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Daniel Braun - One of the best experts on this subject based on the ideXlab platform.
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bounded Rational Decision making with adaptive neural network priors
arXiv: Artificial Intelligence, 2018Co-Authors: Heinke Hihn, Sebastian Gottwald, Daniel BraunAbstract:Bounded Rationality investigates utility-optimizing Decision-makers with limited information-processing power. In particular, information theoretic bounded Rationality models formalize resource constraints abstractly in terms of relative Shannon information, namely the Kullback-Leibler Divergence between the agents' prior and posterior policy. Between prior and posterior lies an anytime deliberation process that can be instantiated by sample-based evaluations of the utility function through Markov Chain Monte Carlo (MCMC) optimization. The most simple model assumes a fixed prior and can relate abstract information-theoretic processing costs to the number of sample evaluations. However, more advanced models would also address the question of learning, that is how the prior is adapted over time such that generated prior proposals become more efficient. In this work we investigate generative neural networks as priors that are optimized concurrently with anytime sample-based Decision-making processes such as MCMC. We evaluate this approach on toy examples.
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non equilibrium relations for bounded Rational Decision making in changing environments
Entropy, 2017Co-Authors: Jordi Graumoya, Daniel Braun, Matthias KrugerAbstract:Living organisms from single cells to humans need to adapt continuously to respond to changes in their environment. The process of behavioural adaptation can be thought of as improving Decision-making performance according to some utility function. Here, we consider an abstract model of organisms as Decision-makers with limited information-processing resources that trade off between maximization of utility and computational costs measured by a relative entropy, in a similar fashion to thermodynamic systems undergoing isothermal transformations. Such systems minimize the free energy to reach equilibrium states that balance internal energy and entropic cost. When there is a fast change in the environment, these systems evolve in a non-equilibrium fashion because they are unable to follow the path of equilibrium distributions. Here, we apply concepts from non-equilibrium thermodynamics to characterize Decision-makers that adapt to changing environments under the assumption that the temporal evolution of the utility function is externally driven and does not depend on the Decision-maker's action. This allows one to quantify performance loss due to imperfect adaptation in a general manner and, additionally, to find relations for Decision-making similar to Crooks' fluctuation theorem and Jarzynski's equality. We provide simulations of several exemplary Decision and inference problems in the discrete and continuous domains to illustrate the new relations.
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bounded Rational Decision making in feedforward neural networks
arXiv: Artificial Intelligence, 2016Co-Authors: Felix Leibfried, Daniel BraunAbstract:Bounded Rational Decision-makers transform sensory input into motor output under limited computational resources. Mathematically, such Decision-makers can be modeled as information-theoretic channels with limited transmission rate. Here, we apply this formalism for the first time to multilayer feedforward neural networks. We derive synaptic weight update rules for two scenarios, where either each neuron is considered as a bounded Rational Decision-maker or the network as a whole. In the update rules, bounded Rationality translates into information-theoretically motivated types of regularization in weight space. In experiments on the MNIST benchmark classification task for handwritten digits, we show that such information-theoretic regularization successfully prevents overfitting across different architectures and attains results that are competitive with other recent techniques like dropout, dropconnect and Bayes by backprop, for both ordinary and convolutional neural networks.
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adaptive information theoretic bounded Rational Decision making with parametric priors
Neural Information Processing Systems, 2015Co-Authors: Jordi Graumoya, Daniel BraunAbstract:Deviations from Rational Decision-making due to limited computational resources have been studied in the field of bounded Rationality, originally proposed by Herbert Simon. There have been a number of different approaches to model bounded Rationality ranging from optimality principles to heuristics. Here we take an information-theoretic approach to bounded Rationality, where information-processing costs are measured by the relative entropy between a posterior Decision strategy and a given fixed prior strategy. In the case of multiple environments, it can be shown that there is an optimal prior rendering the bounded Rationality problem equivalent to the rate distortion problem for lossy compression in information theory. Accordingly, the optimal prior and posterior strategies can be computed by the well-known Blahut-Arimoto algorithm which requires the computation of partition sums over all possible outcomes and cannot be applied straightforwardly to continuous problems. Here we derive a sampling-based alternative update rule for the adaptation of prior behaviors of Decision-makers and we show convergence to the optimal prior predicted by rate distortion theory. Importantly, the update rule avoids typical infeasible operations such as the computation of partition sums. We show in simulations a proof of concept for discrete action and environment domains. This approach is not only interesting as a generic computational method, but might also provide a more realistic model of human Decision-making processes occurring on a fast and a slow time scale.
