A. Blum and C. Burch. On-line learning and the metrical task system problem. Proceedings of the 10th Annual Conference on Computational Learning Theory, pages 45--53, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....paper lead to several questions. Although, as remarked in the introduction, dynamic optimality is impossible without additional costs, it is possible to be competitive with the best dynamic solution that is allowed to change k times [13] Using a simple trick presented for the experts framework in [1], any (1 ) competitive algorithm with an additive a= term can be used to get a (1 ) competitive algorithm against a solution that can change k times, with an additive ka= term. One natural question that arises is: what happens if we introduce a cost for moving, say proportional to jx j x ....

Avrim Blum. On-line Learning and the Metrical Task System Problem. Presented at the DIMACS workshop on Online Decision Making, July 1999. See <http://www.cs.cmu.edu/ avrim/surveys.html>.

....paper lead to several questions. Although, as remarked in the introduction, dynamic optimality is impossible without additional costs, it is possible to be competitive with the best dynamic solution that is allowed to change k times [13] Using a simple trick presented for the experts framework in [1], any (1 ) competitive algorithm with an additive a= term can be used to get a (1 ) competitive algorithm against a solution that can change k times, with an additive ka= term. One natural question that arises is: what happens if we introduce a cost for moving, say proportional to jx j ....

Avrim Blum. On-line Learning and the Metrical Task System Problem. Presented at the DIMACS workshop on Online Decision Making, July 1999. See <http://www.cs.cmu.edu/ avrim/surveys.html>.

....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 [CBFH 97] boosting [FS97] pruning of decision trees [HS95] Metrical Task Systems [BB97] online paging [BBK89] adaptive disk spin down for mobile computing [HLS96] and repeated game playing [FS97] Moreover, there are evidences that expert advice algorithms have practical significance, and as noted by Blum and others these algorithms have exceptionally good performance in the ....

....study we generated several simple synthetic expert sets and outcome sequences that attempt to simulate several extreme scenarios, which point out the relative advantage of di#erent algorithms in di#erent scenarios. Our experiments with the calendar data follow and refine the experiments of Blum [BB97] which show that expert advice algorithms can outperform decision tree learning algorithm in a real life prediction problem. We consider the question of which expert advice algorithm to use. The rest of this paper is organized as follows. In Section 2 we formulate the problem setup, discuss ....

[Article contains additional citation context not shown here]

A. Blum and C. Burch. On-line learning and the metrical task system problem. Proceedings of the 10th Annual Conference on Computational Learning Theory, pages 45--53, 1997.

....for arbitrary linear threshold functions that are allowed to shift. These types of algorithms have been shown to be useful in practice, learning shifting concepts such as predicting disk idle times for mobile applications [8] and solving load balancing problems on a network of computers [9]. The additional knowledge that some of these algorithms have good bounds when learning arbitrary shifting linear threshold concepts may help justify applying these algorithms to a wider range of tracking problems. Another contribution of this paper is to show that the tracking version of Winnow ....

Blum, A., Burch, C.: On-line learning and the metrical task system problem. Machine Learning 39 (2000) 35-58

....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 [CBFH 97] boosting [FS97] pruning of decision trees [HS95] Metrical Task Systems [BB97] online paging [BBK89] adaptive disk spin down for mobile computing [HLS96] and repeated game playing [FS97] Moreover, there are evidences that expert advice algorithms have practical significance, and as noted by Blum and others these algorithms have exceptionally good performance in the ....

....study we generated several simple synthetic expert sets and outcome sequences that attempt to simulate several extreme scenarios, which point out the relative advantage of di#erent algorithms in di#erent scenarios. Our experiments with the calendar data follow and refine the experiments of Blum [BB97] which show that expert advice algorithms can outperform decision tree learning algorithm in a real life prediction problem. We consider the question of which expert advice algorithm to use. The rest of this paper is organized as follows. In Section 2 we formulate the problem setup, discuss ....

[Article contains additional citation context not shown here]

A. Blum and C. Burch. On-line learning and the metrical task system problem. Proceedings of the 10th Annual Conference on Computational Learning Theory, pages 45--53, 1997. 35

....individual s growth rate by the inverse of the overall success of the population. This will cause the population s composition to change more quickly when the population as a whole is performing poorly. A form of this also appears as a modification to the randomized weighted majority algorithm (Blum Burch, 1997). In this algorithm, when an expert makes a mistake, a portion of its weight loss is redistributed among the other experts. If the algorithm is placing large weights on mistaken experts (i.e. the algorithm is losing ) then a larger portion of the weights are redistributed (i.e. the algorithm ....

