{"id":14757,"date":"2022-05-26T22:58:33","date_gmt":"2022-05-27T02:58:33","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=14757"},"modified":"2026-06-09T11:08:57","modified_gmt":"2026-06-09T15:08:57","slug":"tr-159-epsilon-optimal-stubborn-learning-mechanisms","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1989\/tr-159-epsilon-optimal-stubborn-learning-mechanisms\/","title":{"rendered":"TR-159: Epsilon-Optimal Stubborn Learning Mechanisms"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-159: Epsilon-Optimal Stubborn Learning Mechanisms\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1989\/\">Technical Report<\/a>&nbsp;<strong>TR-159<\/strong><br>June 1989<\/p>\n\n\n\n<h2 id=\"epsilon-optimal-stubborn-learning-mechanisms\" class=\"wp-block-heading\">Epsilon-Optimal Stubborn Learning Mechanisms<\/h2>\n\n\n\n<p>J.P.R. Christensen &amp; B.J. Oommen<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>In this paper we present a learning algorithm which has been but marginally referred to in the field of learning machines. The machine is an automaton whose structure changes with time and is assumed to be interacting with a random environment. The machine is essentially a stubborn machine. In other words, once the machine has chosen a particular action it increases the probability of choosing the action irrespective of whether the response from the environment was favourable or unfavourable. However this increase in the action probability is done in a systematic and methodical way so that the machine ultimately learns the best action which the environment offers. We show that the learning mechanism is e-optimal and that the probability of it choosing the optimal action converges uniformly to unity. Apart from the fact that the machine is shown to be e-optimal, a major contribution of this paper is that the mathematical tools used in the proof are quite novel to the field of learning. Besides the above theoretical results, the paper also contains various simulation results which demonstrate the properties of stubbornly learning mechanism. The mechanism is also shown to be inferior to the learning machine which merely ignores the penalty responses of the environment. Some open problems are also presented.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-159.pdf\">TR-159.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report&nbsp;TR-159June 1989 Epsilon-Optimal Stubborn Learning Mechanisms J.P.R. Christensen &amp; B.J. Oommen Abstract In this paper we present a learning algorithm which has been but marginally referred to in the field of learning machines. The machine is an automaton whose structure changes with time and is assumed to be interacting with a random environment. 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