T. Chung. Approximate methods for sequential decision making using expert advice. In Proc ACM Workshop on Computational Learning Theory, pages 183 189. ACM Press, New York, NY, 1994. S. M. Eskicioglu. Process migration in distributed systems: A comparitive survey. Technical Report TR 90-3, University of Alberta, January 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sequence of requests. Can we combine these algorithms in some generic way into an on line strategy whose performance will never be too much worse than the best of them in hindsight Scenario 1 could be modeled in the decision theoretic experts framework of Freund and Schapire [10] and Chung [7] as follows. We view the machines as ezTverts and the loads on the machine as losses. An unloaded machine has loss 0, indicating that the process would have wasted no time if it had been on that machine, and a heavily loaded machine (not counting the load caused by our process itself) has loss ....

....algorithms and others for the process migration scenario discussed above. 2. Definitions 2.1. T acking exloerts in the decision theoretic setting The first setting we consider is the decision theoretic fi amework for learning fi om expert advice (also called the on line allocation problem) [10, 7]. In this problem the learning algorithm has access to n eloerts and faces a sequence of trials. For trial Z, the algorithm chooses a probability distribution pt over the experts. After choosing this distribution, a loss vector t C [0, 1] is revealed, and the learning algorithm is penalized with ....

T. Chung. Approximate methods for sequential decision making using expert advice. In Proc ACM Workshop on Computational Learning Theory, pages 183 189. ACM Press, New York, NY, 1994. S. M. Eskicioglu. Process migration in distributed systems: A comparitive survey. Technical Report TR 90-3, University of Alberta, January 1990.

....length of the game, T . In the case where the state of the world in each period is not binary, Littlestone and Warmuth [25] and Kivinen and Warmuth [24] show that Theorem 2 holds, but only for particular loss function. Within this literature, Theorem 2 as we have stated it was obtained by Chung [6] and Freund and Schapire [14] A similar result can be found in [12] The loss at time t is jp t Gamma XT j, where the p t is the prediction at time t and X t = 0; 1 is the state of the world. We close this section with a pleasing implication of Theorem 2. In any sequence of 0 s and 1 s ....

Chung, T. H., `Approximate methods for sequential decision making using expert advice ', Proceedings of the 7th Annual ACM Conference on Computational Learning Theory, 183-189, 1994. 26

....load averages during that minute, and then uses this information to decide whether and where to move for the next minute. We could imagine modeling the question of when and where such a process should move in the decision theoretic experts framework of Freund and Schapire [FS95] and Chung [Chu94] as follows. We view the loads on the machine as losses, where an unloaded machine has loss 0, indicating that the process would have wasted 0 time if it had been on that machine, and a heavily loaded machine has loss approaching 1, indicating the process would have wasted nearly the entire ....

.... j for a task. This parameter r is known to the on line and off line MTS algorithms. 2. 2 Tracking experts in the decision theoretic setting The second setting we consider is the decision theoretic framework for learning from expert advice (also called the on line allocation problem) FS95, Chu94] In this problem the learning algorithm faces a sequence of trials. For trial t, the algorithm chooses a probability distribution p over a set of n experts. After choosing this distribution, a loss 2 [0; 1] is revealed, and the learning algorithm is penalized with loss p . This ....

T. Chung. Approximate methods for sequential decision making using expert advice. In Proc Annu. ACM Workshop on Comput. Learning Theory, pages 183-- 189. ACM Press, New York, NY, 1994.

....is that it can make a large loss if none of the experts is good. Our framework for on line prediction is based on the work of Vovk [16, 17] and Cesa Bianchi et al. 2] Similar frameworks have also been considered by Cover [6] Dawid [7] Feder et al. 9, 14, 19] and Mycielski [15] See Chung [5] for recent related results. In this paper, we start by considering the case in which the outcomes are binary, i.e. y t 2 f 0; 1 g for all t. The predictions y t of the algorithm and x t;i of the experts are still allowed to range continuously from 0 to 1. Thus, the algorithm could predict ....

....possible to produce such bounds for arbitrary loss functions. The next challenge is to extend the results for continuous valued outcomes to more general loss functions. Another direction worth exploring is to let outcomes be discrete valued with more than two choices. The recent results of Chung [5] address some of these problems. In this paper we restricted the predictions of the experts to lie between zero and one, except in specific examples where we have indicated how scaling tricks can be used. It would be nice to do a thorough investigation of how scaling the range of the variables ....