Blum, A., & Burch, C. (1997). On-line learning and the metrical task system problem. Tenth Annual Conference on Computational Learning Theory. Nashville, TN.

....the individuals growth rate by the inverse of the overall success of the population. This will cause the population s composition to change more quickly when the population as a whole is performing poorly. A form of this also appears as a modification to the randomized weighted majority algorithm [Blum and Burch, 1997] . In this algorithm, when an expert makes a mistake, a portion of its weight loss is redistributed among the other experts. If the algorithm is placing large weights on mistaken experts (i.e. the algorithm is losing ) then a larger portion of the weights are redistributed (i.e. the algorithm ....

A. Blum and C. Burch. On-line learning and the metrical task system problem. In Tenth Annual Conference on Computational Learning Theory, 1997.

.... plus the total cost for switching between the experts (say, a constant times the number of switches) plus a small overhead (such as the logarithm of the number of experts) The work on tracking the best expert has been applied to predicting disk idle times [34] and load balancing problems [6]; there is no doubt that this work will find further important applications. 5.3 Bandit problems and reinforcement learning We already mentioned that the philosophy of competitive on line statistics, as described above, only works when Nature is oblivious to Statistician s decisions ( T does ....

Avrim Blum and Carl Burch. On-line learning and the metrical task system problem. In Proceedings of the 10th Annual Conference on Computational Learning Theory, pages 45--53, New York, 1997. Assoc Comput Mach. Also published in Mach Learning.

....is ffd. So classical d PRP is (d; 1) PRP. There does not seem to be a practical motivation for the unfair model, but it turns out to be useful in analyzing existing algorithms on rings. This idea of unfairness has also proved useful in other contexts, notably the metrical task system problem [21, 11]. 3 Single Edges The simplest network consists of two nodes s and t and an edge of length 1 connecting them. d; ff) PRP on an edge is fully understood. Table 2 gives the exact competitive ratio for all deterministic models. The results for the unit size l 0 model are not new; the discrete ....

A. Blum and C. Burch. On-line learning and the metrical task system problem. In Proceedings of the 10th Conference on Computational Learning Theory, pages 45--53, 1997.

....the individuals growth rate by the inverse of the overall success of the population. This will cause the population s composition to change more quickly when the population as a whole is performing poorly. A form of this also appears as a modification to the randomized weighted majority algorithm [1]. In this algorithm, when an expert makes a mistake, a portion of its weight loss is redistributed among the other experts. If the algorithm is placing large weights on mistaken experts (i.e. the algorithm is losing ) then a larger portion of the weights are redistributed (i.e. the algorithm ....

Avrim Blum and Carl Burch. On-line learning and the metrical task system problem. In Tenth Annual Conference on Computational Learning Theory, Nashville, TN, 1997.

....is ffd. So classical d PRP is (d; 1) PRP. There does not seem to be a practical motivation for the unfair model, but it turns out to be useful in analyzing existing algorithms on rings. This idea of unfairness has also proved useful in other contexts, notably the metrical task system problem [24, 11]. 3 Single Edges The simplest network consists of two nodes s and t and an edge of length 1 connecting them. d; ff) PRP on an edge is fully understood. Table 2 gives the exact competitive ratio for all deterministic models. The results for the unit size l 0 model are not new; the discrete model ....

A. Blum and C. Burch. On-line learning and the metrical task system problem. In Proceedings of the 10th Conference on Computational Learning Theory, pages 45--53, 1997.

.... plus the total cost for switching between the experts (say, a constant times the number of switches) plus a small overhead (such as the logarithm of the number of experts) The work on tracking the best expert has been applied to predicting disk idle times [32] and load balancing problems [5]; there is no doubt that this work will nd further important applications. 5.3 Bandit problems We already mentioned that the philosophy of competitive on line statistics, as described above, only works when Nature is oblivious to Statistician s decisions ( T does not depend on 1 ; ....

