Finely-competitive paging

Blum, Avrim; Burch, Carl; Kalai, Adam Tauman

doi:10.1109/sffcs.1999.814617

Cited by 28 publications

(29 citation statements)

References 14 publications

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“…Blum et al (2003) discuss algorithms for decision making on lists and trees, for both a competitive analysis setting and an online learning setting, and show how they can be combined using the hedge algorithm (Freund and Schapire (1997)) to provide simultaneous guarantees. Papers such as Blum et al (1999) and Abernethy et al (2010) discuss competitive-analysis algorithms derived using tools from online learning, e.g., regularization. Other works attempt to strengthen the standard regret framework of online learning, such as learning with global cost functions (Even-Dar et al (2009)) and using more adaptive notions of regret as discussed above.…”

Section: Introductionmentioning

confidence: 99%

Unified Algorithms for Online Learning and Competitive Analysis

et al. 2016

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Online learning and competitive analysis are two widely studied frameworks for online decisionmaking settings. Despite the frequent similarity of the problems they study, there are significant differences in their assumptions, goals and techniques, hindering a unified analysis and richer interplay between the two. In this paper, we provide several contributions in this direction. We provide a single unified algorithm which by parameter tuning, interpolates between optimal regret for learning from experts (in online learning) and optimal competitive ratio for the metrical task systems problem (MTS) (in competitive analysis), improving on the results of Blum and Burch (1997). The algorithm also allows us to obtain new regret bounds against "drifting" experts, which might be of independent interest. Moreover, our approach allows us to go beyond experts/MTS, obtaining similar unifying results for structured action sets and "combinatorial experts", whenever the setting has a certain matroid structure.

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Section: Introductionmentioning

confidence: 99%

Unified Algorithms for Online Learning and Competitive Analysis

et al. 2016

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“…To a large extent this extensive focus on the expert advice problem can be attributed to the wide range of applications of expert advice algorithms. Some of these applications are related to agnostic learning (Cesa-Bianchi et al, 1997), boosting , pruning of decision trees (Helmbold & Schapire, 1995), Metrical Task Systems (Blum & Burch, 1997), online paging (Blum, Burch, & Kalai, 1989), adaptive disk spin-down for mobile computing (Helmbold, Long, & Sherrod, 1996), and repeated game playing . Moreover, there is evidence that expert advice algorithms have practical significance, and as noted by Blum and others, these algorithms have "exceptionally good performance in the face of irrelevant features, noise, or a target function changing with time" (Blum, 1997).…”

Section: Introductionmentioning

confidence: 99%

How to Better Use Expert Advice

Yaroshinsky¹,

El‐Yaniv²,

Seiden³

2004

Machine Learning

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Abstract. This work is concerned with online learning from expert advice. Extensive work on this problem generated numerous "expert advice algorithms" whose total loss is provably bounded above in terms of the loss incurred by the best expert in hindsight. Such algorithms were devised for various problem variants corresponding to various loss functions. For some loss functions, such as the square, Hellinger and entropy losses, optimal algorithms are known. However, for two of the most widely used loss functions, namely the 0/1 and absolute loss, there are still gaps between the known lower and upper bounds.In this paper we present two new expert advice algorithms and prove for them the best known 0/1 and absolute loss bounds. Given an expert advice algorithm ALG, the goal is to form an upper bound on the regret L ALG − L * of ALG, where L ALG is the loss of ALG and L * is the loss of the best expert in hindsight. Typically, regret bounds of a "canonical form" C · √ L * ln N are sought where N is the number of experts and C is a constant. So far, the best known constant for the absolute loss function is C = 2.83, which is achieved by the recent IAWM algorithm of Auer et al. (2002). For the 0/1 loss function no bounds of this canonical form are known and the best known regret bound is2 N , where C 1 = e − 2 and C 2 = 2 √ e. This bound is achieved by a "P-norm" algorithm of Gentile and Littlestone (1999). Our first algorithm is a randomized extension of the "guess and double" algorithm of Cesa-Bianchi et al. (1997). While the guess and double algorithm achieves a canonical regret bound with C = 3.32, the expected regret of our randomized algorithm is canonically bounded with C = 2.49 for the absolute loss function. The algorithm utilizes one random choice at the start of the game. Like the deterministic guess and double algorithm, a deficiency of our algorithm is that it occasionally restarts itself and therefore "forgets" what it learned. Our second algorithm does not forget and enjoys the best known asymptotic performance guarantees for both the absolute and 0/1 loss functions. Specifically, in the case of the absolute loss, our algorithm is canonically bounded with C approaching √ 2 and in the case of the 0/1 loss, with C approaching 3/ √ 2 ≈ 2.12. In the 0/1 loss case the algorithm is randomized and the bound is on the expected regret.