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bounded Rational Decision making in changing environments
arXiv: Artificial Intelligence, 2013Co-Authors: Jordi Graumoya, Daniel BraunAbstract:A perfectly Rational Decision-maker chooses the best action with the highest utility gain from a set of possible actions. The optimality principles that describe such Decision processes do not take into account the computational costs of finding the optimal action. Bounded Rational Decision-making addresses this problem by specifically trading off information-processing costs and expected utility. Interestingly, a similar trade-off between energy and entropy arises when describing changes in thermodynamic systems. This similarity has been recently used to describe bounded Rational agents. Crucially, this framework assumes that the environment does not change while the Decision-maker is computing the optimal policy. When this requirement is not fulfilled, the Decision-maker will suffer inefficiencies in utility, that arise because the current policy is optimal for an environment in the past. Here we borrow concepts from non-equilibrium thermodynamics to quantify these inefficiencies and illustrate with simulations its relationship with computational resources.
Samuel J Gershman - One of the best experts on this subject based on the ideXlab platform.
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resource Rational Decision making
Current opinion in behavioral sciences, 2021Co-Authors: Rahul Bhui, Lucy Lai, Samuel J GershmanAbstract:Across many domains of Decision making, people seem both Rational and irRational. We review recent work that aims to reconcile these apparently contradictory views by modeling human Decisions as optimal under a set of cognitive resource constraints. This ‘resource-Rational’ analysis connects psychology and neuroscience to ideas from engineering, economics, and machine learning. Here, we focus on an information-theoretic formalization of cognitive resources, highlighting its implications for understanding three important and widespread phenomena: reference dependence, stochastic choice, and perseveration. While these phenomena have traditionally been viewed as irRational biases or errors, we suggest that they may arise from a Rational solution to the problem of resource-limited Decision making.
Daniel A. Braun - One of the best experts on this subject based on the ideXlab platform.
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bounded Rational Decision making from elementary computations that reduce uncertainty
arXiv: Information Theory, 2019Co-Authors: Sebastian Gottwald, Daniel A. BraunAbstract:In its most basic form, Decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can be reduced is limited by the amount of available computational resources. Here, we introduce the notion of elementary computation based on a fundamental principle for probability transfers that reduce uncertainty. Elementary computations can be considered as the inverse of Pigou-Dalton transfers applied to probability distributions, closely related to the concepts of majorization, T-transforms, and generalized entropies that induce a preorder on the space of probability distributions. As a consequence we can define resource cost functions that are order-preserving and therefore monotonic with respect to the uncertainty reduction. This leads to a comprehensive notion of Decision-making processes with limited resources. Along the way, we prove several new results on majorization theory, as well as on entropy and divergence measures.
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bounded Rational Decision making from elementary computations that reduce uncertainty
Entropy, 2019Co-Authors: Sebastian Gottwald, Daniel A. BraunAbstract:In its most basic form, Decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can be reduced is limited by the amount of available computational resources. Here, we introduce the notion of elementary computation based on a fundamental principle for probability transfers that reduce uncertainty. Elementary computations can be considered as the inverse of Pigou–Dalton transfers applied to probability distributions, closely related to the concepts of majorization, T-transforms, and generalized entropies that induce a preorder on the space of probability distributions. Consequently, we can define resource cost functions that are order-preserving and therefore monotonic with respect to the uncertainty reduction. This leads to a comprehensive notion of Decision-making processes with limited resources. Along the way, we prove several new results on majorization theory, as well as on entropy and divergence measures.
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A reward-maximizing spiking neuron as a bounded Rational Decision maker
Neural Computation, 2015Co-Authors: Felix Leibfried, Daniel A. BraunAbstract:Rate distortion theory describes how to communicate relevant information most efficiently over a channel with limited capacity. One of the many applications of rate distortion theory is bounded Rational Decision making, where Decision makers are modeled as information channels that transform sensory input into motor output under the constraint that their channel capacity is limited. Such a bounded Rational Decision maker can be thought to optimize an objective function that trades off the Decision maker's utility or cumulative reward against the information processing cost measured by the mutual information between sensory input and motor output. In this study, we interpret a spiking neuron as a bounded Rational Decision maker that aims to maximize its expected reward under the computational constraint that the mutual information between the neuron's input and output is upper bounded. This abstract computational constraint translates into a penalization of the deviation between the neuron's instantaneous and average firing behavior. We derive a synaptic weight update rule for such a rate distortion optimizing neuron and show in simulations that the neuron efficiently extracts reward-relevant information from the input by trading off its synaptic strengths against the collected reward.
