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13
A new understanding of prediction markets via noregret learning
 In ACM EC
, 2010
"... We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and noregret learning. We first show that any cost function based prediction market can be interpreted as an algorithm for the commonly studied problem of learning from ..."
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Cited by 31 (10 self)
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We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and noregret learning. We first show that any cost function based prediction market can be interpreted as an algorithm for the commonly studied problem of learning from expert advice by equating the set of outcomes on which bets are placed in the market with the set of experts in the learning setting, and equating trades made in the market with losses observed by the learning algorithm. If the loss of the market organizer is bounded, this bound can be used to derive an O ( √ T) regret bound for the corresponding learning algorithm. We then show that the class of markets with convex cost functions exactly corresponds to the class of Follow the Regularized Leader learning algorithms, with the choice of a cost function in the market corresponding to the choice of a regularizer in the learning problem. Finally, we show an equivalence between market scoring rules and prediction markets with convex cost functions. This implies both that any market scoring rule can be implemented as a cost function based market maker, and that market scoring rules can be interpreted naturally as Follow the Regularized Leader algorithms. These connections provide new insight into how it is that commonly studied markets, such as the Logarithmic Market Scoring Rule, can aggregate opinions into accurate estimates of the likelihood of future events.
Complexity of Combinatorial Market Makers ∗
"... We analyze the computational complexity of market maker pricing algorithms for combinatorial prediction markets. We focus on Hanson’s popular logarithmic market scoring rule market maker (LMSR). Our goal is to implicitly maintain correct LMSR prices across an exponentially large outcome space. We ex ..."
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Cited by 30 (17 self)
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We analyze the computational complexity of market maker pricing algorithms for combinatorial prediction markets. We focus on Hanson’s popular logarithmic market scoring rule market maker (LMSR). Our goal is to implicitly maintain correct LMSR prices across an exponentially large outcome space. We examine both permutation combinatorics, where outcomes are permutations of objects, and Boolean combinatorics, where outcomes are combinations of binary events. We look at three restrictive languages that limit what traders can bet on. Even with severely limited languages, we find that LMSR pricing is #Phard, even when the same language admits polynomialtime matching without the market maker. We then propose an approximation technique for pricing permutation markets based on a recent algorithm for online permutation learning. The connections we draw between LMSR pricing and the vast literature on online learning with expert advice may be of independent interest.
An OptimizationBased Framework for Automated MarketMaking
 EC'11
, 2011
"... We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any ..."
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Cited by 14 (6 self)
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We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any market satisfying a set of intuitive conditions must price securities via a convex cost function, which is constructed via conjugate duality. Rather than deal with an exponentially large or infinite outcome space directly, our framework only requires optimization over a convex hull. By reducing the problem of automated market making to convex optimization, where many efficient algorithms exist, we arrive at a range of new polynomialtime pricing mechanisms for various problems. We demonstrate the advantages of this framework with the design of some particular markets. We also show that by relaxing the convex hull we can gain computational tractability without compromising the market institution’s bounded budget.
A Collaborative Mechanism for Crowdsourcing Prediction Problems
"... Machine Learning competitions such as the Netflix Prize have proven reasonably successful as a method of “crowdsourcing ” prediction tasks. But these competitions have a number of weaknesses, particularly in the incentive structure they create for the participants. We propose a new approach, called ..."
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Cited by 9 (3 self)
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Machine Learning competitions such as the Netflix Prize have proven reasonably successful as a method of “crowdsourcing ” prediction tasks. But these competitions have a number of weaknesses, particularly in the incentive structure they create for the participants. We propose a new approach, called a Crowdsourced Learning Mechanism, in which participants collaboratively “learn ” a hypothesis for a given prediction task. The approach draws heavily from the concept of a prediction market, where traders bet on the likelihood of a future event. In our framework, the mechanism continues to publish the current hypothesis, and participants can modify this hypothesis by wagering on an update. The critical incentive property is that a participant will profit an amount that scales according to how much her update improves performance on a released test set. 1
Prediction without Markets
 Association for Computing Machinery
, 2010
"... Citing recent successes in forecasting elections, movies, products, and other outcomes, prediction market advocates call for widespread use of marketbased methods for government and corporate decision making. Though theoretical and empirical evidence suggests that markets do often outperform altern ..."
