Kevin Leyton-Brown

To design good policy, we need accurate models of how the decision makers that operate within a given system will respond to policy changes. For example, an economist reasoning about the design of an auction needs a model of human behavior in order to predict how changes to the auction design will be reflected in outcomes; or a doctor deciding on treatments needs a model of people's health responses under different treatments to select the best treatment policy. We would like to leverage the accuracy of modern deep learning approaches to estimate these models, but this setting brings two non-standard challenges. First, decision problems often involve reasoning over sets of items, so we need deep networks that reflect this structure. The first part of this thesis develops a deep network layer that reflects this structural assumption, and shows that the resulting layer is maximally expressive among parameter tying schemes. We then evaluate deep network architectures composed of these layers on a variety of decision problems from human decision making in a game theory setting, to algorithmic decision making on propositional satisfiability problems. The second challenge is that predicting the effect of policy changes involves reasoning about shifts in distribution: any policy change will, by definition, change the conditions under which decision makers operate. This violates the standard machine learning assumption that models will be evaluated under the same conditions as those under which they were trained (the ``independent and identically distributed'' data assumption). The second part of this thesis shows how we can train deep networks that make valid predictions of the results of such policy interventions, by adapting the classical causal inference method of instrumental variables. Finally, we develop methods that are robust to some violations of the instrumental variable assumptions in settings with multiple instrumental variables.

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Increasingly, electronic interactions between individuals are mediated by specialized algorithms. One might hope to optimize the relevant algorithms for various objectives. An aspect of online platforms that complicates such optimization is that the interactions are often strategic: many agents are involved, all with their own distinct goals and priorities, and the outcomes for each agent depend both on their own actions, and upon the actions of the other agents. My thesis is that human behavior can be predicted effectively in a wide range of strategic settings by a single model that synthesizes known deviations from economic rationality. In particular, I claim that such a model can predict human behavior better than the standard economic models. Economic mechanisms are currently designed under behavioral assumptions (i.e., full rationality) that are known to be unrealistic. A mechanism designed based on a more accurate model of behavior will be more able to achieve its goal. In the first part of the dissertation, we develop increasingly sophisticated data-driven models to predict human behavior in strategic settings. We begin by applying machine learning techniques to compare many existing models from behavioral game theory on a large body of experimental data. We then construct a new family of models called quantal cognitive hierarchy (QCH), which have even better predictive performance than the best of the existing models. We extend this model with a richer notion of nonstrategic behavior that takes into account features such as fairness, optimism, and pessimism, yielding further performance improvements. Finally, we perform some initial explorations into applying techniques from deep learning in order to automatically learn features of strategic settings that influence human behavior. A major motivation for modeling human strategic behavior is to improve the design of practical mechanisms for real-life settings. In the second part of the dissertation, we study an applied strategic setting (peer grading), beginning with an analysis of the question of how to optimally apply teaching assistant resources to incentivize students to grade each others' work accurately. We then report empirical results from using a variant of this system in a real-life undergraduate class.

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In practical applications, some important classes of problems are NP-complete. Although no worst-case polynomial time algorithm exists for solving them, state-of-the-art algorithms can solve very large problem instances quickly, and algorithm performance varies significantly across instances. In addition, such algorithms are rather complex and have largely resisted theoretical average-case analysis. Empirical studies are often the only practical means for understanding algorithms’ behavior and for comparing their performance.My thesis focuses on two types of research questions. On the science side, the thesis seeks a in better understanding of relations among problem instances, algorithm performance, and algorithm design. I propose many instance features/characteristics based on instance formulation, instance graph representations, as well as progress statistics from running some solvers. With such informative features, I show that solvers’ runtime can be predicted by predictive performance models with high accuracy. Perhaps more surprisingly, I demonstrate that the solution of NP-complete decision problems (e.g., whether a given propositional satisfiability problem instance is satisfiable) can also be predicted with high accuracy. On the engineering side, I propose three new automated techniques for achieving state-of-the-art performance in solving NP-complete problems. In particular, I construct portfolio-based algorithm selectors that outperform any single solver on heterogeneous benchmarks. By adopting automated algorithm configuration, our highly parameterized local search solver, SATenstein-LS, achieves state-of- the-art performance across many different types of SAT benchmarks. Finally, I show that portfolio-based algorithm selection and automated algorithm configuration could be combined into an automated portfolio construction procedure. It requires significant less domain knowledge, and achieved similar or better performance than portfolio-based selectors based on known high-performance candidate solvers.The experimental results on many solvers and benchmarks demonstrate that the proposed prediction methods achieve high predictive accuracy for predicting algorithm performance as well as predicting solutions, while our automatically constructed solvers are state of the art for solving the propositional satisfiability problem (SAT) and the mixed integer programming problem (MIP). Overall, my research results in more than 8 publications including the 2010 IJCAI/JAIR best paper award. The portfolio-based algorithm selector, SATzilla, won 17 medals in the international SAT solver competitions from 2007 to 2012.

