## Competitive collaborative learning (2005)

Venue: | In Proceedings of the 18th Annual Conference on Learning Theory (COLT |

Citations: | 17 - 3 self |

### BibTeX

@INPROCEEDINGS{Awerbuch05competitivecollaborative,

author = {Baruch Awerbuch and Robert D. Kleinberg},

title = {Competitive collaborative learning},

booktitle = {In Proceedings of the 18th Annual Conference on Learning Theory (COLT},

year = {2005},

pages = {233--248},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. We develop algorithms for a community of users to make decisions about selecting products or resources, in a model characterized by two key features: – The quality of the products or resources may vary over time. – Some of the users in the system may be dishonest, manipulating their actions in a Byzantine manner to achieve other goals. We formulate such learning tasks as an algorithmic problem based on the multi-armed bandit problem, but with a set of users (as opposed to a single user), of whom a constant fraction are honest and are partitioned into coalitions such that the users in a coalition perceive the same expected quality if they sample the same resource at the same time. Our main result exhibits an algorithm for this problem which converges in polylogarithmic time to a state in which the average regret (per honest user) is an arbitrarily small constant. 1

### Citations

3247 | The Anatomy of a Large-Scale Hypertextual Web Search Engine
- Brin, Page
- 1998
(Show Context)
Citation Context ...thms (e.g. eBay’s reputation system, the Eigentrust algorithm [10], the ⋆ Supported by NSF grants ANIR-0240551 and CCR-0311795. ⋆⋆ Supported by a Fannie and John Hertz Foundation Fellowship.sPageRank =-=[5, 13]-=- and HITS [11] algorithms for web search) have thus far not been placed on an adequate theoretical foundation. Our goal in this paper is to provide a theoretical framework for understanding the capabi... |

2704 | Authoritative sources in a hyperlinked environment
- Kleinberg
- 1998
(Show Context)
Citation Context ... reputation system, the Eigentrust algorithm [10], the ⋆ Supported by NSF grants ANIR-0240551 and CCR-0311795. ⋆⋆ Supported by a Fannie and John Hertz Foundation Fellowship.sPageRank [5, 13] and HITS =-=[11]-=- algorithms for web search) have thus far not been placed on an adequate theoretical foundation. Our goal in this paper is to provide a theoretical framework for understanding the capabilities and lim... |

2136 | T.: The pagerank citation ranking: Bringing order to the web
- Page, Brin, et al.
- 1998
(Show Context)
Citation Context ...thms (e.g. eBay’s reputation system, the Eigentrust algorithm [10], the ⋆ Supported by NSF grants ANIR-0240551 and CCR-0311795. ⋆⋆ Supported by a Fannie and John Hertz Foundation Fellowship.sPageRank =-=[5, 13]-=- and HITS [11] algorithms for web search) have thus far not been placed on an adequate theoretical foundation. Our goal in this paper is to provide a theoretical framework for understanding the capabi... |

1115 | Grouplens: An Open Architecture for Collaborative Filtering of Netnews
- Resnick, Iacovou, et al.
- 1994
(Show Context)
Citation Context ...positive constants. For ease of exposition, we will adhere to this assumption when stating the theorems in this section, absorbing such constants into the O(·) notation. See equations (11),(12),(13), =-=(14)-=- in Section 5 for bounds which explicitly indicate the dependence on α, β, and δ; in all cases, this dependence is polynomial. Theorem 1. Suppose the set of honest agents may be partitioned into k sub... |

705 | The EigenTrust algorithm for reputation management in P2P networks
- Kamvar, Schlosser, et al.
- 2003
(Show Context)
Citation Context ...d heuristics for such systems have been proposed and studied experimentally or phenomenologically [5, 11–13, 15–17]. Yet well-known algorithms (e.g. eBay’s reputation system, the Eigentrust algorithm =-=[10]-=-, the ⋆ Supported by NSF grants ANIR-0240551 and CCR-0311795. ⋆⋆ Supported by a Fannie and John Hertz Foundation Fellowship.sPageRank [5, 13] and HITS [11] algorithms for web search) have thus far not... |

692 | Using collaborative filtering to weave an information tapestry
- Goldberg, Nichols, et al.
- 1992
(Show Context)
Citation Context ... consistent. Let’s introduce the following notations: � T� � ¯C(u) 1 = E ˜Ct(u, u) T Then (7) may be rewritten as t=1 B = log 3 (βn)T −1/4 d(u, v) = (Hm+nw(u, v)) −1 . ¯C(u) − ¯ C(v) = d(u, v) · O(B) =-=(8)-=- Note that for a product y ∈ Y , ¯ C(y) is simply the average cost of y, and for an agent x ∈ H, ¯ C(x) is the average cost of the products sampled by x. Let S be a consistent cluster containing x, an... |

331 | document clustering: A feasibility demonstration
- Zamir, Etzioni, et al.
(Show Context)
Citation Context ...combining links — i.e. recommendations — of different web sites). Not surprisingly, many algorithms and heuristics for such systems have been proposed and studied experimentally or phenomenologically =-=[5, 11, 12, 13, 15, 16, 17]-=-. Yet wellknown algorithms (e.g. eBay’s reputation system, the Eigentrust algorithm [10], the PageRank [5, 13] and HITS [11] algorithms for web search) have thus far not been placed on an adequate the... |

319 |
Introduction to Algorithms, 2 nd edition
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...(If not, we may round each wi down to the next-lowest power of 2, then round some of them up to restore the property that their sum is 1.) Now define T to be the Huffman tree of the distribution {wi} =-=[6]-=-. This tree has the property that for any node at depth d, the combined weight of all leaves in its subtree is 2 −d . For a node z of depth d in T, let ˜w(z) = 2 −d · d −2 ; note that if z is a leaf c... |

