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The prescriptive (normative) Bayesian theory of decision making under uncertainty has reached a high level of maturity. The assumption that the decision maker is rational (i.e. that they optimize expected utility, in Savage’s formulation) is central to this theory. However, empirical research indicates that this central assumption is often violated by real decisionmakers. This limits the ability of the prescriptive Bayesian theory to provide a descriptive theory of the real world. One of the reasons that have been proposed for why the assumption of rationality might be violated by real decision makers is the limited cognitive and computational resources of those decision makers, [1][5]. This workshop intends to inspect this core assumption and to consider possible ways to modify or complement it.
Many of the precise issues related to this theme – some of which will be addressed in the invited talks  can be formulated as questions:
• Does the concept of rationality require Bayesian reasoning?
• Does quantum probability theory (extending classical Kolmogorov probability) provide novel insights into the relation between decision making and cognition?
• Do the extensions of expected utility (which is a linear function of the relevant probabilities) to nonlinear functions of probabilities enhance the flexibility of decisionmaking task formulating while respecting the limited cognitive resources of decision makers?
• How can good (meta)heuristics, so successfully used by realworld decision makers, be elicited?
The list is definitely not complete and we expect that contributed talks, posters and informal discussions will extend it. To stimulate the informal discussions, the invited talks will be complemented by discussants challenging them. Altogether, the workshop aims to bring together diverse scientific communities, to brainstorm possible research directions, and to encourage collaboration among researchers with complementary ideas and expertise. The intended outcome is to understand and diminish the discrepancy between the established prescriptive theory and realworld decision making.
The targeted audience is scientists and students from the diverse scientific communities (decision science, cognitive science, natural science, artificial intelligence, machine learning, social science, economics, etc.) interested in various aspects of rationality.
All accepted submissions will be published in a special issue of the Workshop and Conference Proceedings series of the Journal of Machine Learning Research (JMRL).
[1] H.A. Simon: Theories Of DecisionMaking In Economics and Behavioral Science, The American Economic Review, XLIX, 253283, 1959
[2] C.A. Sims Implications of Rational Inattention, J. of Monetary Economics, 50, 3, 665  690, 2003
[3] A. Tversky, D. Kahneman: Advances in Prospect Theory: Cumulative Representation of Uncertainty, J. of Risk and Uncertainty, 5, 297323, 1992
[4] 2011 NIPS Workshop on Decision Making with Multiple Imperfect Decision Makers
[5] 2015 NIPS Workshop on Bounded Optimality and Metareasoning
Thu 11:20 p.m.  11:30 p.m.

Opening session
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Introductory comments by the organisers. 

Thu 11:30 p.m.  12:00 a.m.

Bounded Optimality and Rational Metareasoning in Human Cognition
(Invited talk)
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Human decisionmaking is often described as irrational, being the result of applying errorprone heuristics. I will argue that this is partly a consequence of the use of an unrealistic standard of rationality, and that the notion of bounded optimality from the artificial intelligence literature provides a better framework for understanding human behaviour. Within this framework a rational agent seeks to execute the best algorithm for solving a problem, taking into account available computational resources and the cost of time. We find that several classic heuristics from the decisionmaking literature are bounded optimal, assuming people have access to particular computational resources. This establishes a new problem: how do people find such good heuristics? I will discuss how this problem can be addressed via rational metareasoning, which examines how rational agents should decide what algorithm to use in solving a problem. The result is a view of human decisionmaking in which people are intelligently and flexibly making the most of their limited computational resources. 
Tom Griffiths 
Fri 12:00 a.m.  12:30 a.m.

Rationality and the Bayesian Paradigm
(Invited talk)
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It is argued that, contrary to a rather prevalent view within economic theory, rationality does not imply Bayesianism. The note begins by defining these terms and justifying the choice of these definitions, proceeds to survey the main justification for this prevalent view, and concludes by highlighting its weaknesses. 
Tzachi Gilboa 
Fri 12:30 a.m.  1:00 a.m.

InformationTheoretic Bounded Rationality for Learning and DecisionMaking
(Invited talk)
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We study an informationtheoretic framework of bounded rational decisionmaking that trades off utility maximization against informationprocessing costs. We apply the basic principle of this framework to perceptionaction systems and show how the formation of abstractions and decisionmaking hierarchies depends on informationprocessing costs. 
Daniel A Braun 
Fri 1:00 a.m.  1:30 a.m.

Poster Spotlights
(Poster session)
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Posters: Marcus Buckmann, Özgür Simsek: Decision Heuristics For Comparison: How Good Are They? Sam Ganzfried: Optimal Number of Choices in Rating Contexts. Jan Malte Lichtenberg, Özgür Simsek: Simple Regression Models. Miroslav Kárný: Towards Implementable Prescriptive Decision Making. Krzysztof Drachal: Forecasting Spot Oil Price Using Google Probabilities. Özgür Simsek, Marcus Buckmann: On Learning Decision Heuristics. Marko Ruman, František Hula, Tatiana V. Guy, Miroslav Kárný: RealLife Performance of DeliberationAware Responder in MultiProposer Ultimatum Game. Shaudi Mahdavi, Mohammad Amin Rahimian: Does Hindsight Bias Impede Learning? Vladimíra Seckarová: Performance of KullbackLeibler Based Expert Opinion Pooling for Unlikely Events. Jakub Štech, T.V.Guy: Lazylearning fully probabilistic decision making. Dimitri Ognibene, Vincenzo G. Fiore, Xiaosi Gu: Addiction in a Bounded Rational Model: the role of Exploration and Environment Structure. 

Fri 1:30 a.m.  2:00 a.m.

