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@Article { OrtegaB2013,
   title = {Thermodynamics as a theory of decision-making with information-processing costs},
   journal = {Proceedings of the Royal Society of London A},
   year = {2013},
   month = {3},
   volume = {Epub ahead},
   abstract = {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.},
   department = {Research Group Braun},
   department2 = {Department B{\"u}lthoff},
   web_url = {http://rspa.royalsocietypublishing.org/content/469/2153/20120683.short},
   DOI = {10.1098/rspa.2012.0683},
   author = {Ortega, PA and Braun, DA}
}

@Article { GeneweinB2012,
   title = {A sensorimotor paradigm for Bayesian model selection},
   journal = {Frontiers in Human Neuroscience},
   year = {2012},
   month = {10},
   volume = {6},
   number = {291},
   pages = {1-16},
   abstract = {Sensorimotor control is thought to rely on predictive internal models in order to cope efficiently with uncertain environments. Recently, it has been shown that humans not only learn different internal models for different tasks, but that they also extract common structure between tasks. This raises the question of how the motor system selects between different structures or models, when each model can be associated with a range of different task-specific parameters. Here we design a sensorimotor task that requires subjects to compensate visuomotor shifts in a three-dimensional virtual reality setup, where one of the dimensions can be mapped to a model variable and the other dimension to the parameter variable. By introducing probe trials that are neutral in the parameter dimension, we can directly test for model selection. We found that model selection procedures based on Bayesian statistics provided a better explanation for subjects’ choice behavior than simple non-probabilistic heuristics. Our experimental design lends itself to the general study of model selection in a sensorimotor context as it allows to separately query model and parameter variables from subjects.},
   department = {Department B{\"u}lthoff},
   department2 = {Research Group Braun},
   web_url = {http://www.frontiersin.org/Human_Neuroscience/10.3389/fnhum.2012.00291/abstract},
   DOI = {10.3389/fnhum.2012.00291},
   author = {Genewein, T and Braun, DA}
}

@Article { GrauMoyaOB2012,
   title = {Risk-Sensitivity in Bayesian Sensorimotor Integration},
   journal = {PLoS Computational Biology},
   year = {2012},
   month = {9},
   volume = {8},
   number = {9},
   pages = {1-7},
   abstract = {Information processing in the nervous system during sensorimotor tasks with inherent uncertainty has been shown to be consistent with Bayesian integration. Bayes optimal decision-makers are, however, risk-neutral in the sense that they weigh all possibilities based on prior expectation and sensory evidence when they choose the action with highest expected value. In contrast, risk-sensitive decision-makers are sensitive to model uncertainty and bias their decision-making processes when they do inference over unobserved variables. In particular, they allow deviations from their probabilistic model in cases where this model makes imprecise predictions. Here we test for risk-sensitivity in a sensorimotor integration task where subjects exhibit Bayesian information integration when they infer the position of a target from noisy sensory feedback. When introducing a cost associated with subjects' response, we found that subjects exhibited a characteristic bias towards low cost responses when their uncertainty was high. This result is in accordance with risk-sensitive decision-making processes that allow for deviations from Bayes optimal decision-making in the face of uncertainty. Our results suggest that both Bayesian integration and risk-sensitivity are important factors to understand sensorimotor integration in a quantitative fashion.},
   department = {Department B{\"u}lthoff},
   department2 = {Research Group Braun},
   web_url = {http://www.ploscompbiol.org/article/info\%3Adoi\%2F10.1371\%2Fjournal.pcbi.1002698},
   DOI = {10.1371/journal.pcbi.1002698},
   EPUB = {e1002698},
   author = {Grau-Moya, J and Ortega, PA and Braun, DA}
}

@Article { TurnhamBW2012,
   title = {Facilitation of learning induced by both random and gradual visuomotor task variation},
   journal = {Journal of Neurophysiology},
   year = {2012},
   month = {2},
   volume = {107},
   number = {4},
   pages = {1111-1122},
   abstract = {Motor task variation has been shown to be a key ingredient in skill transfer, retention and structural learning. However, many studies only compare training of randomly varying tasks to either blocked or null training, and it is not clear how experiencing different non-random temporal orderings of tasks might affect meta-learning processes. Here we study learning in human subjects who experience the same set of visuomotor rotations, evenly spaced between -60\(^{\circ}\) and +60\(^{\circ}\), either in a random order or in an order in which the rotation angle changed gradually. We compared subsequent learning of three test blocks of +30\(^{\circ}\) &rarr; -30\(^{\circ}\) &rarr; +30\(^{\circ}\) rotations. The groups that underwent either random or gradual training showed significant (p<0.01) facilitation of learning in the test blocks compared to a control group who had not experienced any visuomotor rotations before. We also found that movement initiation times in the random group during the test blocks were significantly (p<0.05) lower than for the gradual or the control group. When we fit a state-space model with fast and slow learning processes to our data, we found that the differences in performance in the test block were consistent with the gradual or random task variation changing the learning and retention rates of only the fast learning process. Such adaptation of learning rates may be a key feature of ongoing meta-learning processes. Our results therefore suggest that both gradual and random task variation can induce meta-learning and that random learning has an advantage in terms of shorter initiation times, suggesting less reliance on cognitive processes.},
   department = {Research Group Braun},
   web_url = {http://jn.physiology.org/content/107/4/1111.full},
   DOI = {10.​1152/​jn.​00635.​2011},
   author = {Turnham, EJA and Braun, DA and Wolpert, DM}
}

