vertices that match. Each agent can choose to hide some of its vertices, and then privately match the hidden vertices with any of its own vertices that go unmatched by the mechanism. A prominent application of this model is to kidney exchange, where agents correspond to hospitals and vertices to donor-patient pairs. Here hospitals may game an exchange by holding back pairs and harm social welfare. In this paper we seek to design mechanisms that are strategyproof, in the sense that agents cannot benefit from hiding vertices, and approximately maximize efficiency, i.e., produce a matching that is close in cardinality to the maximum cardinality matching. Our main result is the design and analysis of the eponymous Mix-and-Match mechanism; we show that this randomized mechanism is strategyproof and provides a 2-approximation. Lower bounds establish that the mechanism is near optimal.

cs.GT↗

arXiv2010

On Iterated Dominance, Matrix Elimination, and Matched Paths

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.

cs.GT↗

arXiv2009

Sum of Us: Strategyproof Selection from the Selectors

We consider directed graphs over a set of n agents, where an edge (i,j) is taken to mean that agent i supports or trusts agent j. Given such a graph and an integer k\leq n, we wish to select a subset of k agents that maximizes the sum of indegrees, i.e., a subset of k most popular or most trusted agents. At the same time we assume that each individual agent is only interested in being selected, and may misreport its outgoing edges to this end. This problem formulation captures realistic scenarios where agents choose among themselves, which can be found in the context of Internet search, social networks like Twitter, or reputation systems like Epinions. Our goal is to design mechanisms without payments that map each graph to a k-subset of agents to be selected and satisfy the following two constraints: strategyproofness, i.e., agents cannot benefit from misreporting their outgoing edges, and approximate optimality, i.e., the sum of indegrees of the selected subset of agents is always close to optimal. Our first main result is a surprising impossibility: for k \in {1,...,n-1}, no deterministic strategyproof mechanism can provide a finite approximation ratio. Our second main result is a randomized strategyproof mechanism with an approximation ratio that is bounded from above by four for any value of k, and approaches one as k grows.

cs.GT↗

arXiv2009

The Complexity of Computing Minimal Unidirectional Covering Sets

Given a binary dominance relation on a set of alternatives, a common thread in the social sciences is to identify subsets of alternatives that satisfy certain notions of stability. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08] proved that it is NP-hard to decide whether an alternative is contained in some inclusion-minimal upward or downward covering set. For both problems, we raise this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other natural problems regarding minimal or minimum-size covering sets are hard or complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of our results is that neither minimal upward nor minimal downward covering sets (even when guaranteed to exist) can be computed in polynomial time unless P=NP. This sharply contrasts with Brandt and Fischer's result that minimal bidirectional covering sets (i.e., sets that are both minimal upward and minimal downward covering sets) are polynomial-time computable.

cs.CC↗