Prediction with Expert Advice under Discounted Loss

Chernov, Alexey; Zhdanov, Fedor

doi:10.1007/978-3-642-16108-7_22

Cited by 15 publications

(17 citation statements)

References 25 publications

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“…see [29]. By setting the initial weights to , and with the choice , one obtains for all (3) If, on the other hand, for some the function is concave for any fixed (such loss functions are called exp-concave) then, choosing and , one has for all (4) We note that the regret bounds in (2)-(4) do not require a fixed time horizon, that is, they hold simultaneously for all .…”

Section: A Prediction With Expert Advicementioning

confidence: 98%

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Efficient Tracking of Large Classes of Experts

György

Linder

Lugosi

2012

IEEE Trans. Inform. Theory

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In the framework of prediction of individual sequences, sequential prediction methods are to be constructed that perform nearly as well as the best expert from a given class. We consider prediction strategies that compete with the class of switching strategies that can segment a given sequence into several blocks, and follow the advice of a different "base" expert in each block. As usual, the performance of the algorithm is measured by the regret defined as the excess loss relative to the best switching strategy selected in hindsight for the particular sequence to be predicted. In this paper, we construct prediction strategies of low computational cost for the case where the set of base experts is large. In particular, we provide a method that can transform any prediction algorithm that is designed for the base class into a tracking algorithm. The resulting tracking algorithm can take advantage of the prediction performance and potential computational efficiency of in the sense that it can be implemented with time and space complexity only times larger than that of , where is the time horizon and is a parameter of the algorithm. With properly chosen, our algorithm achieves a regret bound of optimal order for , and only times larger than the optimal order for for all typical regret bound types we examined. For example, for predicting binary sequences with switching parameters under the logarithmic loss, our method achieves the optimal regret rate with time complexity for any .

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Section: A Prediction With Expert Advicementioning

confidence: 98%

“…Let be defined by (27). If is convex in its first argument and takes values in the interval and for , then for all and any , the tracking regret satisfies (28) where the function is defined as Furthermore, for and , the adaptive regret of the algorithm satisfies (29) where the function is defined as…”

Section: Lemma 3: For Anymentioning

confidence: 99%

Efficient Tracking of Large Classes of Experts

György

Linder

Lugosi

2012

IEEE Trans. Inform. Theory

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“…As a consequence of this result, the expected regret of mSD matches that of EWA, so the performance bound of EWA, mentioned in the previous section, holds for the mSD algorithm as well [14,Lemma 2]). That is, the following result can be obtained by a slight modification of the proof of [17,Lemma 1] for EWA (the same bound for the specific time-dependent choice of η t discussed after the lemma follows directly as a special case of [18,Theorem 2]).…”

Section: Algorithmmentioning

confidence: 92%

“…A well-known solution to this problem (which is optimal under various conditions) is the EWA prediction method that, at time step t, chooses action i with probability proportional to e −ηtD t−1,i for some sequence of positive step size parameters {η t } T t=1 [2]- [4]. 2 It can be shown (using techniques developed in [17], [18]) that if η t+1 ≤ η t for all t then the average expected regret of this algorithm satisfies E…”

Section: The Shrinking Dartboard Algorithm Revisitedmentioning

confidence: 99%

Near-Optimal Rates for Limited-Delay Universal Lossy Source Coding

György

Neu²

2014

IEEE Trans. Inform. Theory

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International audienceWe consider the problem of limited-delay lossy coding of individual sequences. Here, the goal is to design (fixed-rate) compression schemes to minimize the normalized expected distortion redundancy relative to a reference class of coding schemes, measured as the difference between the average distortion of the algorithm and that of the best coding scheme in the reference class. In compressing a sequence of length T, the best schemes available in the literature achieve an O(T^-1/3) normalized distortion redundancy relative to finite reference classes of limited delay and limited memory, and the same redundancy is achievable, up to logarithmic factors, when the reference class is the set of scalar quantizers. It has also been shown that the distortion redundancy is at least of order T^-1/2 in the latter case, and the lower bound can easily be extended to sufficiently powerful (possibly finite) reference coding schemes. In this paper, we narrow the gap between the upper and lower bounds, and give a compression scheme whose normalized distortion redundancy is O(ln(T)/ T^1/2) relative to any finite class of reference schemes, only a logarithmic factor larger than the lower bound. The method is based on the recently introduced shrinking dartboard prediction algorithm, a variant of exponentially weighted average prediction. The algorithm is also extended to the problem of joint source-channel coding over a (known) stochastic noisy channel and to the case when side information is also available to the decoder (the Wyner–Ziv setting). The same improvements are obtained for these settings as in the case of a noiseless channel. Our method is also applied to the problem of zero-delay scalar quantization, where O(ln(T)/ T^1/2) normalized distortion redundancy is achieved relative to the (infinite) class of scalar quantizers of a given rate, almost achieving the known lower bound of order 1/ T^-1/2. The computationally efficient algorithms known for scalar quantization and the Wyner–Ziv setting carry over to our (improved) coding schemes presented in this paper

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“…If the prediction and outcome spaces are an interval Ω = Γ = [A, B] and the square loss function is 2 we have c(η) = 1 (see [1], [12]) and therefore the optimal value is η = 2 (B−A) 2 . For these values of η we can use a simple substitution function…”

Section: Aggregating Algorithmmentioning

confidence: 99%

Specialist Experts for Prediction with Side Information

Kalnishkan

Adamskiy

Chernov

et al. 2015

2015 IEEE International Conference on Data Mining Workshop (ICDMW)

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Abstract-The paper proposes the vicinities merging algorithm for prediction with side information. The algorithm is based on specialist experts techniques. We use vicinities in the side information domain to identify relevant past examples, apply standard learning techniques to them, and then use prediction with expert advice tools to merge those predictions. Guarantees from the theory of prediction with expert advice ensure that helpful vicinities are selected dynamically. The algorithm automatically converges on the right vicinities from an initial broad selection. We apply the resulting algorithms to two problems, prediction of implied volatility of options and prediction of students' performance at tests. On the problem of predicting implied volatility, the algorithm consistently outperforms naive competitors and a highly-tuned proprietary method used in the industry. When applied to the students' performance, the algorithm never falls behind the baseline and outperforms it when the side information is beneficial.

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Prediction with Expert Advice under Discounted Loss

Cited by 15 publications

References 25 publications

Efficient Tracking of Large Classes of Experts

Efficient Tracking of Large Classes of Experts

Near-Optimal Rates for Limited-Delay Universal Lossy Source Coding

Specialist Experts for Prediction with Side Information

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