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: Potential games and decentralised partially observable MDPs (Dec–POMDPs) are two commonly used models of multi–agent interaction, for static optimisation and sequential decision– making settings, respectively. In this paper we introduce filtered fictitious play for solving repeated potential games in which each player’s observations of others’ actions are perturbed by random noise, and use this algorithm to construct an online learning method for solving Dec–POMDPs. Specifically, we prove that noise in observations prevents standard fictitious play from converging to Nash equilibrium in potential games, which also makes fictitious play impractical for solving Dec–POMDPs. To combat this, we derive filtered fictitious play, and provide conditions under which it converges to a Nash equilibrium in potential games with noisy observations. We then use filtered fictitious play to construct a solver for Dec–POMDPs, and demonstrate our new algorithm’s performance in a box pushing problem. Our results show that we consistently outperform the state–of–the–art Dec– POMDP solver by an average of 100% across the range of noise in the observation function.

SOLUTION: Filtered Fictitious Play for Perturbed Observation Potential Games and Decentralised POMDPs

PROBLEM: In this paper, we introduce a new deep convolutional neural network (ConvNet) module that promotes competition among a set of multi-scale convolutional filters. This new module is inspired by the inception module, where we replace the original collaborative pooling stage (consisting of a concatenation of the multi-scale filter outputs) by a competitive pooling represented by a maxout activation unit. This extension has the following two objectives: 1) the selection of the maximum response among the multi-scale filters prevents filter co-adaptation and allows the formation of multiple sub-networks within the same model, which has been shown to facilitate the training of complex learning problems; and 2) the maxout unit reduces the dimensionality of the outputs from the multi-scale filters. We show that the use of our proposed module in typical deep ConvNets produces classification results that are either better than or comparable to the state of the art on the following benchmark datasets: MNIST, CIFAR-10, CIFAR-100 and SVHN.

SOLUTION: Competitive Multi-scale Convolution

PROBLEM: Recent work (Bengio et al., 2013) has shown how Denoising Auto-Encoders(DAE) become generative models as a density estimator. However, in practice, the framework suffers from a mixing problem in the MCMC sampling process and no direct method to estimate the test loglikelihood. We consider a directed model with an stochastic identity mapping (simple corruption process) as an inference model and a DAE as a generative model. By cascading these models, we propose Cascading Denoising AutoEncoders(CDAE) which can generate samples of data distribution from tractable prior distribution under the assumption that probabilistic distribution of corrupted data approaches tractable prior distribution as the level of corruption increases. This work tries to answer two questions. On the one hand, can deep directed models be successfully trained without intractable posterior inference and difficult optimization of very deep neural networks in inference and generative models? These are unavoidable when recent successful directed model like VAE (Kingma & Welling, 2014) is trained on complex dataset like real images. On the other hand, can DAEs get clean samples of data distribution from heavily corrupted samples which can be considered of tractable prior distribution far from data manifold? so-called global denoising scheme. Our results show positive responses of these questions and this work can provide fairly simple framework for generative models of very complex dataset. Proceedings of the 32 International Conference on Machine Learning, Lille, France, 2015. JMLR: W&CP volume 37. Copyright 2015 by the author(s).

SOLUTION:
Cascading Denoising Auto-Encoder as a Deep Directed Generative Model