Learning cooperative policies for multi-agent systems is often challenged by partial observability and a lack of coordination. In some settings, the structure of a problem allows a distributed solution with limited communication. Here, we consider a scenario where no communication is available, and instead we learn local policies for all agents that collectively mimic the solution to a centralized multi-agent static optimization problem. Our main contribution is an information theoretic framework based on rate distortion theory which facilitates analysis of how well the resulting fully decentralized policies are able to reconstruct the optimal solution. Moreover, this framework provides a natural extension that addresses which nodes an agent should communicate with to improve the performance of its individual policy.

Goal-oriented dialog has been given attention due to its numerous applications in artificial intelligence. Goal-oriented dialogue tasks occur when a questioner asks an action-oriented question and an answerer responds with the intent of letting the questioner know a correct action to take. To ask the adequate question, deep learning and reinforcement learning have been recently applied. However, these approaches struggle to find a competent recurrent neural questioner, owing to the complexity of learning a series of sentences. Motivated by theory of mind, we propose Answerer in Questioner's Mind (AQM), a novel information theoretic algorithm for goal-oriented dialog. With AQM, a questioner asks and infers based on an approximated probabilistic model of the answerer.

There is also a large body of work on distributed and decentralized methods from systems and control theory, which should be mentioned in this context (see e.g.

For MNIST, the approximated answerer is count-based and its recognition accuracy can be controlled proportional to the actual answerer's accuracy. For GuessWhat, the approximated answerer is trained in a variety of ways -- on the same training data as the actual answerer, on predicted answers from the actual answerer, on a different training data split as the actual answerer, and on a different training data split as the actual answerer followed by imitation of predicted answers on the other split. And the proposed approach outperforms the random baseline. Interestingly, the authors find that the depA* models perform better than the indA* models -- showing that training on predicted answers is a stronger signal for building an accurate mental model than just sharing training data. I'm happy to recommend this for publication.

Uncertainty Quantification in Machine Learning has progressed to predicting the source of uncertainty in a prediction: Uncertainty from stochasticity in the data (aleatoric), or uncertainty from limitations of the model (epistemic). Generally, each uncertainty is evaluated in isolation, but this obscures the fact that they are often not truly disentangled. This work proposes a set of experiments to evaluate disentanglement of aleatoric and epistemic uncertainty, and uses these methods to compare two competing formulations for disentanglement (the Information Theoretic approach, and the Gaussian Logits approach). The results suggest that the Information Theoretic approach gives better disentanglement, but that either predicted source of uncertainty is still largely contaminated by the other for both methods. We conclude that with the current methods for disentangling, aleatoric and epistemic uncertainty are not reliably separated, and we provide a clear set of experimental criteria that good uncertainty disentanglement should follow.

We discuss in this paper architectures for executing probabilistic rule-bases in a par(cid:173) allel manner, using as a theoretical basis recently introduced information-theoretic models. We will begin by describing our (non-neural) learning algorithm and theory of quantitative rule modelling, followed by a discussion on the exact nature of two particular models. Finally we work through an example of our approach, going from database to rules to inference network, and compare the network's performance with the theoretical limits for specific problems.

We introduce an information theoretic method for nonparametric, non- linear dimensionality reduction, based on the infinite cluster limit of rate distortion theory. By constraining the information available to manifold coordinates, a natural probabilistic map emerges that assigns original data to corresponding points on a lower dimensional manifold. With only the information-distortion trade off as a parameter, our method de- termines the shape of the manifold, its dimensionality, the probabilistic map and the prior that provide optimal description of the data. Some data sets may not be as complicated as they appear. Consider the set of points on a plane in Figure 1.

Learning cooperative policies for multi-agent systems is often challenged by partial observability and a lack of coordination. In some settings, the structure of a problem allows a distributed solution with limited communication. Here, we consider a scenario where no communication is available, and instead we learn local policies for all agents that collectively mimic the solution to a centralized multi-agent static optimization problem. Our main contribution is an information theoretic framework based on rate distortion theory which facilitates analysis of how well the resulting fully decentralized policies are able to reconstruct the optimal solution. Moreover, this framework provides a natural extension that addresses which nodes an agent should communicate with to improve the performance of its individual policy.

Goal-oriented dialog has been given attention due to its numerous applications in artificial intelligence. Goal-oriented dialogue tasks occur when a questioner asks an action-oriented question and an answerer responds with the intent of letting the questioner know a correct action to take. To ask the adequate question, deep learning and reinforcement learning have been recently applied. However, these approaches struggle to find a competent recurrent neural questioner, owing to the complexity of learning a series of sentences. Motivated by theory of mind, we propose "Answerer in Questioner's Mind" (AQM), a novel information theoretic algorithm for goal-oriented dialog.

We present a variation of the Autoencoder (AE) that explicitly maximizes the mutual information between the input data and the hidden representation. The proposed model, the InfoMax Autoencoder (IMAE), by construction is able to learn a robust representation and good prototypes of the data. IMAE is compared both theoretically and then computationally with the state of the art models: the Denoising and Contractive Autoencoders in the one-hidden layer setting and the Variational Autoencoder in the multi-layer case. Computational experiments are performed with the MNIST and Fashion-MNIST datasets and demonstrate particularly the strong clusterization performance of IMAE.