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A mechanism is a formal protocol for collective decision making among self-interested agents. Mechanisms model many important social processes from auctions to elections. They are also widely studied in computer science: the participants in real-world mechanisms are often autonomous software systems (e.g., algorithmic bidding and trading agents), and algorithmic problems (e.g., job scheduling) give rise to mechanisms when users have competing interests.Strategic behavior (or "gaming") poses a major obstacle to understanding mechanisms. Although real-world mechanisms are often fairly simple functions (consider, e.g., plurality voting), a mechanism's outcome depends on both this function and on agents' strategic choices. Game theory provides a principled means for analyzing such choices. Unfortunately, game theoretic analysis is a difficult process requiring either human effort or very large amounts of computation.My thesis is that mechanism analysis can be done computationally, due to recent advances in compact representations of games. Compact representation is possible when a game's description has a suitable independence structure. Exploiting this structure can exponentially decrease the space required to represent games, and exponentially decrease the time required to analyze them. The contributions of my thesis revolve around showing that the relevant kinds of structure (specifically, the structure exploited by action-graph games) are present in important mechanisms of interest. Specifically, I studied two major classes of mechanisms, position auctions (as used for internet advertising) and voting rules. In both cases, I was able to provide exponential improvements in the space and time complexity of analysis, and to use those improvements to address important open questions in the literature. I also introduced a new algorithm for analyzing action-graph games, with faster empirical performance and additional benefits over the previous state-of-the-art. Finally, I created the Positronic Economist system, which consists of a python-based descriptive language for mechanism games, with automatic discovery of computationally useful structure.

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In the last decade, there has been much research at the interface of computer science and game theory. One important class of problems at this interface is the computation of solutionconcepts (such as Nash equilibrium or correlated equilibrium) of a finite game. In order to take advantage of the highly-structured utility functions in games of practical interest, itis important to design compact representations of games as well as efficient algorithms for computing solution concepts on such representations. In this thesis I present several novel contributions in this direction:The design and analysis of Action-Graph Games (AGGs), a fully-expressive modeling language for representing simultaneous-move games.We propose a polynomial-time algorithm for computing expected utilities given arbitrary mixed strategy profiles, and leverage the algorithm to achieve exponential speedups of existing algorithms for computing Nash equilibria. Designing efficient algorithms for computing pure-strategy Nash equilibria in AGGs. For symmetric AGGs with bounded treewidth our algorithm runs in polynomial time.Extending the AGG framework beyond simultaneous-move games. We propose Temporal Action-Graph Games (TAGGs) for representing dynamic games and Bayesian Action-Graph Games (BAGGs) for representing Bayesian games. For certain subclasses of TAGGs and BAGGs we gave efficient algorithms for equilibria that achieve exponential speedups over existing approaches.Efficient computation of correlated equilibria. In a landmark paper, Papadimitriou and Roughgarden described a polynomial-time algorithm ("Ellipsoid Against Hope") for computing sample correlated equilibria of compactly-represented games. Recently, Stein, Parrilo and Ozdaglar showed that this algorithm can fail to find an exact correlated equilibrium. We present a variant of the Ellipsoid Against Hope algorithm that guarantees the polynomial-time identification of exact correlated equilibrium.Efficient computation of optimal correlated equilibria. We show that the polynomial-time solvability of what we call the deviation-adjusted social welfare problem is a sufficient condition for the tractability of the optimal correlated equilibrium problem.

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