@Inproceedings { OrtegaGGBB2012,
   title = {A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function},
   year = {2012},
   month = {12},
   pages = {3014-3022},
   abstract = {We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the distribution over extrema. To this end, we devise a non-parametric conjugate prior where the natural parameter corresponds to a given kernel function and the sufficient statistic is composed of the observed function values. The resulting posterior distribution directly captures the uncertainty over the maximum of the unknown function.},
   url = {http://www.kyb.tuebingen.mpg.defileadmin/user_upload/files/publications/2012/NIPS-2012-Ortega.pdf},
   department = {Department B{\"u}lthoff},
   department2 = {Research Group Braun},
   department3 = {Department Sch{\"o}lkopf},
   web_url = {http://nips.cc/Conferences/2012/},
   editor = {Bartlett, P. , F.C.N. Pereira, L. Bottou, C.J.C. Burges, K.Q. Weinberger},
   booktitle = {Advances in Neural Information Processing Systems 25},
   event_place = {Lake Tahoe, NV, USA},
   event_name = {Twenty-Sixth Annual Conference on Neural Information Processing Systems (NIPS 2012)},
   author = {Ortega, PA and Grau-Moya, J and Genewein, T and Balduzzi, D and Braun, DA}
}

@Inproceedings { OrtegaB2012,
   title = {Adaptive Coding of Actions and Observations},
   year = {2012},
   month = {12},
   pages = {1-4},
   abstract = {The application of expected utility theory to construct adaptive agents is both computationally intractable and statistically questionable. To overcome these difficulties,
agents need the ability to delay the choice of the optimal policy to a later stage when they have learned more about the environment. How should agents do this optimally? An information-theoretic answer to this question is given by the Bayesian control rule&mdash;the solution to the adaptive coding problem when there are not only observations but also actions. This paper reviews the central ideas behind the Bayesian control rule.},
   url = {http://www.kyb.tuebingen.mpg.defileadmin/user_upload/files/publications/2012/NIPS-Workshop-2012-Ortega.pdf},
   department = {Research Group Braun},
   web_url = {http://www.montefiore.ulg.ac.be/\verb=~=tjung/nips12workshop},
   event_place = {Lake Tahoe, NV, USA},
   event_name = {NIPS Workshop on Information in Perception and Action 2012},
   author = {Ortega, PA and Braun, DA}
}

@Inproceedings { OrtegaB2012_2,
   title = {Free Energy and the Generalized Optimality Equations for Sequential Decision Making},
   year = {2012},
   month = {7},
   pages = {1-10},
   abstract = {The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees that include both adversarial and stochastic environments.
We derive generalized sequential optimality equations that not only include the Bellman optimality equations as a limit case, but also lead to well-known decision-rules
such as Expectimax, Minimax and Expectiminimax. We show how these decision-rules can be derived from a single free energy principle that assigns a resource parameter to each
node in the decision tree. These resource parameters express a concrete computational cost that can be measured as the amount of samples that are needed from the distribution that belongs to each node. The free energy principle therefore provides the normative basis for generalized optimality equations that account for both adversarial and stochastic environments.},
   url = {http://www.kyb.tuebingen.mpg.defileadmin/user_upload/files/publications/2012/EWRL-2012-Ortega.pdf},
   department = {Research Group Braun},
   web_url = {http://ewrl.wordpress.com/ewrl10-2012/\#papers},
   event_place = {Edinburgh, Scotland},
   event_name = {10th European Workshop on Reinforcement Learning (EWRL 2012)},
   author = {Ortega, PA and Braun, DA}
}

@Poster { Genewein2012,
   title = {A Sensorimotor Paradigm for Bayesian Model Selection},
   year = {2012},
   month = {9},
   department = {Department B{\"u}lthoff},
   department2 = {Research Group Braun},
   web_url = {http://www.uni-tuebingen.de/einrichtungen/zentrale-einrichtungen/forum-scientiarum/studium/akademien/archiv/sa-2012-2-decisions.html},
   event_place = {Heiligkreuztal, Germany},
   event_name = {T{\"u}bingen International Summerschool 2012 (TISS 2012)},
   author = {Genewein, T}
}

@Poster { GrauMoya2012,
   title = {Risk-sensitivity in Bayesian Sensorimotor Integration},
   year = {2012},
   month = {9},
   department = {Department B{\"u}lthoff},
   department2 = {Research Group Braun},
   web_url = {http://www.uni-tuebingen.de/einrichtungen/zentrale-einrichtungen/forum-scientiarum/studium/akademien/archiv/sa-2012-2-decisions.html},
   event_place = {Heiligkreuztal, Germany},
   event_name = {T{\"u}bingen International Summerschool 2012 (TISS 2012)},
   author = {Grau-Moya, J}
}

@Inproceedings { Ortega2011,
   title = {Bayesian Causal Induction},
   year = {2011},
   month = {12},
   pages = {1-4},
   abstract = {Discovering causal relationships is a hard task, often hindered by the need for intervention, and often requiring large amounts of data to resolve statistical uncertainty.
However, humans quickly arrive at useful causal relationships. One possible reason is that humans extrapolate from past experience to new, unseen situations: that is, they encode beliefs over causal invariances, allowing for sound generalization from the observations they obtain from directly acting in the world. Here we outline a Bayesian model of causal induction where beliefs over competing causal hypotheses are modeled using probability trees. Based on this model, we illustrate why, in the general case, we need interventions plus constraints on our causal hypotheses in order to extract causal information from our experience.},
   url = {http://www.kyb.tuebingen.mpg.defileadmin/user_upload/files/publications/2011/NIPS-2011-Workshop-Ortega.pdf},
   department = {Research Group Braun},
   web_url = {http://www.dsi.unive.it/PhiMaLe2011/},
   event_place = {Sierra Nevada, Spain},
   event_name = {NIPS 2011 Workshop on Philosophy and Machine Learning},
   author = {Ortega, PA}
}