TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: <lb>Recent price-of-anarchy analyses of games of complete information suggest that coarse correlated<lb>equilibria, which characterize outcomes resulting from no-regret learning dynamics, have near-optimal<lb>welfare. This work provides two main technical results that lift this conclusion to games of incomplete<lb>information, a.k.a., Bayesian games. First, near-optimal welfare in Bayesian games follows directly from<lb>the smoothness-based proof of near-optimal welfare in the same game when the private information<lb>is public. Second, no-regret learning dynamics converge to Bayesian coarse correlated equilibrium in<lb>these incomplete information games. These results are enabled by interpretation of a Bayesian game<lb>as a stochastic game of complete information.

SOLUTION: No-Regret Learning in Repeated Bayesian Games

PROBLEM: This paper studies theoretically and empirically a method of turning machinelearning algorithms into probabilistic predictors that automatically enjoys a property of validity (perfect calibration) and is computationally efficient. The price to pay for perfect calibration is that these probabilistic predictors produce imprecise (in practice, almost precise for large data sets) probabilities. When these imprecise probabilities are merged into precise probabilities, the resulting predictors, while losing the theoretical property of perfect calibration, are consistently more accurate than the existing methods in empirical studies. The conference version of this paper is to appear in Advances in Neural Information Processing Systems 28, 2015.

SOLUTION: Large-scale probabilistic prediction with and without validity guarantees

PROBLEM: Variational autoencoders (VAE) often use Gaussian or category distribution to model the inference process. This puts a limit on variational learning because this simplified assumption does not match the true posterior distribution, which is usually much more sophisticated. To break this limitation and apply arbitrary parametric distribution during inference, this paper derives a semi-continuous latent representation, which approximates a continuous density up to a prescribed precision, and is much easier to analyze than its continuous counterpart because it is fundamentally discrete. We showcase the proposition by applying polynomial exponential family distributions as the posterior, which are universal probability density function generators. Our experimental results show consistent improvements over commonly used VAE models.

SOLUTION:
Coarse Grained Exponential Variational Autoencoders