T. H. Chung. Approximate methods for sequential decision making using expert advice. In Proc. 7th Annu. ACM Workshop on Comput. Learning Theory, pages 183--189. ACM Press, New York, NY, 1994.

....sequence of requests. Can we combine these algorithms in some generic way into an on line strategy whose performance will never be too much worse than the best of them in hindsight Scenario 1 could be modeled in the decision theoretic experts framework of Freund and Schapire [10] and Chung [7] as follows. We view the machines as experts and the loads on the machine as losses. An unloaded machine has loss 0, indicating that the process would have wasted no time if it had been on that machine, and a heavily loaded machine (not counting the load caused by our process itself) has loss ....

....these algorithms and others for the process migration scenario discussed above. 2. Definitions 2.1. Tracking experts in the decision theoretic setting The first setting we consider is the decision theoretic framework for learning from expert advice (also called the on line allocation problem) [10, 7]. In this problem the learning algorithm has access to n experts and faces a sequence of trials. For trial t, the algorithm chooses a probability distribution p t over the experts. After choosing this distribution, a loss vector t 2 [0; 1] n is revealed, and the learning algorithm is ....

T. Chung. Approximate methods for sequential decision making using expert advice. In Proc ACM Workshop on Computational Learning Theory, pages 183--189. ACM Press, New York, NY, 1994.

....of the learning algorithm approaches that of the best expert. Related generalizations of the expert prediction model were studied by Vovk [12] Kivinen and Warmuth [9] and Haussler, Kivinen and Warmuth [8] Like us, these authors focused primarily on multiplicative weight update algorithms. Chung [2] also presented a generalization, giving the problem a game theoretic treatment. Finally, in Section 4, we show how a similar algorithm can be used for boosting, i.e. for converting any weak PAC learning algorithm into a strong PAC learning algorithm. Unlike the previous boosting algorithms of ....

....roughly, O( ln N) T ) Lemma 3 can also be applied to the other bounds given in Theorem 2 to obtain analogous results. 3 Applications The framework described up to this point is quite general and can be applied in a wide variety of learning problems. Consider the following set up used by Chung [2]. We are given a decision space D, a space of outcomes Y , and a bounded loss function : D Theta Y [0; 1] Actually, our results require only that be bounded, but, by rescaling, we can assume that its range is [0; 1] At every time step t, the learning algorithm selects a decision d t 2 ....

Thomas H. Chung. Approximate methods for sequential decision making using expert advice. In Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, pages 183--189, 1994.

....their load averages during that minute, and then uses this information to decide whether and where to move for the next minute. We could imagine modeling the question of when and where such a process should move in the decision theoretic experts framework of Freund and Schapire [FS95] and Chung [Chu94] as follows. We view the loads on the machine as losses, where an unloaded machine has loss 0, indicating that the process would have wasted 0 time if it had been on that machine, and a heavily loaded machine has loss approaching 1, indicating the process would have wasted nearly the entire ....

.... j for a task. This parameter r is known to the on line and off line MTS algorithms. 2. 2 Tracking experts in the decision theoretic setting The second setting we consider is the decision theoretic framework for learning from expert advice (also called the on line allocation problem) FS95, Chu94] In this problem the learning algorithm faces a sequence of trials. For trial t, the algorithm chooses a probability distribution p t over a set of n experts. After choosing this distribution, a loss vector t 2 [0; 1] n is revealed, and the learning algorithm is penalized with loss p ....

T. Chung. Approximate methods for sequential decision making using expert advice. In Proc Annu. ACM Workshop on Comput. Learning Theory, pages 183-- 189. ACM Press, New York, NY, 1994.

....z UC Santa Cruz, haussler cse.ucsc.edu. x UC Santa Cruz, dph cse.ucsc.edu AT T Laboratories, schapire research.att.com k UC Santa Cruz, manfred cse.ucsc.edu. Haussler, Warmuth and Freund were supported by ONR grant N0001491 J 1162 and NSF grant IRI 9123692. Vov92, Chu94] that no assumptions whatsoever can be made about the actual sequence y = y 1 ; y of outcomes that is observed; the analysis is done in the worst case over all possible binary outcome sequences. Of course no method of prediction can do better than random guessing in the worst case, so ....

