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Potential buyers of a product or service tend to read reviews from previous consumers before making their decisions. This behavior is modeled by a market of Bayesian consumers with heterogeneous preferences, who sequentially decide whether to buy an item of unknown quality, based on previous buyers reviews. The quality is multi-dimensional and the reviews can assume one of different forms and can also be multi-dimensional. The belief about the items quality in simple uni-dimensional settings is known to converge to its true value. Our paper extends this result to the more general case of a multidimensional quality, possibly in a continuous space, and provides anytime convergence rates. In practice, the quality of an item may vary over time, due to some change in the production process or the need to keep up with the competition. This paper also studies the learning dynamic when the unknown quality changes at random times and shows that the cost of learning is rather small
Levy walks are found in the migratory behaviour patterns of various organisms, and the reason for this phenomenon has been much discussed. We use simulations to demonstrate that learning causes the changes in confidence level during decision-making i
We investigate stochastic optimization problems under relaxed assumptions on the distribution of noise that are motivated by empirical observations in neural network training. Standard results on optimal convergence rates for stochastic optimization
In data stream mining, predictive models typically suffer drops in predictive performance due to concept drift. As enough data representing the new concept must be collected for the new concept to be well learnt, the predictive performance of existin
We consider a class of sequential decision-making problems under uncertainty that can encompass various types of supervised learning concepts. These problems have a completely observed state process and a partially observed modulation process, where
We study a non standard infinite horizon, infinite dimensional linear-quadratic control problem arising in the physics of non-stationary states (see e.g. cite{BDGJL4,BertiniGabrielliLebowitz05}): finding the minimum energy to drive a given stationary