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“…Another interesting line of research would be an attempt to apply the techniques of this and previous papers to the randomized k-server problem, or even for a special case such as the randomized weighted caching on k pages problem; see also [8,19].…”

Section: Discussionmentioning

confidence: 99%

Better Algorithms for Unfair Metrical Task Systems and Applications

Fiat¹,

Mendel²

2003

SIAM J. Comput.

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Unfair metrical task systems are a generalization of online metrical task systems. In this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain improved randomized online algorithms for metrical task systems on arbitrary metric spaces. IntroductionMetrical task systems, introduced by Borodin, Linial, and Saks [11], can be described as follows: A server in some internal state receives tasks that have a service cost associated with each of the internal states. The server may switch states, paying a cost given by a metric space defined on the state space, and then pays the service cost associated with the new state.Metrical task systems have been the subject of a great deal of study. A large part of the research into online algorithms can be viewed as a study of some particular metrical task system. In modelling some of these problems as metrical task systems, the set of permissible tasks is constrained to fit the particulars of the problem. In this paper we consider the original definition of metrical task systems where the set of tasks can be arbitrary. A deterministic algorithm for any n-state metrical task system with a competitive ratio of 2n−1 is given in [11], along with a matching lower bound for any metric space.The randomized competitive ratio of the MTS problem is not as well understood. For the uniform metric space, where all distances are equal, the randomized competitive ratio is known to within a constant factor, and is Θ(log n) [11,14]. In fact, it has been conjectured that the randomized competitive ratio for MTS is Θ(log n) in any n-point metric space. Previously, the best upper bound on the competitive ratio for arbitrary n-point metric space was O(log 5 n log log n) due Bartal, Blum, Burch and Tomkins [3] and Bartal [2]. The best lower for any n-point metric space is Ω(log n/ log log n) due to Bartal, Bollobás and Mendel [4] and Bartal, Linial, Mendel and Naor [5], improving previous lower bounds of Karloff, Rabani and Ravid [16], and Blum, Karloff, Rabani, and Saks [10].As observed in [16,10,1] , we obtain an improved algorithm for HSTs. In order to reduce the MTS problem on arbitrary metric space to a MTS problem on a HST we use probabilistic embedding of metric spaces into HSTs [1]. It is shown in [2] that any n-point metric space has probabilistic embedding in k-HSTs with distortion O(k log n log log n). Thus, an MTS problem on an arbitrary n-point metric space, can be reduced to an MTS problem on a k-HST with overhead of O(k log n log log n) [1].Our algorithm for HSTs follows the general framework given in [10] and explicitly formulated in [18,3], where the recursive structure of the HST is modelled by defining an unfair metrical task system problem [18, 3] on a uniform metric space. In an unfair MTS problem, associated with every point v i of the metric space is a cost ratio r i . We charge the online algorithm a cost of r i c i for dealing with the task (c 1 , . . . , c i , . . . , c n ) in state v i . which...

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Finely-competitive paging

Cited by 28 publications

References 14 publications

Unified Algorithms for Online Learning and Competitive Analysis

Unified Algorithms for Online Learning and Competitive Analysis

How to Better Use Expert Advice

Better Algorithms for Unfair Metrical Task Systems and Applications

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