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Mach Learn (2007) 67:77115 DOI 10.1007/s10994-006-0219-y

Summary: Mach Learn (2007) 67:77­115
DOI 10.1007/s10994-006-0219-y
Online calibrated forecasts: Memory efficiency versus
universality for learning in games
Shie Mannor · Jeff S. Shamma · G¨urdal Arslan
Received: 29 September 2005 / Revised: 24 July 2006 / Accepted: 13
August 2006 / Published online: 27 September 2006
Springer Science + Business Media, LLC 2007
Abstract We provide a simple learning process that enables an agent to forecast a
sequence of outcomes. Our forecasting scheme, termed tracking forecast, is based
on tracking the past observations while emphasizing recent outcomes. As opposed
to other forecasting schemes, we sacrifice universality in favor of a significantly re-
duced memory requirements. We show that if the sequence of outcomes has certain
properties--it has some internal (hidden) state that does not change too rapidly--then
the tracking forecast is weakly calibrated so that the forecast appears to be correct
most of the time. For binary outcomes, this result holds without any internal state
assumptions. We consider learning in a repeated strategic game where each player
attempts to compute some forecast of the opponent actions and play a best response
to it. We show that if one of the players uses a tracking forecast, while the other player
uses a standard learning algorithm (such as exponential regret matching or smooth


Source: Arslan, Gürdal - Department of Electrical Engineering, University of Hawai'i at Manoa


Collections: Engineering