Mälardalen University Press Licentiate Theses

The goal of this thesis is to study the economics of computational learning. Attention is also paid to applications of computational learning models, especially Valiant's so-called `probably approximately correctly' (PAC) learning model, in econometric situations. Specifically, an economically reasonable stopping time model of learning is the subject of two attached papers. In the rst paper, Paper A, the economics of PAC learning are considered. It is shown how a general form of the optimal stopping time bounds can be achieved using the PAC convergence rates for a `pessimistic-rational' learner in the most standard binary case of passive supervised PAC model of finite Vapnik-Chervonenkis (VC) dimension. The second paper, Paper B, states precisely and improves the ideas introduced in Paper A and tests them in a specific and mathematically simple case. Using the maxmin procedure of Gilboa and Schmeidler the bounds for the stopping time are expressed in terms of the largest expected error of recall, and thus, effectively, in terms of the least expected reward. The problem of locating a real number θ by testing whether x i ≤ θ , with x i drawn from an calculated for a range of term rates, sample costs and rewards/penalties from a recall ae included. The standard econometric situations, such as product promotion, market research, credit risk assessment, and bargaining and tenders, where such bounds could be of interest, are pointed. These two papers are the essence of this thesis, and form it togheter with an introduction to the subject of learning. Målet med denna avhandling är att studera optimering av inlärning när det finns kostnader. Speciellt studerar jag Valiants så kallade PAC-inlärningsmodell (Probably Approximately Correctly), ofta använd inom datavetenskap. I två artiklar behandlar jag hur länge, ur ekonomisk synvinkel, inlärningsperioden bör fortsätta. I den första artikeln visar vi hur en generell form av begränsningar av den optimala inlärningsperioden kan fås med hjälp av PAC-konvergenshastigheten för en ’pessimistiskt rationell’ studerande (i det vanligaste binära fallet av passiv PAC-inlärningsmodell med ändlig VC-dimension). I den andra artikeln fördjupar och förbättrar vi idéerna från den första artikeln, och testar dem i en specifik situation som är matematiskt enkel. Med hjälp av Gilboa – Schmeidlers max - minprocedur uttrycker vi begränsningarna av den optimala inlärningsperioden som funktion av det största förväntade felet och därme