Avrim Blum and Carl Burch. On-line learning and the metrical task system problem. In Proceedings of the 10th Annual Conference on Computational Learning Theory, pages 45-53, New York, 1997. Assoc Comput Mach. Also published in Mach Learning.

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A. Blum and C. Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35-58, April 2000.

.... for search trees, and that Move to Front is constant competitive for the list update problem [ST85a, ST85b] In a parallel development, powerful algorithms have been developed in Machine Learning for problems of online prediction [LW94, FS96] This paper is inspired by the observation made in [BB00] that if computational decision making costs are not considered, then these weighted experts techniques from Machine Learning allow one to achieve a 1 ratio against the best static object in hindsight for a wide range of data structure problems. In this paper, we give two results. First, ....

....tree algorithm. An interesting point is that in terms of competing against the best static object in hindsight, one can in principle achieve a ratio of 1 for a wide variety of data structure problems, if we ignore time spent computing which update to perform. In particular, Blum and Burch [BB00] show the following general result. email: avrim cs.cmu.edu, Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213 email: shuchi cs.cmu.edu, Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213 email: akalai math.mit.edu, Department of ....

[Article contains additional citation context not shown here]

A. Blum and C. Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35-58, April 2000.

....with competitive ratio ln(p max p min ) 1, which we show is the best possible. A simpler algorithm has ratio twice this, and can be used even if expiration times are not known. These algorithms build on analysis of [7] for the one way trading problem. We also show how online learning results [17, 8, 4] can be used to produce algorithms with even stronger guarantees in certain stationary settings. Maximize liquidity. Liquidity maximization is important for a marketplace for several reasons. The success and reputation of an electronic marketplace is often measured in terms of liquidity, and ....

....xed threshold, and in these cases, the modi ed strategy would be within a (1 ) factor of optimal. The basic idea of this approach is to probabilistically combine all the xed threshold strategies using the Randomized Weighted Majority (also called Hedge) algorithm of [17, 8] as adapted by [4] for the case of experts with internal state. In particular, at any point in time, for each threshold The competitive ratio of Lavi and Nisan [15] is lower than this because they compare their algorithm to the o ine Vickrey auction, not the optimal o ine algorithm. 12 , we can calculate how ....

[Article contains additional citation context not shown here]

A. Blum and C. Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35-58, April 2000.

....with competitive ratio ln(p . P,i) 1, which we show is the best possible. A simpler algorithm has ratio twice this, and can be used even if expiration times are not known. These algorithms build on analysis of [7] for the one way trading problem. 5 We also show how online learning results [17, 8, 4] can be used to produce algorithms with even stronger guarantees in certain stationary settings. Maximize liquidity. Liquidity maximization is important for a marketplace for several reasons. The success and reputation of an electronic marketplace is often measured in terms of liquidity, and this ....

....this threshold as a pair (surpluse, statee) where surplu is the surplus acheived so far, and statee is the set of its current outstanding bids. What we can now do is combine all these fixed threshold algorithms using the Randomized Weighted Majority (Hedge) algorithm of [17, 8] as adapted by [4] for the case of experts with internal state. The important issue here is the following. When the overall master algorithm tells us to switch from threshold to 2, we may not be in as good a state as statee 2 (in particular, we may have fewer outstanding bids) However, suppose we have an ....

[Article contains additional citation context not shown here]

A. Blum and C. Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35 58, April 2000.

....with competitive ratio ln(p max min ) 1, which we show is the best possible. A simpler algorithm has ratio twice this, and can be used even if expiration times are not known. These algorithms build on analysis of [7] for the one way trading problem. We also show how online learning results [17, 8, 4] can be used to produce algorithms with even stronger guarantees in certain stationary settings. Maximize liquidity. Liquidity maximization is important for a marketplace for several reasons. The success and reputation of an electronic marketplace is often measured in terms of liquidity, and ....

....fixed threshold, and in these cases, the modified strategy would be within a (1 #) factor of optimal. The basic idea of this approach is to probabilistically combine all the fixed threshold strategies using the Randomized Weighted Majority (also called Hedge) algorithm of [17, 8] as adapted by [4] for the case of experts with internal state. In particular, at any point in time, for each threshold The competitive ratio of Lavi and Nisan [15] is lower than this because they compare their algorithm to the o#ine Vickrey auction, not the optimal o#ine algorithm. 12 #, we can calculate how ....