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thermodynamics as a theory of Decision making with information processing costs
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2013Co-Authors: Pedro A Ortega, Daniel A. BraunAbstract:Perfectly Rational Decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here, we propose a thermodynamically inspired formalization of bounded Rational Decision-making where information processing is modelled as state changes in thermodynamic systems that can be quantified by differences in free energy. By optimizing a free energy, bounded Rational Decision-makers trade off expected utility gains and information-processing costs measured by the relative entropy. As a result, the bounded Rational Decision-making problem can be rephrased in terms of well-known variational principles from statistical physics. In the limit when computational costs are ignored, the maximum expected utility principle is recovered. We discuss links to existing Decision-making frameworks and applications to human Decision-making experiments that are at odds with expected utility theory. Since most of the mathematical machinery can be borrowed from statistical physics, the main contribution is to re-interpret the formalism of thermodynamic free-energy differences in terms of bounded Rational Decision-making and to discuss its relationship to human Decision-making experiments.
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thermodynamics as a theory of Decision making with information processing costs
arXiv: Statistics Theory, 2012Co-Authors: Pedro A Ortega, Daniel A. BraunAbstract:Perfectly Rational Decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we propose an information-theoretic formalization of bounded Rational Decision-making where Decision-makers trade off expected utility and information processing costs. Such bounded Rational Decision-makers can be thought of as thermodynamic machines that undergo physical state changes when they compute. Their behavior is governed by a free energy functional that trades off changes in internal energy-as a proxy for utility-and entropic changes representing computational costs induced by changing states. As a result, the bounded Rational Decision-making problem can be rephrased in terms of well-known concepts from statistical physics. In the limit when computational costs are ignored, the maximum expected utility principle is recovered. We discuss the relation to satisficing Decision-making procedures as well as links to existing theoretical frameworks and human Decision-making experiments that describe deviations from expected utility theory. Since most of the mathematical machinery can be borrowed from statistical physics, the main contribution is to axiomatically derive and interpret the thermodynamic free energy as a model of bounded Rational Decision-making.
Felix Leibfried - One of the best experts on this subject based on the ideXlab platform.
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bounded Rational Decision making in feedforward neural networks
arXiv: Artificial Intelligence, 2016Co-Authors: Felix Leibfried, Daniel BraunAbstract:Bounded Rational Decision-makers transform sensory input into motor output under limited computational resources. Mathematically, such Decision-makers can be modeled as information-theoretic channels with limited transmission rate. Here, we apply this formalism for the first time to multilayer feedforward neural networks. We derive synaptic weight update rules for two scenarios, where either each neuron is considered as a bounded Rational Decision-maker or the network as a whole. In the update rules, bounded Rationality translates into information-theoretically motivated types of regularization in weight space. In experiments on the MNIST benchmark classification task for handwritten digits, we show that such information-theoretic regularization successfully prevents overfitting across different architectures and attains results that are competitive with other recent techniques like dropout, dropconnect and Bayes by backprop, for both ordinary and convolutional neural networks.
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A reward-maximizing spiking neuron as a bounded Rational Decision maker
Neural Computation, 2015Co-Authors: Felix Leibfried, Daniel A. BraunAbstract:Rate distortion theory describes how to communicate relevant information most efficiently over a channel with limited capacity. One of the many applications of rate distortion theory is bounded Rational Decision making, where Decision makers are modeled as information channels that transform sensory input into motor output under the constraint that their channel capacity is limited. Such a bounded Rational Decision maker can be thought to optimize an objective function that trades off the Decision maker's utility or cumulative reward against the information processing cost measured by the mutual information between sensory input and motor output. In this study, we interpret a spiking neuron as a bounded Rational Decision maker that aims to maximize its expected reward under the computational constraint that the mutual information between the neuron's input and output is upper bounded. This abstract computational constraint translates into a penalization of the deviation between the neuron's instantaneous and average firing behavior. We derive a synaptic weight update rule for such a rate distortion optimizing neuron and show in simulations that the neuron efficiently extracts reward-relevant information from the input by trading off its synaptic strengths against the collected reward.
Sopnamayee Acharya - One of the best experts on this subject based on the ideXlab platform.
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impact of procedural Rationality on Decision making in supply chain management
Social Science Research Network, 2012Co-Authors: Sopnamayee AcharyaAbstract:Individual differences in Decision making may account for much order variation in the supply chain settings and bear significant responsibility for supply chain inefficiencies. In a supply chain, sharing information among Decision makers is required to justify the ordering inefficiencies. But individual perceptions may mediate in the use of available information in Decision-making processes. This paper experiments the backlog costs for supply chain to minimize inventory holding. The analysis shows that when Rational Decision making with backlog information was applied, costs decreased, whereas consumer demand information increased the costs.