Thomas H. Chung. Approximate methods for sequential decision making using expert advice. In Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, pages 183--189, 1994.

....in its network to determine their load averages during that minute, and may use this information to decide what to do next. We could imagine modeling the question of when and where such a process should move in the decision theoretic experts framework of Freund and Schapire [FS95] and Chung [Chu94] as follows. We view the loads on the machine as losses, where an unloaded machine has loss 0, Supported in part by NSF National Young Investigator grant CCR 9357793. y Supported in part by a National Science Foundation Graduate Fellowship. indicating that the process would have wasted no ....

....This is somewhat like diversifying one s holdings in the stock market, for instance. 2. 2 Tracking experts in the decision theoretic setting The second setting we consider is the decision theoretic framework for learning from expert advice (also called the on line allocation problem) FS95, Chu94] In this problem the learning algorithm faces a sequence of trials. For trial t, the algorithm chooses a probability distribution p t over a set of n experts. After choosing this distribution, a loss vector t 2 [0; 1] n is revealed, and the learning algorithm is penalized with loss p t ....

T. Chung. Approximate methods for sequential decision making using expert advice. In Proc Annu. ACM Workshop on Comput. Learning Theory, pages 183--189. ACM Press, New York, NY, 1994.

....at least 3 experts the difference between its performance and the performance of the strategy being optimal for this expert group is O( p log n=n) where n stands for the number of outcomes. 1 Introduction The problem how to use expert advice has been studied in several papers (see, for example [1, 3]) The common feature of studied settings of this problem is Dept. of General Psychology, Faculty of Psychology, Moscow State University, Mohovaya 8 5, Moscow, Russia 103009. E mail: mitina psych1.cogsci.msu.su y Dept. of Mathematical Logic, Faculty of Mechanics and Mathematics, Moscow State ....

T. H. Chung. Approximate methods for sequential decision making using expert advice. In Proc. Seventh Annual ACM Conference on Computational Learning Theory, pages 183--189, 1994.

....the learning algorithm approaches that of the best expert. Related generalizations of the expert prediction model were studied by Vovk [19] Kivinen and Warmuth [14] and Haussler, Kivinen and Warmuth [11] Like us, these authors focused primarily on multiplicative weight update algorithms. Chung [3] also presented a generalization, giving the problem a game theoretic treatment. Boosting Returning to the horse racing story, suppose now that the gambler grows weary of choosing among the experts and instead wishes to create a computer program that will accurately predict the winner of a ....

....roughly, O( ln N) T ) Lemma 4 can also be applied to the other bounds given in Theorem 2 to obtain analogous results. 3 Applications The framework described up to this point is quite general and can be applied in a wide variety of learning problems. Consider the following set up used by Chung [3]. We are given a decision space Delta, a space of outcomes Omega Gamma and a bounded loss function : Delta Theta Omega [0; 1] Actually, our results require only that be bounded, but, by rescaling, we can assume that its range is [0; 1] At every time step t, the learning algorithm ....

Thomas H. Chung. Approximate methods for sequential decision making using expert advice. In Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, pages 183--189, 1994.

.... Closely related work has also been done in the area of mathematical finance, where one seeks a stock portfolio re balancing strategy that performs almost as well as the best strategy in a given comparison class on any market [12, 22] More general decision theoretic scenarios are considered in [10, 37, 1]. Also related is the work on on line competitive algorithms in computer science (see e.g. 34] In this paper we focus on the case in which the comparison class E is finite. Our goal is to develop the most general results possible for this finite case. Whereas most previous papers (with the ....

....is the work on on line competitive algorithms in computer science (see e.g. 34] In this paper we focus on the case in which the comparison class E is finite. Our goal is to develop the most general results possible for this finite case. Whereas most previous papers (with the exception of [35, 37, 10]) have each focused on a single loss function, which has often been different in different disciplines, we give a unified treatment of a very general class of loss functions, including the usual ones. Whereas in many previous papers, very specific forms for the comparison class are studied, e.g. ....

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T. H. Chung, "Approximate methods for sequential decision making using expert advice, " in Proc. 7th Annual ACM Workshop on Computational Learning Theory, New York: ACM Press, 1994, pp. 183--189.

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