190 | Agents That Buy and Sell, in
- Maes, Guttman, et al.
- 1999
(Show Context)
Citation Context ... δ are all positive constants. For ease of exposition, we will adhere to this assumption when stating the theorems in this section, absorbing such constants into the O(·) notation. See equations (11),=-=(12)-=-,(13), (14) in Section 5 for bounds which explicitly indicate the dependence on α, β, and δ; in all cases, this dependence is polynomial. Theorem 1. Suppose the set of honest agents may be partitioned... |

186 | Gambling in a rigged casino: The adversarial multi-armed bandit problem
- Auer, Cesa-Bianchi, et al.
- 1995
(Show Context)
Citation Context ... of such systems as a model of distributed computation. We propose a new paradigm for addressing these issues, which is inspired by online learning theory, specifically the multi-armed bandit problem =-=[1]-=-. Our approach aims to highlight the following challenges which confront the users of collaborative decision-making systems such as those cited above. Malicious users. Since the Internet is open for a... |

158 | Latent class models for collaborative filtering
- Hofmann, Puzicha
- 1999
(Show Context)
Citation Context ...test path from x to y ∗ in the directed graph with vertex set S ∪ Y and edge lengths given by d(·, ·), we may sum up the bounds (8) over the edges of P to obtain ¯C(x) − ¯ C(y ∗ ) = O(length(P ) · B) =-=(9)-=- Observe that the left side is the expected normalized regret of agent x. The random edge lengths d(u, v) on the m + n outgoing edges from u are simply the numbers {1, 2, . . . , m + n} in a random pe... |

150 | Spectral analysis of data
- Azar, Fiat, et al.
- 2001
(Show Context)
Citation Context ...n: � T� � E (Ct(ℓt(r)) − Ct(i)) = � � T� E (Ct(ℓt(z)) − Ct(ℓt(z ′ � ))) t=1 = O (z,z ′ )∈P � � z∈P t=1 ρ(z) −1 T 1/2 � � � = O ˜w(z) −1 T 3/4 � z∈P � = O ˜w(i) −1 T 3/4� � 1 = O log 2 � � 1 T 3/4 � . =-=(4)-=- Finally, we may account for the cost of the steps in which zt �= r as follows: � T� � T� E Ct(it) − Ct(ℓt(r)) ≤ Pr(it �= ℓt(r)) t=1 wi ≤ t=1 wi T� Pr(zt �= r) t=1 = T · � ρ(z) = O(T 3/4 ). (5) Summin... |

139 | A social mechanism of reputation management in electronic communities
- Yu, Singh
(Show Context)
Citation Context ...combining links — i.e. recommendations — of different web sites). Not surprisingly, many algorithms and heuristics for such systems have been proposed and studied experimentally or phenomenologically =-=[5, 11, 12, 13, 15, 16, 17]-=-. Yet wellknown algorithms (e.g. eBay’s reputation system, the Eigentrust algorithm [10], the PageRank [5, 13] and HITS [11] algorithms for web search) have thus far not been placed on an adequate the... |

109 | Collaborative reputation mechanisms in electronic marketplaces
- Zacharia, Moukas, et al.
- 1999
(Show Context)
Citation Context ...combining links — i.e. recommendations — of different web sites). Not surprisingly, many algorithms and heuristics for such systems have been proposed and studied experimentally or phenomenologically =-=[5, 11, 12, 13, 15, 16, 17]-=-. Yet wellknown algorithms (e.g. eBay’s reputation system, the Eigentrust algorithm [10], the PageRank [5, 13] and HITS [11] algorithms for web search) have thus far not been placed on an adequate the... |

50 |
Competitive Recommendation Systems
- Drineas, Kerenidis, et al.
- 2002
(Show Context)
Citation Context ...fact that 1/w(u, v) = O(βn log(βn)), and that ˜C(u, v) = ˜ C(v, v) when u, v are consistent, we may rewrite (6) as �� T� � � T� �� E ˜Ct(u, u) − ˜Ct(v, v) t=1 t=1 � 1 = O w(u, v) T 3/4 log 2 � (βn) , =-=(7)-=- provided that u and v are consistent. Let’s introduce the following notations: � T� � ¯C(u) 1 = E ˜Ct(u, u) T Then (7) may be rewritten as t=1 B = log 3 (βn)T −1/4 d(u, v) = (Hm+nw(u, v)) −1 . ¯C(u) ... |

33 |
Improved Recommendation Systems
- Awerbuch, Patt-Shamir, et al.
(Show Context)
Citation Context ...we consider a general, i.e. adversarial, input model. Matrix reconstruction techniques do not suffice in our model. Firstly, they are vulnerable to manipulation by dishonest users, as was observed in =-=[3]-=- and [2]. Dishonest users, who may be in the overwhelming majority, may certainly disrupt the low rank assumption which is crucial in matrix reconstruction approaches. Alternatively, they may report p... |

1 |
Collaboration of untrusting peers
- Awerbuch, Patt-Shamir, et al.
- 2004
(Show Context)
Citation Context ...bsets S1, S2, . . . , Sk, such that the agents in each subset are mutually consistent. Then the normalized regret ˆ R and δ-convergence time T (δ) of TrustFilter satisfy � ˆR = O k · log4 (n) T 1/4 � =-=(2)-=- T (δ) = O(k 4 log 16 (n)). (3) The δ-convergence time bound follows from the regret bound. Typically we are interested in the case where α, β, δ, k are constants, hence we will summarize this result ... |