Adaptive and Self-Confident On-Line Learning Algorithms

Auer, Péter; Cesa-Bianchi, Nicolò; Gentile, Claudio

doi:10.1006/jcss.2001.1795

Cited by 154 publications

(216 citation statements)

References 35 publications

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“…A simple algebraic manipulation of the above implies the following theorem We can optimize for β in advance, or do it dynamically using Auer et al (2002b) …”

Section: Where L Hi = ∑ T I(t) T H Is the Loss Of The Online Algoritmentioning

confidence: 99%

From External to Internal Regret

2005

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External regret compares the performance of an online algorithm, selecting among N actions, to the performance of the best of those actions in hindsight. Internal regret compares the loss of an online algorithm to the loss of a modified online algorithm, which consistently replaces one action by another.In this paper we give a simple generic reduction that, given an algorithm for the external regret problem, converts it to an efficient online algorithm for the internal regret problem. We provide methods that work both in the full information model, in which the loss of every action is observed at each time step, and the partial information (bandit) model, where at each time step only the loss of the selected action is observed. The importance of internal regret in game theory is due to the fact that in a general game, if each player has sublinear internal regret, then the empirical frequencies converge to a correlated equilibrium.For external regret we also derive a quantitative regret bound for a very general setting of regret, which includes an arbitrary set of modification rules (that possibly modify the online algorithm) and an arbitrary set of time selection functions (each giving different weight to each time step). The regret for a given time selection and modification rule is the difference between the cost of the online algorithm and the cost of the modified online algorithm, where the costs are weighted by the time selection function. This can be viewed as a generalization of the previously-studied sleeping experts setting.

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“…A simple algebraic manipulation of the above implies the following theorem We can optimize for β in advance, or do it dynamically using Auer et al (2002b) …”

Section: Where L Hi = ∑ T I(t) T H Is the Loss Of The Online Algoritmentioning

confidence: 99%

From External to Internal Regret

2005

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“…The algorithm used to update the weights of the second layer is the Incrementally Adaptive Weighted Majority (IAWM) [15]. Denote with o …”

Section: B Implementation and Analysismentioning

confidence: 99%

“…We refer the reader to [15] for the exact details of the update rule of IAWM. Chaining the bound of the PA with the bound of IAWM we have that…”

Section: B Implementation and Analysismentioning

confidence: 99%

A theoretical framework for transfer of knowledge across modalities in artificial and biological systems

Orabona

Caputo

Fillbrandt

et al. 2009

2009 IEEE 8th International Conference on Development and Learning

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Abstract-Learning from sensory patterns associated with different kinds of sensors is paramount for biological systems, as it permits them to cope with complex environments where events rarely appear twice in the same way. In this paper 1 we want to investigate how perceptual categories formed in one sensory modality can be transferred to another modality in biological and artificial systems. We first present a study on Mongolian gerbils that show clear evidence of transfer of knowledge for a perceptual category from the auditory modality to the visual modality. We then introduce an algorithm that mimics the behavior of the rodents within an online learning framework. Experiments on simulated data produced promising results, showing the pertinence of our approach.

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“…The tuning parameter η can be set optimally only when the time length n is known in advance. However, we recall a simple modification of the exponentially weighted average algorithm, proposed by Auer, Cesa-Bianchi, and Gentile (2002), which does not need to know n in advance. A natural adaptive version of the optimal parameter η determined in the case of known time length is formed by defining the tuning parameter at round t by η t = B −1 8 ln N/t.…”

Section: Sequential Prediction: External Regretmentioning

confidence: 99%

Internal Regret in On-Line Portfolio Selection

Stoltz

Lugosi

2003

Learning Theory and Kernel Machines

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Abstract. This paper extends the game-theoretic notion of internal regret to the case of on-line potfolio selection problems. New sequential investment strategies are designed to minimize the cumulative internal regret for all possible market behaviors. Some of the introduced strategies, apart from achieving a small internal regret, achieve an accumulated wealth almost as large as that of the best constantly rebalanced portfolio. It is argued that the low-internal-regret property is related to stability and experiments on real stock exchange data demonstrate that the new strategies achieve better returns compared to some known algorithms.

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Adaptive and Self-Confident On-Line Learning Algorithms

Cited by 154 publications

References 35 publications

From External to Internal Regret

From External to Internal Regret

A theoretical framework for transfer of knowledge across modalities in artificial and biological systems

Internal Regret in On-Line Portfolio Selection

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