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Cited by 7 (1 self)
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Citing recent successes in forecasting elections, movies, products, and other outcomes, prediction market advocates call for widespread use of marketbased methods for government and corporate decision making. Though theoretical and empirical evidence suggests that markets do often outperform alternative mechanisms, less attention has been paid to the magnitude of improvement. Here we compare the performance of prediction markets to conventional methods of prediction, namely polls and statistical models. Examining thousands of sporting and movie events, we find that the relative advantage of prediction markets is surprisingly small, as measured by squared error, calibration, and discrimination. Moreover, these domains also exhibit remarkably steep diminishing returns to information, with nearly all the predictive power captured by only two or three parameters. As policy makers consider adoption of prediction markets, costs should be weighed against potentially modest benefits.
Efficient market making via convex optimization, and a connection to online learning
 ACM Transactions on Economics and Computation. To Appear
, 2012
"... We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any ..."
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Cited by 6 (2 self)
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We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any market satisfying a set of intuitive conditions must price securities via a convex cost function, which is constructed via conjugate duality. Rather than deal with an exponentially large or infinite outcome space directly, our framework only requires optimization over a convex hull. By reducing the problem of automated market making to convex optimization, where many efficient algorithms exist, we arrive at a range of new polynomialtime pricing mechanisms for various problems. We demonstrate the advantages of this framework with the design of some particular markets. We also show that by relaxing the convex hull we can gain computational tractability without compromising the market institution’s bounded budget. Although our framework was designed with the goal of deriving efficient automated market makers for markets with very large outcome spaces, this framework also provides new insights into the relationship between market design and machine learning, and into the complete market setting. Using our framework, we illustrate the mathematical parallels between cost function based markets and online learning and establish a correspondence between cost function based markets and market scoring rules for complete markets. 1
Isoelastic agents and wealth updates in machine learning markets. ICML
, 2012
"... Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium ..."
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Cited by 1 (0 self)
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Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium prices corresponding to alphamixtures, with a particular form of mixing component relating to each agent’s wealth. We also demonstrate that wealth accumulation for logarithmic and other isoelastic agents (through payoffs on prediction of training targets) can implement both Bayesian model updates and mixture weight updates by imposing different market payoff structures. An iterative algorithm is given for market equilibrium computation. We demonstrate that inhomogeneous markets of agents with isoelastic utilities outperform state of the art aggregate classifiers such as random forests, as well as single classifiers (neural networks, decision trees) on a number of machine learning benchmarks, and show that isoelastic combination methods are generally better than their logarithmic counterparts. 1.
Prediction markets: alternative mechanisms for complex environments with few traders. Manag Sci 56(11):1977–1996 Lambert NS, Pennock DM, Shoham Y (2008) Eliciting properties of probability distributions. In: Proceedings of the 9th ACM conference on electr
 In: ACM Conference on Electronic Commerce (EC), pp 253–254 123
, 2010
"... doi 10.1287/mnsc.1100.1226 ..."
An OptimizationBased Framework for Combinatorial Prediction Market Design ∗
"... We build on ideas from convex optimization to create a general framework for the design of efficient prediction markets over very large outcome spaces. 1 ..."
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We build on ideas from convex optimization to create a general framework for the design of efficient prediction markets over very large outcome spaces. 1
Connections Between Markets and Learning
, 2010
"... We provide an overview of recent research exploring the striking mathematical connections that exist between market maker mechanisms for prediction markets and noregret learning. We describe how these connections can be used in the design of efficient prediction markets over combinatorial outcome s ..."
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We provide an overview of recent research exploring the striking mathematical connections that exist between market maker mechanisms for prediction markets and noregret learning. We describe how these connections can be used in the design of efficient prediction markets over combinatorial outcome spaces.