[Article contains additional citation context not shown here]

A. Blum and C. Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35--58, April 2000.

....tree algorithm. An interesting point is that in terms of competing against the best static object in hindsight, one can in principle achieve a ratio of l e for a wide variety of data structure problems, if we ignore time spent computing which update to perform. In particular, Blum and Burch [BB00] show the following general result. THEOREM 1.1. THEOREM 4 OF [BB00] Given N on line algorithms for a Metrical Task System Problem of diameter D, and given e O, one can use the Randomized Weighted Majority algorithm to achieve on any request sequence er an expected cost at most (1 e)L ....

....against the best static object in hindsight, one can in principle achieve a ratio of l e for a wide variety of data structure problems, if we ignore time spent computing which update to perform. In particular, Blum and Burch [BB00] show the following general result. THEOREM 1.1. THEOREM 4 OF [BB00]) Given N on line algorithms for a Metrical Task System Problem of diameter D, and given e O, one can use the Randomized Weighted Majority algorithm to achieve on any request sequence er an expected cost at most (1 e)L O(DlogN) where L is the cost of the best of the N algorithms on er in ....

A. Blum and C. Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35-58, April 2000.

....competitive ratio ln(p max Gamma pmin ) 1, which we show is the best possible. A simpler algorithm has ratio twice this, and can be used even if expiration times are not known. These algorithms build on analysis of [7] for the one way trading problem. 5 We also show how online learning results [17, 8, 4] can be used to produce algorithms with even stronger guarantees in certain stationary settings. ffl Maximize liquidity. Liquidity maximization is important for a marketplace for several reasons. The success and reputation of an electronic marketplace is often measured in terms of liquidity, and ....

....threshold as a pair (surplus ; state ) where surplus is the surplus acheived so far, and state is the set of its current outstanding bids. What we can now do is combine all these fixed threshold algorithms using the Randomized Weighted Majority (Hedge) algorithm of [17, 8] as adapted by [4] for the case of experts with internal state. The important issue here is the following. When the overall master algorithm tells us to switch from threshold 1 to 2 , we may not be in as good a state as state 2 (in particular, we may have fewer outstanding bids) However, suppose we have an ....

[Article contains additional citation context not shown here]

A. Blum and C. Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35--58, April 2000.

....tree algorithm. An interesting point is that in terms of competing against the best static object in hindsight, one can in principle achieve a ratio of 1 for a wide variety of data structure problems, if we ignore time spent computing which update to perform. In particular, Blum and Burch [BB00] show the following general result. Theorem 1.1. Theorem 4 of [BB00] Given N on line algorithms for a Metrical Task System Problem of diameter D, and given 0, one can use the Randomized Weighted Majority algorithm to achieve on any request sequence an expected cost at most (1 )L ....

....against the best static object in hindsight, one can in principle achieve a ratio of 1 for a wide variety of data structure problems, if we ignore time spent computing which update to perform. In particular, Blum and Burch [BB00] show the following general result. Theorem 1.1. Theorem 4 of [BB00]) Given N on line algorithms for a Metrical Task System Problem of diameter D, and given 0, one can use the Randomized Weighted Majority algorithm to achieve on any request sequence an expected cost at most (1 )L O( 1 D log N) where L is the cost of the best of the N ....

A. Blum and C. Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35-58, April 2000.

.... of Littlestone and Warmuth and the Fixed Share algorithm of Herbster and Warmuth are variations of the weighted majority algorithm; they work to achieve this type of goal [LW94, HW98] Blum and Burch adapt these algorithm to the DTF Experts setting and respectively call them Thresh and Share [BB97] Given a partition P , let k P denote the number of intervals and L P denote the sum over intervals of the loss incurred by the best expert within that interval. Both algorithms have the property that their total expected loss is bounded by (approximately) E [loss A ] 1 )L P 1 1 ....

....per time step by 1. As Blum and Burch observe, these differences are not always substantial. Indeed, any uniform space MTS algorithm with a reasonable competitive ratio translates to an Experts DTF algorithm with a partitioning bound (though not necessarily as good as bound (1) Theorem 3 ( BB97] Let A be a randomized uniform space MTS algorithm achieving r unfair competitive ratio ae n;r . Then it can be used in the oblivious Experts DTF setting with a partitioning bound of E [loss A ] ae n;r Delta L P ae n;r r Delta k P i ; for any k P segment partition of loss L P . Here i ....

