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Register a new userLearning Game Representations from Data Using Rationality Constraints
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Xi Alice Gao
Publication date
2012
fields
Informatics Engineering
and research's language is
English
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While game theory is widely used to model strategic interactions, a natural question is where do the game representations come from? One answer is to learn the representations from data. If one wants to learn both the payoffs and the players strategies, a naive approach is to learn them both directly from the data. This approach ignores the fact the players might be playing reasonably good strategies, so there is a connection between the strategies and the data. The main contribution of this paper is to make this connection while learning. We formulate the learning problem as a weighted constraint satisfaction problem, including constraints both for the fit of the payoffs and strategies to the data and the fit of the strategies to the payoffs. We use quantal response equilibrium as our notion of rationality for quantifying the latter fit. Our results show that incorporating rationality constraints can improve learning when the amount of data is limited.
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Hindsight rationality is an approach to playing general-sum games that prescribes no-regret learning dynamics for individual agents with respect to a set of deviations, and further describes jointly rational behavior among multiple agents with mediated equilibria. To develop hindsight rational learning in sequential decision-making settings, we formalize behavioral deviations as a general class of deviations that respect the structure of extensive-form games. Integrating the idea of time selection into counterfactual regret minimization (CFR), we introduce the extensive-form regret minimization (EFR) algorithm that achieves hindsight rationality for any given set of behavioral deviations with computation that scales closely with the complexity of the set. We identify behavioral deviation subsets, the partial sequence deviation types, that subsume previously studied types and lead to efficient EFR instances in games with moderate lengths. In addition, we present a thorough empirical analysis of EFR instantiated with different deviation types in benchmark games, where we find that stronger types typically induce better performance.
Driven by recent successes in two-player, zero-sum game solving and playing, artificial intelligence work on games has increasingly focused on algorithms that produce equilibrium-based strategies. However, this approach has been less effective at producing competent players in general-sum games or those with more than two players than in two-player, zero-sum games. An appealing alternative is to consider adaptive algorithms that ensure strong performance in hindsight relative to what could have been achieved with modified behavior. This approach also leads to a game-theoretic analysis, but in the correlated play that arises from joint learning dynamics rather than factored agent behavior at equilibrium. We develop and advocate for this hindsight rationality framing of learning in general sequential decision-making settings. To this end, we re-examine mediated equilibrium and deviation types in extensive-form games, thereby gaining a more complete understanding and resolving past misconceptions. We present a set of examples illustrating the distinct strengths and weaknesses of each type of equilibrium in the literature, and prove that no tractable concept subsumes all others. This line of inquiry culminates in the definition of the deviation and equilibrium classes that correspond to algorithms in the counterfactual regret minimization (CFR) family, relating them to all others in the literature. Examining CFR in greater detail further leads to a new recursive definition of rationality in correlated play that extends sequential rationality in a way that naturally applies to hindsight evaluation.
The TARK conference (Theoretical Aspects of Rationality and Knowledge) is a biannual conference that aims to bring together researchers from a wide variety of fields, including computer science, artificial intelligence, game theory, decision theory, philosophy, logic, linguistics, and cognitive science. Its goal is to further our understanding of interdisciplinary issues involving reasoning about rationality and knowledge. Topics of interest include, but are not limited to, semantic models for knowledge, belief, awareness and uncertainty, bounded rationality and resource-bounded reasoning, commonsense epistemic reasoning, epistemic logic, epistemic game theory, knowledge and action, applications of reasoning about knowledge and other mental states, belief revision, and foundations of multi-agent systems. These proceedings contain the papers that have been accepted for presentation at the Eighteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2021), held between June 25 and June 27, 2021, at Tsinghua University at Beijing, China.
Suppose that an $m$-simplex is partitioned into $n$ convex regions having disjoint interiors and distinct labels, and we may learn the label of any point by querying it. The learning objective is to know, for any point in the simplex, a label that occurs within some distance $epsilon$ from that point. We present two algorithms for this task: Constant-Dimension Generalised Binary Search (CD-GBS), which for constant $m$ uses $poly(n, log left( frac{1}{epsilon} right))$ queries, and Constant-Region Generalised Binary Search (CR-GBS), which uses CD-GBS as a subroutine and for constant $n$ uses $poly(m, log left( frac{1}{epsilon} right))$ queries. We show via Kakutanis fixed-point theorem that these algorithms provide bounds on the best-response query complexity of computing approximate well-supported equilibria of bimatrix games in which one of the players has a constant number of pure strategies. We also partially extend our results to games with multiple players, establishing further query complexity bounds for computing approximate well-supported equilibria in this setting.
We design mechanisms for online procurement of data held by strategic agents for machine learning tasks. The challenge is to use past data to actively price future data and give learning guarantees even when an agents cost for revealing her data may depend arbitrarily on the data itself. We achieve this goal by showing how to convert a large class of no-regret algorithms into online posted-price and learning mechanisms. Our results in a sense parallel classic sample complexity guarantees, but with the key resource being money rather than quantity of data: With a budget constraint $B$, we give robust risk (predictive error) bounds on the order of $1/sqrt{B}$. Because we use an active approach, we can often guarantee to do significantly better by leveraging correlations between costs and data. Our algorithms and analysis go through a model of no-regret learning with $T$ arriving pairs (cost, data) and a budget constraint of $B$. Our regret bounds for this model are on the order of $T/sqrt{B}$ and we give lower bounds on the same order.
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