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AIBO, adapted from, created by Rama, and licensed under the CC-BY-SA-2.0-FR
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Examples of such applications include the problems of navigation, or human-robot interaction. We note that the focus on such classical environments is by no means a restriction of our scheme. For a quantum environment, the actions that the agent can perform could, e.g., be quantum measurements (as components of his actuators), and percepts the measurement outcomes-such scenarios are certainly not without interest. The results we present in this work apply equally to such environments. However, we will not explore the applications of learning agents in quantum environments in this paper
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Examples of such applications include the problems of navigation, or human-robot interaction. We note that the focus on such classical environments is by no means a restriction of our scheme. For a quantum environment, the actions that the agent can perform could, e.g., be quantum measurements (as components of his actuators), and percepts the measurement outcomes-such scenarios are certainly not without interest. The results we present in this work apply equally to such environments. However, we will not explore the applications of learning agents in quantum environments in this paper
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Even if we were to allow superpositions of actions, the amount of control the agent must have over the degrees of freedom of the environment, in order to apply quantum query algorithms, may be prohibitive. This problem constitutes one of the fundamental operative distinctions between quantum algorithms, where full control is assumed, and quantum agents, where such control is limited
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Even if we were to allow superpositions of actions, the amount of control the agent must have over the degrees of freedom of the environment, in order to apply quantum query algorithms, may be prohibitive. This problem constitutes one of the fundamental operative distinctions between quantum algorithms, where full control is assumed, and quantum agents, where such control is limited
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In embodied agents, these physical processes may, e.g., realize some internal representation of the environment, which the agent itself has to develop as it interacts with the environment. For example, in the context of artificial neural networks, such internal models are known as selforganizing maps and, more specifically, sensorimotor maps [58,59]
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In embodied agents, these physical processes may, e.g., realize some internal representation of the environment, which the agent itself has to develop as it interacts with the environment. For example, in the context of artificial neural networks, such internal models are known as selforganizing maps and, more specifically, sensorimotor maps [58,59]
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In the PS framework, one formally distinguishes between real percepts and actions s and a and their internal representations, denoted as ({eth}s{Thorn} and ({eth}a{Thorn}, which comprise clips. For our purposes, by abuse of notation, we will omit the mapping (. For more details, see Appendix C
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In the PS framework, one formally distinguishes between real percepts and actions s and a and their internal representations, denoted as μ{eth}s{Thorn} and μ{eth}a{Thorn}, which comprise clips. For our purposes, by abuse of notation, we will omit the mapping μ. For more details, see Appendix C
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In the PS, the hopping probabilities themselves are encoded in the so-called h matrix, which is an unnormalized representation of the transition matrix [19]
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In the PS, the hopping probabilities themselves are encoded in the so-called h matrix, which is an unnormalized representation of the transition matrix [19]
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Each agent is equipped with input and output couplers, which translate, through sensors and actuators (see Fig. 1), real percepts to the internal representations of percepts, and internal representations of actions to real actions
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Each agent is equipped with input and output couplers, which translate, through sensors and actuators (see Fig. 1), real percepts to the internal representations of percepts, and internal representations of actions to real actions
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In this paper, we do not consider logarithmically contributing terms in the complexity analysis; thus, we use the Õ -level analysis of the limiting behavior (instead of the standard "big-O" O)
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In this paper, we do not consider logarithmically contributing terms in the complexity analysis; thus, we use the Õ -level analysis of the limiting behavior (instead of the standard "big-O" O)
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The optimality claim holds provided that no additional mechanisms, except for diffusion and checking, are available to the agent
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The optimality claim holds provided that no additional mechanisms, except for diffusion and checking, are available to the agent
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*, so V can be constructed from U by conjugating it with the swap operator of the two registers. Here, we present the construction for the general case of irreducible, aperiodic Markov chains
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*, so V can be constructed from U by conjugating it with the swap operator of the two registers. Here, we present the construction for the general case of irreducible, aperiodic Markov chains
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Here, we note that concrete applications of quantum walks specified by nonsymmetric Markov chains have, to our knowledge and aside from this work, only been studied in Refs. [60,61], by two of the authors and other collaborators, in a significantly different context
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Here, we note that concrete applications of quantum walks specified by nonsymmetric Markov chains have, to our knowledge and aside from this work, only been studied in Refs. [60,61], by two of the authors and other collaborators, in a significantly different context
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For completeness, we note, as a technicality, following Ref. [24], that if ?s is always bounded below by a known constant (say, 3=4, as in Ref. [43]), the quantum agent can immediately measure the initial state and efficiently produce the desired output by iterating this process a constant number of times. However, in the scenarios we envision, ?s is very small
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s is very small
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We note that some of the only logarithmically contributing terms, which appear in a more detailed analysis omitted here, can be further avoided using more complicated constructions, as has, for instance, been done in Ref. [24]
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We note that some of the only logarithmically contributing terms, which appear in a more detailed analysis omitted here, can be further avoided using more complicated constructions, as has, for instance, been done in Ref. [24]
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We acknowledge that the interpretation of these results in the sense of their practical impact on the field is not without controversy. Nonetheless, the validity of the mathematical statements is not contested. See Ref. [62] for more details
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We acknowledge that the interpretation of these results in the sense of their practical impact on the field is not without controversy. Nonetheless, the validity of the mathematical statements is not contested. See Ref. [62] for more details
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That is, a comparison can be made with no further assumptions on the environment beyond the trivial ones -that the percept and action sets are compatible with the environment and that the environment provides a rewarding scheme
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That is, a comparison can be made with no further assumptions on the environment beyond the trivial ones -that the percept and action sets are compatible with the environment and that the environment provides a rewarding scheme
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Additionally, the quality of the approximation can be, probabilistically, arbitrarily raised by one round of the phase-estimation algorithm for the walk operator, provided that no phase is detected. Should this process fail, the unsearching process is repeated
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Additionally, the quality of the approximation can be, probabilistically, arbitrarily raised by one round of the phase-estimation algorithm for the walk operator, provided that no phase is detected. Should this process fail, the unsearching process is repeated
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An introduction to discussions regarding the no free lunch theorems, and their interpretations, can be found at
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An introduction to discussions regarding the no free lunch theorems, and their interpretations, can be found at http:// no-free-lunch.org/
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