We provide a unifying framework for the design and analysis of multi-calibrated predictors. By placing the multi-calibration problem in the general setting of multi-objective learning---where learning guarantees must hold simultaneously over a set of distributions and loss functions---we exploit connections to game dynamics to achieve state-of-the-art guarantees for a diverse set of multi-calibration learning problems. In addition to shedding light on existing multi-calibration guarantees and greatly simplifying their analysis, our approach also yields improved guarantees, such as error tolerances that scale with the square-root of group size versus the constant tolerances guaranteed by prior works, and improving the complexity of $k$-class multi-calibration by an exponential factor of $k$ versus Gopalan et al.. Beyond multi-calibration, we use these game dynamics to address emerging considerations in the study of group fairness and multi-distribution learning.

We provide a unifying framework for the design and analysis of multi-calibrated predictors. By placing the multi-calibration problem in the general setting of multi-objective learning---where learning guarantees must hold simultaneously over a set of distributions and loss functions---we exploit connections to game dynamics to achieve state-of-the-art guarantees for a diverse set of multi-calibration learning problems. In addition to shedding light on existing multi-calibration guarantees and greatly simplifying their analysis, our approach also yields improved guarantees, such as error tolerances that scale with the square-root of group size versus the constant tolerances guaranteed by prior works, and improving the complexity of k -class multi-calibration by an exponential factor of k versus Gopalan et al.. Beyond multi-calibration, we use these game dynamics to address emerging considerations in the study of group fairness and multi-distribution learning.

We provide a unifying framework for the design and analysis of multi-calibrated predictors. By placing the multi-calibration problem in the general setting of multi-objective learning---where learning guarantees must hold simultaneously over a set of distributions and loss functions---we exploit connections to game dynamics to achieve state-of-the-art guarantees for a diverse set of multi-calibration learning problems. In addition to shedding light on existing multi-calibration guarantees and greatly simplifying their analysis, our approach also yields improved guarantees, such as error tolerances that scale with the square-root of group size versus the constant tolerances guaranteed by prior works, and improving the complexity of k -class multi-calibration by an exponential factor of k versus Gopalan et al.. Beyond multi-calibration, we use these game dynamics to address emerging considerations in the study of group fairness and multi-distribution learning.

During 2023, two interesting results were proven about the limit behavior of game dynamics: First, it was shown that there is a game for which no dynamics converges to the Nash equilibria. Second, it was shown that the sink equilibria of a game adequately capture the limit behavior of natural game dynamics. These two results have created a need and opportunity to articulate a principled computational theory of the meaning of the game that is based on game dynamics. Given any game in normal form, and any prior distribution of play, we study the problem of computing the asymptotic behavior of a class of natural dynamics called the noisy replicator dynamics as a limit distribution over the sink equilibria of the game. When the prior distribution has pure strategy support, we prove this distribution can be computed efficiently, in near-linear time to the size of the best-response graph. When the distribution can be sampled -- for example, if it is the uniform distribution over all mixed strategy profiles -- we show through experiments that the limit distribution of reasonably large games can be estimated quite accurately through sampling and simulation.

Game theory is one of the most fascinating areas of mathematics that have influenced diverse fields such as economics, social sciences, biology and, obviously, computer science. Games are playing a key role in the evolution of artificial intelligence(AI). For starters, game environments are becoming a popular training mechanism in areas such as reinforcement learning or imitation learning. In theory, any multi-agent AI system can be subjected to gamified interactions between its participants. The branch of mathematics that formulates the principles of games is known as game theory.

Game theory is one of the most fascinating areas of mathematics that have influenced diverse fields such as economics, social sciences, biology and, obviously, computer science. Games are playing a key role in the evolution of artificial intelligence(AI). For starters, game environments are becoming a popular training mechanism in areas such as reinforcement learning or imitation learning. In theory, any multi-agent AI system can be subjected to gamified interactions between its participants. The branch of mathematics that formulates the principles of games is known as game theory.

We introduce a new class of context dependent, incomplete information games to serve as structured prediction models for settings with significant strategic interactions. Our games map the input context to outcomes by first condensing the input into private player types that specify the utilities, weighted interactions, as well as the initial strategies for the players. The game is played over multiple rounds where players respond to weighted aggregates of their neighbors' strategies. The predicted output from the model is a mixed strategy profile (a near-Nash equilibrium) and each observation is thought of as a sample from this strategy profile. We introduce two new aggregator paradigms with provably convergent game dynamics, and characterize the conditions under which our games are identifiable from data. Our games can be parameterized in a transferable manner so that the sets of players can change from one game to another. We demonstrate empirically that our games as models can recover meaningful strategic interactions from real voting data.

Games are playing a key role in the evolution of artificial intelligence(AI). For starters, game environments are becoming a popular training mechanism in areas such as reinforcement learning or imitation learning. In theory, any multi-agent AI system can be subjected to gamified interactions between its participants. The branch of mathematics that formulates the principles of games is known as game theory. In the context of artificial intelligence(AI) and deep learning systems, game theory is essential to enable some of the key capabilities required in multi-agent environments in which different AI programs need to interact or compete in order to accomplish a goal.