Tracking the Best Quantizer

György, András; Linder, Tamás; Lugosi, Gábor

doi:10.1109/tit.2008.917651

Cited by 29 publications

(5 citation statements)

References 36 publications

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“…In this paper we study the on-line shortest path problem, a representative example of structured expert classes that has received attention in the literature for its many applications, including, among others, routing in communication networks; see, e.g., Takimoto and Warmuth [28], Awerbuch et al [3], or György and Ottucsák [17], and adaptive quantizer design in zero-delay lossy source coding; see, György et al [13,14,16]. In this problem, a weighted directed (acyclic) graph is given whose edge weights can change in an arbitrary manner, and the decision maker has to pick in each round a path between two given vertices, such that the weight of this path (the sum of the weights of its composing edges) be as small as possible.…”

Section: Introductionmentioning

confidence: 99%

The Shortest Path Problem Under Partial Monitoring

2006

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The on-line shortest path problem is considered under various models of partial monitoring. Given a weighted directed acyclic graph whose edge weights can change in an arbitrary (adversarial) way, a decision maker has to choose in each round of a game a path between two distinguished vertices such that the loss of the chosen path (defined as the sum of the weights of its composing edges) be as small as possible. In a setting generalizing the multi-armed bandit problem, after choosing a path, the decision maker learns only the weights of those edges that belong to the chosen path. For this problem, an algorithm is given whose average cumulative loss in n rounds exceeds that of the best path, matched off-line to the entire sequence of the edge weights, by a quantity that is proportional to 1/ √ n and depends only polynomially on the number of edges of the graph. The algorithm can be implemented with linear complexity in the number of rounds n and in the number of edges. An extension to the so-called label efficient setting is also given, in which the decision maker is informed about the weights of the edges corresponding to the chosen path at a total of m ≪ n time instances. Another extension is shown where the decision maker competes against a time-varying path, a generalization of the problem of tracking the best expert. A version of the multi-armed bandit setting for shortest path is also discussed where the decision maker learns only the total weight of the chosen path but not the weights of the individual edges on the path. Applications to routing in packet switched networks along with simulation results are also presented.

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Section: Introductionmentioning

confidence: 99%

The Shortest Path Problem Under Partial Monitoring

2006

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“…The following theorem, which bounds the regret with respect to the optimal parameter-drift model, is an analogue of Theorem 5 for Fixed Share. The theorem applies to a wide class of kernel EHMMs, but in particular it holds for the parameter-drift model PD α , for which the transition dynamics are governed by the one-dimensional exponential family (17). It is a strong result that uses the full generality of Lemma 3.…”

Section: G Parameter Driftmentioning

confidence: 95%

“…Important precursors of this work include [13], [14]; the algorithms described there do not combine expert predictions arXiv:1311.6536v1 [cs.IT] 26 Nov 2013 but can be used for that purpose (see Section IV-B for details). The tradeoff between time complexity and regret has received substantial further analysis, see [15], [16], [17], [18], [19], but such work is outside the scope of this introduction. On the other hand, the learning theory community has produced a lot of work on universal prediction under the heading "prediction with expert advice" [7], [20], [21], [22], [6], [23].…”

Section: Introductionmentioning

confidence: 99%

Universal Codes From Switching Strategies

Koolen

Rooij

2013

IEEE Trans. Inform. Theory

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We discuss algorithms for combining sequential prediction strategies, a task which can be viewed as a natural generalisation of the concept of universal coding. We describe a graphical language based on Hidden Markov Models for defining prediction strategies, and we provide both existing and new models as examples. The models include efficient, parameterless models for switching between the input strategies over time, including a model for the case where switches tend to occur in clusters, and finally a new model for the scenario where the prediction strategies have a known relationship, and where jumps are typically between strongly related ones. This last model is relevant for coding time series data where parameter drift is expected. As theoretical contributions we introduce an interpolation construction that is useful in the development and analysis of new algorithms, and we establish a new sophisticated lemma for analysing the individual sequence regret of parameterised models.

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“…Under the deterministic analysis framework, the performance of the algorithm is determined by the time-accumulated squared error [5], [7], [16]. When applied to any sequence {y t } t ≥1 , the algorithm of (1) yields the total accumulated loss…”

Section: Problem Descriptionmentioning

confidence: 99%

A Deterministic Analysis of an Online Convex Mixture of Experts Algorithm

Özkan

Donmez

Tunç

et al. 2015

IEEE Trans. Neural Netw. Learning Syst.

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We analyze an online learning algorithm that adaptively combines outputs of two constituent algorithms (or the experts) running in parallel to estimate an unknown desired signal. This online learning algorithm is shown to achieve and in some cases outperform the mean-square error (MSE) performance of the best constituent algorithm in the steady state. However, the MSE analysis of this algorithm in the literature uses approximations and relies on statistical models on the underlying signals. Hence, such an analysis may not be useful or valid for signals generated by various real-life systems that show high degrees of nonstationarity, limit cycles and that are even chaotic in many cases. In this brief, we produce results in an individual sequence manner. In particular, we relate the time-accumulated squared estimation error of this online algorithm at any time over any interval to the one of the optimal convex mixture of the constituent algorithms directly tuned to the underlying signal in a deterministic sense without any statistical assumptions. In this sense, our analysis provides the transient, steady-state, and tracking behavior of this algorithm in a strong sense without any approximations in the derivations or statistical assumptions on the underlying signals such that our results are guaranteed to hold. We illustrate the introduced results through examples.

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Tracking the Best Quantizer

Cited by 29 publications

References 36 publications

The Shortest Path Problem Under Partial Monitoring

The Shortest Path Problem Under Partial Monitoring

Universal Codes From Switching Strategies

A Deterministic Analysis of an Online Convex Mixture of Experts Algorithm

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