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Technical Perspective: A Graph-Theoretic Framework Traces Task Planning

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Algorithmic game theory has made great strides in recent decades by assuming standard economic models of rational agent behavior to study outcomes in distributed computational settings. From the analysis of Internet routing to the design of advertisement auctions and crowdsourcing tasks, researchers leveraged these models to characterize the performance of the underlying systems and guide practitioners in their optimization. These models have tractable mathematical formulations and broadly applicable conclusions that drive their success, but they rely strongly on the assumption of rationality.

The assumption of rationality is at times questionable, particularly in systems in which human actors make most of the decisions and in systems that evolve over time. Humans, simply put, are bad at thinking about the impact of their actions on their environment and their future. We see this every day in the way we manage our time. Students cram for exams despite planning not to, and even though it is well documented that well-spaced studying produces improved learning results with equal effort. Humans in lab experiments also consistently exhibit similar irrational time-inconsistent planning and procrastination behavior.

In the 1990s, economists proposed an alternate model of agent behavior called quasi-hyperbolic discounting, which incorporates time-inconsistencies and procrastination. In this model, agents overinflate the cost of current actions with respect to future days' actions. Thus, an hour of studying today might be as painful as two hours of studying on any future day. Note this causes agents to have a time-inconsistent view of the future: today, the student thinks that tomorrow's costs are equal to that of the day after, but when tomorrow comes, the student will re-evaluate and decide that in fact tomorrow's costs are greater than those of the day after. This time-inconsistency can cause agents to procrastinate indefinitely and abandon valuable goals.

With the growth of personalized computing, it is especially important for researchers to design and analyze systems in the presence of irrational human behavior, such as that described by quasi-hyperbolic discounting. Our cellphones guide us through our lives, helping us, for example, to manage our time, optimize our diets, and achieve our fitness goals. To do so effectively, these apps need a predictive and mathematically tractable model of our behavior. The quasi-hyperbolic discounting model is promising: economists have shown in both lab and field experiments that it is highly predictive. However, the prior literature fails to provide a suitable framework in which to reason about quasi-hyperbolic discounting in the presence of complex planning tasks.

In the following paper, Kleinberg and Oren describe a graph-theoretic framework for task planning with quasi-hyperbolic discounting. In their framework, the goal and the intermediate tasks are nodes in a graph, and the weights of the (directed) edges represent the costs of advancing from one task to the next. The intended present and future actions of a quasi-hyperbolic discounter are simply weighted shortest-paths in this graph.

The framework of Kleinberg and Oren is a step forward in incorporating sophisticated models of human behavior into computational systems.

This formulation allows researchers to use the extensive existing knowledge of graph algorithms to analyze and optimize task planning. In the paper, Kleinberg and Oren use their framework to derive many results. Among these, they characterize tasks that are particularly susceptible to procrastination: they are those that contain a simple structure as a graph minor. They also explore ways to reduce procrastination by choice reduction: by scheduling a midterm exam, an instructor can remove the choice of cramming for the final in the last week of class, resulting in better study habits.

The framework of Kleinberg and Oren, and the characterization and optimization results it enables, is a step forward in incorporating sophisticated models of human behavior into computational systems. Apps designed to increase individual effectiveness and related products can use this framework to help us achieve our personal goals. They can predict when we are in danger of procrastinating, and perhaps, by cleverly hiding the availability of certain actions, they can even help us mitigate the extent of procrastination. Subsequent and future work has and will continue to use the framework to develop many more such useful results. In our complex modern world with its growing plethora of choices, automated planning of the sort aided by this paper and the research it inspires is indispensable.

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Nicole Immorlica ( is a senior researcher at Microsoft Research New England, Cambridge, MA, USA.

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