Coffee break & Poster session
(Poster Session)


Fri 2:00 a.m.  2:30 a.m.

Principles and Algorithms for SelfMotivated Behaviour
(Invited talk)
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For planning with high uncertainty, or with too many possible end positions as in games like Go or even chess, one can almost never solve the optimal control problem and must use some receding horizon heuristics. One such heuristics is based on the idea of maximizing empowerment, namely, keep the number of possible options maximal. This has been formulated using information theoretic ideas as maximizing the information capacity between the sequence of actions and the possible state of the system at some finite horizon, but no efficient algorithm for calculating this capacity was suggested. In this work we propose a concrete and efficient way for calculating the capacity between a sequence of actions and future states, based on local linearization of the dynamics and Gaussian channel capacity calculation. I will describe the new algorithm and some of its interesting implications. 
Naftali Tishby 
Fri 2:30 a.m.  2:50 a.m.

Rational beliefs real agents can have  A logical point of view
(Contributed talk)
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The purpose of this note is to outline a framework for uncertain reasoning which drops unrealistic assumptions about the agents' inferential capabilities. To do so, we envisage a pivotal role for the recent research programme of depthbounded Boolean logics (D'Agostino et al., 2013). We suggest that this can be fruitfully extended to the representation of rational belief under uncertainty. By doing this we lay the foundations for a prescriptive account of rational belief, namely one that realistic agents, as opposed to idealised ones, can feasibly act upon. 

Fri 2:50 a.m.  3:10 a.m.

Overcoming temptation: Incentive design for intertemporal choice
(Contributed talk)
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Individuals are often faced with temptations that can lead them astray from longterm goals. We’re interested in developing interventions that steer individuals toward making good initial decisions and then maintaining those decisions over time. In the realm of financial decision making, a particularly successful approach is the prizelinked savings account: individuals are incentivized to make deposits by tying deposits to a periodic lottery that awards bonuses to the savers. Although these lotteries have been very effective in motivating savers across the globe, they are a onesizefitsall solution. We investigate whether customized bonuses can be more effective. We formalize a delayedgratification task as a Markov decision problem and characterize individuals as rational agents subject to temporal discounting, costs associated with effort, and momenttomoment fluctuations in willpower. Our theory is able to explain key behavioral findings in intertemporal choice. We created an online delayedgratification game in which the player scores points by choosing a queue to wait in and patiently advancing to the front. Data collected from the game is fit to the model, and the instantiated model is then used to optimize predicted player performance over a space of incentives. We demonstrate that customized incentive structures can improve goaldirected decision making. 
Mike Mozer 
Fri 3:10 a.m.  3:30 a.m.

(Ir)rationality of human decision making
(Panel Discussion)

Peter Grünwald 
Fri 3:30 a.m.  5:00 a.m.

Lunch break
(Break)


Fri 5:00 a.m.  5:30 a.m.

The Rational Status of Quantum Probability Theory Applied to Human Decision Making
(Invited talk)
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Quantum probability theory (QPT) is a probabilistic framework, alternative to Classic Probability Theory (CPT) that has been employed to model some of the paradoxical phenomena found with human judgments and decisions. One question that arises, however, is why an agent might behave this way especially given that these judgments and decisions appear to deviate from rationality? We will argue that QPT can fulfill the requirement for the Dutch Book theorem, which has been used to justify the rational status of CPT. A second question is how these quantum processes work? We will show how the heuristic processes people use to make judgments and decisions can be modeled with quantum information theory, which perhaps paradoxically provides a better and more parsimonious description of these boundedly rational heuristic processes people use than models grounded in classic information theory. In sum, we will argue that QPT can offer a principled account of the processes people use to make judgments and decisions with their limited computational resources and those judgments and decisions can nevertheless be quite rational. 
Tim Pleskac 
Fri 5:30 a.m.  5:50 a.m.

Quantum Rational Preferences and Desirability
(Contributed talk)
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We develop a theory of quantum rational decision making in the tradition of Anscombe and Aumann’s axiomatisation of preferences on horse lotteries. It is essentially the Bayesian decision theory generalised to the space of Hermitian matrices. Among other things, this leads us to give a representation theorem showing that quantum complete rational preferences are obtained by means of expected utility considerations. 
Alessio Benavoli 
Fri 5:50 a.m.  6:30 a.m.

Coffee break & Poster session
(Break)


Fri 6:30 a.m.  6:50 a.m.

Safe Probability
(Contributed talk)
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We formalize the idea of probability distributions that lead to reliable predictions about some, but not all aspects of a domain. The resulting notion of 
Peter Grünwald 
Fri 6:50 a.m.  7:20 a.m.

What the Recent Revolution in Network Coding Tells Us About the Organization of Social Groups
(Invited talk)

David H Wolpert 
Fri 7:20 a.m.  7:50 a.m.

Agency and Causality in Decision Making
(Invited talk)
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We review the distinction between evidential and causal decisionmaking and the challenges that this distinction poses to the application of the expected utility principle. We furthermore establish firm connections between causality, informationtheory, and gametheoretic concepts. Finally, we show how to use the aforementioned connections to construct adaptive agents that are universal over a given class of stochastic environments  such as Thompson sampling. 
Pedro Ortega 
Fri 7:50 a.m.  8:20 a.m.

Modelling of Rational Decision Making
(Panel discussion)

David H Wolpert 
Fri 8:20 a.m.  8:30 a.m.

Closing session

Author Information
Miroslav Karny (Institute of Information Theory and Automation)
David H Wolpert (Santa Fe Institute)
David Rios Insua (Rey Juan Carlos University)
Tatiana V. Guy (Institute of Information Theory and Automation)
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