Advice Complexity of the Online Search Problem

Clemente, J.; Hromkovič, Juraj; Komm, Dennis; Kudahl, Christian

doi:10.1007/978-3-319-44543-4_16

Cited by 7 publications

(13 citation statements)

References 22 publications

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“…They also established a relation between one-way trading and randomized algorithms for one-way search. Many variations of one-way search or one-way trading problems have since been studied; some examples include the bounded daily return model [1,14], searching for k minima/maxima instead of one [9], time-varying bounds [4], unbounded prices [2], search with advice complexity [3], etc.…”

Section: Previous Results and Related Workmentioning

confidence: 99%

Optimal Online Two-Way Trading with Bounded Number of Transactions

Fung

2018

Algorithmica

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We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to k trades, where each trade must involve the full amount. We give optimal algorithms for three different models which differ in the knowledge of how the price fluctuates. In the first model, there are global minimum and maximum bounds m and M. We first show an optimal lower bound of ϕ (where ϕ = M/m) on the competitive ratio for one trade, which is the bound achieved by trivial algorithms. Perhaps surprisingly, when we consider more than one trade, we can give a better algorithm that loses only a factor of ϕ 2/3 (rather than ϕ) per additional trade. Specifically, for k trades the algorithm has competitive ratio ϕ (2k+1)/3. Furthermore we show that this ratio is the best possible by giving a matching lower bound. In the second model, m and M are not known in advance, and just ϕ is known. We show that this only costs us an extra factor of ϕ 1/3 , i.e., both upper and lower bounds become ϕ (2k+2)/3. Finally, we consider the bounded daily return model where instead of a global limit, the fluctuation from one day to the next is bounded, and again we give optimal algorithms, and interestingly one of them resembles common trading strategies that involve stop loss limits.

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Section: Previous Results and Related Workmentioning

confidence: 99%

Optimal Online Two-Way Trading with Bounded Number of Transactions

Fung

2018

Algorithmica

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“…The prediction error is defined as the number of erroneous responses to the queries, and we assume non-oblivious algorithms which know an upper bound H < n on the error. Online search was previously studied under an error-free query model in [11], however their proposed solution is non-robust: a single query error can force the algorithm to accept a price as bad as the smallest price in the sequence.…”

Section: Contributionmentioning

confidence: 99%

“…With perfect queries (zero error), it is possible to find L x using binary search on T , which leads to a competitive ratio a x /a x−1 = (M/m) 1/2 n , by choosing a reservation price equal to a x−1 . This is the approach of [11]. Unfortunately this simple approach is very inefficient even if a single error occurs (e.g., if Q 1 receives a wrong response, the search will end in a leaf L y , where |x − y| is as large as 2 n/2 .…”

Section: Robust Binary Interval Search Algorithmmentioning

confidence: 99%

“…Online search is a basic paradigm in the class of online financial optimization problems. Several variants and settings have been studied through the prism of competitive analysis; see, e.g., [13,26,35,11]. The problem has also been studied as a case study for evaluating several performance measures of online algorithms, including measures alternative to competitive analysis [9,1].…”

Section: Introductionmentioning

confidence: 99%

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Online Search With Best-Price and Query-Based Predictions

Angelopoulos¹,

Kamali²,

Zhang³

2021

Preprint

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In the online (time-series) search problem, a player is presented with a sequence of prices which are revealed in an online manner. In the standard definition of the problem, for each revealed price, the player must decide irrevocably whether to accept or reject it, without knowledge of future prices (other than an upper and a lower bound on their extreme values), and the objective is to minimize the competitive ratio, namely the worst case ratio between the maximum price in the sequence and the one selected by the player. The problem formulates several applications of decision-making in the face of uncertainty on the revealed samples.Previous work on this problem has largely assumed extreme scenarios in which either the player has almost no information about the input, or the player is provided with some powerful, and error-free advice. In this work, we study learning-augmented algorithms, in which there is a potentially erroneous prediction concerning the input. Specifically, we consider two different settings: the setting in which the prediction is related to the maximum price in the sequence, as well as the setting in which the prediction is obtained as a response to a number of binary queries. For both settings, we provide tight, or near-tight upper and lower bounds on the worstcase performance of search algorithms as a function of the prediction error. We also provide experimental results on data obtained from stock exchange markets that confirm the theoretical analysis, and explain how our techniques can be applicable to other learning-augmented applications.

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“…The relation between one-way trading and randomized algorithms for one-way search is described in [5]. Many variations of one-way search or one-way trading problems have since been studied; some examples include the bounded daily return model [1,11], searching for k minima/maxima instead of one [7], time-varying bounds [4], unbounded prices [2], search with advice complexity [3], etc.…”

Section: Introductionmentioning

confidence: 99%

Optimal Online Two-Way Trading with Bounded Number of Transactions

Fung

2017

Lecture Notes in Computer Science

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Abstract. We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to k trades, where each trade must involve the full amount. We give optimal algorithms for three different models which differ in the knowledge of how the price fluctuates. In the first model, there are global minimum and maximum bounds m and M . We first show an optimal lower bound of ϕ (where ϕ = M/m) on the competitive ratio for one trade, which is the bound achieved by trivial algorithms. Perhaps surprisingly, when we consider more than one trade, we can give a better algorithm that loses only a factor of ϕ 2/3 (rather than ϕ) per additional trade. Specifically, for k trades the algorithm has competitive ratio ϕ (2k+1)/3 . Furthermore we show that this ratio is the best possible by giving a matching lower bound. In the second model, m and M are not known in advance, and just ϕ is known. We show that this only costs us an extra factor of ϕ 1/3 , i.e., both upper and lower bounds become ϕ (2k+2)/3 . Finally, we consider the bounded daily return model where instead of a global limit, the fluctuation from one day to the next is bounded, and again we give optimal algorithms, and interestingly one of them resembles common trading strategies that involve stop loss limits.

show abstract

Advice Complexity of the Online Search Problem

Cited by 7 publications

References 22 publications

Optimal Online Two-Way Trading with Bounded Number of Transactions

Optimal Online Two-Way Trading with Bounded Number of Transactions

Online Search With Best-Price and Query-Based Predictions

Optimal Online Two-Way Trading with Bounded Number of Transactions

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