[Article contains additional citation context not shown here]

A. Blum and C. Burch. On-line learning and the metrical task system problem. In Proc ACM Workshop on Computational Learning Theory, pages 45--53, 1997.

....that remains at one scheme after paying only to move from the initial scheme s state to that scheme. This is closely related to the kinds of bounds known for algorithms for predicting from expert advice in the Machine Learning setting [HW95] and these parallels are discussed further in [BB97] 8 Conclusions The strategy implied by Corollary 12 is this paper s main result, a randomized on line MTS algorithm whose competitive ratio is O(log 6 n= log log n) for any metric space. As noted in Section 7, some of the key ingredients to this result have other interesting implications as ....

A. Blum and C. Burch. On-line learning and the metrical task system problem. In Proceedings of the 10th Annual Conference on Computational Learning Theory, pages 45--53, 1997.

....of the paging problem in which there are only k 1 distinct pages requested as an MTS problem on a uniform space of k 1 points. For the r unfair version of this problem, Bartal et al. 2] prove that a randomized work function based algorithm achieves competitive ratio r O(logk) Blum and Burch [3] prove that Herbster and Warmuth s simpler experts algorithm Variable Share [9] achieves a similar bound. We begin by showing that an even simpler algorithm (simpler to describe and to analyze) also achieves an O(r log k) bound, though it has somewhat worse constants than the others. We ....

....in order to make it work. In particular, in the standard machine learning setting, one need not worry about costs for switching between experts as we have here. Moreover, the diameter of the space (the maximum possible cost for switching between two experts) is k, so the generic bound of [3] cannot be used here. A drawback of this approach is that the resulting algorithm is not time efficient in its straightforward implementation, though it appears possible to improve on this somewhat. An interesting question is whether an algorithm for the unfair scenario can be used to get improved ....

A. Blum and C. Burch. On-line learning and the metrical task system problem. In Proc ACM Workshop on Computational Learning Theory, pages 45--53, 1997.

....for changing state. Nonetheless, as Computational Learning Theory moves to analyze more general sorts of learning problems, it seems inevitable that the notion of state will begin to play a larger role, and ideas from On Line Algorithms will be crucial. Some work in this direction appears in [8]. Limiting the power of the adversary. In the On Line Algorithms literature, it is usually assumed that the adversary has unlimited power to choose a worst case sequence for the algorithm. In the machine learning setting, it is natural to assume there is some sort of regularity to the world ....

A. Blum and C. Burch. On-line learning and the metrical task system problem. In Proceedings of the 10th Annual Conference on Computational Learning Theory, pages 45--53, 1997.

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A. Blum and C. Burch. On-line learning and the metrical task system problem. Proceedings of the 10th Annual Conference on Computational Learning Theory, pages 45--53, 1997.

No context found.

A. Blum and C. Burch. On-line learning and the metrical task system problem. In Proceedings of the 10th Conference on Computational Learning Theory, pages 45--53, 1997.

No context found.

Avrim Blum and Carl Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35--58, April 2000.

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Avrim Blum and Carl Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35-58, April 2000.

No context found.

Avrim Blum and Carl Burch. On-line learning and the metrical task system problem. Machine Learning, 39(1):35-58, April 2000.

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A. Blum, C. Burch, On-line learning and the metrical task system prob- lem, in: Tenth Annual Conference on Computational Learning Theory, Nashville, TN, 1997.

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Blum, A., Burch, C.: On-line Learning and the Metrical task System Problem. Proceedings of the 10th Annual Conference on Computational Learning Theory (COLT '97), pages 45--53. To appear in Machine Learning.

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A. Blum, C. Burch, On-line learning and the metrical task system problem, in: Tenth Annual Conference on Computational Learning Theory, Nashville, TN, 1997.

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A. Blum and C. Burch. On-line learning and the metrical task system problem. In Proceedings of the 10th Conference on Computational Learning Theory, pages 45--53, 1997.

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A. Blum and C. Burch. On-line learning and the metrical task system problem. In Proceedings of the 10th Conference on Computational Learning Theory, pages 45-53, 1997. 9

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