Interpreting Demands as Divergences
Mindika Premachandra (ANU/NICTA)
NICTA SML SEMINARDATE: 2013-02-28
TIME: 11:15:00 - 12:00:00
LOCATION: NICTA - 7 London Circuit
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ABSTRACT:
In prediction markets a tradersa response to the market price is a demand which specifies how much to buy/sell a particular contract. We show that a well-known class of Maximum Expected Utility (MEU) based demand functions relate to the broader class of I-divergences (Chernoff, 1952). This provides motivation to extend the Mirror Descent result of (Frongillo et al., 2012) in Kelly Betting to more general demands and divergences and to the aggregation of the corresponding equilibrium market. Following (Storkey et al., 2012)as analysis of homogeneous Isoelastic Utility agents in equilibrium and the relationship to the I-intergation of (Amari, 2007) (which minimizes the sum of weighted homogeneous I-divergences), we extend this result for markets with inhomogeneous Isoealstic Utility agents and inhomogeneous Exponential agents by interpreting the aggregation as one which minimizes the sum of weighted inhomogeneous I-divergences (by setting the weights appropriately). This strengths the claim of (Storkey et al., 2012) that the equilibrium of machine learning markets generalize the I-mixture formalism.
