However, most successful demonstrations of these DRL methods are usually trained and deployed under well-controlled situations. In contrast, real-world use cases often encounter inevitable observational uncertainty [Grigorescu et al., 2020, Hafner et al., 2018, Moreno et al., 2018] from an external attacker [Huang et al., 2017] or noisy sensor [Fortunato et al., 2018, Lee et al., 2018]. For examples, playing online video games may experience sudden black-outs or frame-skippings due to network instabilities, and driving on the road may encounter temporary blindness when facing the sun. Such an abrupt interference on the observation could cause serious issues for DRL algorithms. Unlike other machine learning tasks that involve only a single mission at a time (e.g., image classification), an RL agent has to deal with a dynamic [Schmidhuber, 1992] and encoded state [Schmidhuber, 1991, Kaelbling et al., 1998] and to anticipate future rewards. Therefore, DRL-based systems are likely to propagate and even enlarge risks (e.g., delay and noisy pulsed-signals on sensor-fusion [Yurtsever et al., 2020, Johansen et al., 2015]) induced from the uncertain interference.

Bounded rationality is an important consideration stemming from the fact that agents often have limits on their processing abilities, making the assumption of perfect rationality inapplicable to many real tasks. We propose an information-theoretic approach to the inference of agent decisions under Smithian competition. The model explicitly captures the boundedness of agents (limited in their information-processing capacity) as the cost of information acquisition for expanding their prior beliefs. The expansion is measured as the Kullblack-Leibler divergence between posterior decisions and prior beliefs. When information acquisition is free, the \textit{homo economicus} agent is recovered, while in cases when information acquisition becomes costly, agents instead revert to their prior beliefs. The maximum entropy principle is used to infer least-biased decisions, based upon the notion of Smithian competition formalised within the Quantal Response Statistical Equilibrium framework. The incorporation of prior beliefs into such a framework allowed us to systematically explore the effects of prior beliefs on decision-making, in the presence of market feedback. We verified the proposed model using Australian housing market data, showing how the incorporation of prior knowledge alters the resulting agent decisions. Specifically, it allowed for the separation (and analysis) of past beliefs and utility maximisation behaviour of the agent.

Most state of the art decision systems based on Reinforcement Learning (RL) are data-driven black-box neural models, where it is often difficult to incorporate expert knowledge into the models or let experts review and validate the learned decision mechanisms. Knowledge-insertion and model review are important requirements in many applications involving human health and safety. One way to bridge the gap between data and knowledge driven systems is program synthesis: replacing a neural network that outputs decisions with a symbolic program generated by a neural network or by means of genetic programming. We propose a new programming language, BF, designed specifically for automatic programming of agents in a Partially Observable Markov Decision Process (POMDP) setting and apply neural program synthesis to solve standard OpenAI Gym benchmarks. Source code is available at https://github.com/vadim0x60/cibi

In this work, we propose a Bayesian statistical model to simultaneously characterize two or more social networks defined over a common set of actors. The key feature of the model is a hierarchical prior distribution that allows us to represent the entire system jointly, achieving a compromise between dependent and independent networks. Among others things, such a specification easily allows us to visualize multilayer network data in a low-dimensional Euclidean space, generate a weighted network that reflects the consensus affinity between actors, establish a measure of correlation between networks, assess cognitive judgements that subjects form about the relationships among actors, and perform clustering tasks at different social instances. Our model's capabilities are illustrated using several real-world data sets, taking into account different types of actors, sizes, and relations.

Bayesian optimization (BO) is among the most effective and widely-used blackbox optimization methods. BO proposes solutions according to an explore-exploit trade-off criterion encoded in an acquisition function, many of which are computed from the posterior predictive of a probabilistic surrogate model. Prevalent among these is the expected improvement (EI) function. The need to ensure analytical tractability of the predictive often poses limitations that can hinder the efficiency and applicability of BO. In this paper, we cast the computation of EI as a binary classification problem, building on the link between class-probability estimation and density-ratio estimation, and the lesser-known link between density-ratios and EI. By circumventing the tractability constraints, this reformulation provides numerous advantages, not least in terms of expressiveness, versatility, and scalability.

We study the machine learning problem of generalization when quantum operations are used to classify either classical data or quantum channels, where in both cases the task is to learn from data how to assign a certain class $c$ to inputs $x$ via measurements on a quantum state $\rho(x)$. A trained quantum model generalizes when it is able to predict the correct class for previously unseen data. We show that the accuracy and generalization capability of quantum classifiers depend on the (R\'enyi) mutual informations $I(C{:}Q)$ and $I_2(X{:}Q)$ between the quantum embedding $Q$ and the classical input space $X$ or class space $C$. Based on the above characterization, we then show how different properties of $Q$ affect classification accuracy and generalization, such as the dimension of the Hilbert space, the amount of noise, and the amount of neglected information via, e.g., pooling layers. Moreover, we introduce a quantum version of the Information Bottleneck principle that allows us to explore the various tradeoffs between accuracy and generalization.

We study the reinforcement learning for finite-horizon episodic Markov decision processes with adversarial reward and full information feedback, where the unknown transition probability function is a linear function of a given feature mapping. We propose an optimistic policy optimization algorithm with Bernstein bonus and show that it can achieve $\tilde{O}(dH\sqrt{T})$ regret, where $H$ is the length of the episode, $T$ is the number of interaction with the MDP and $d$ is the dimension of the feature mapping. Furthermore, we also prove a matching lower bound of $\tilde{\Omega}(dH\sqrt{T})$ up to logarithmic factors. To the best of our knowledge, this is the first computationally efficient, nearly minimax optimal algorithm for adversarial Markov decision processes with linear function approximation.

Inference is a main task in structured prediction and it is naturally modeled with a graph. In the context of Markov random fields, noisy observations corresponding to nodes and edges are usually involved, and the goal of exact inference is to recover the unknown true label for each node precisely. The focus of this paper is on the fundamental limits of exact recovery irrespective of computational efficiency, assuming the generative process proposed by Globerson et al. (2015). We derive the necessary condition for any algorithm and the sufficient condition for maximum likelihood estimation to achieve exact recovery with high probability, and reveal that the sufficient and necessary conditions are tight up to a logarithmic factor for a wide range of graphs. Finally, we show that there exists a gap between the fundamental limits and the performance of the computationally tractable method of Bello and Honorio (2019), which implies the need for further development of algorithms for exact inference.

Binary classifiers trained on a certain proportion of positive items introduce a bias when applied to data sets with different proportions of positive items. Most solutions for dealing with this issue assume that some information on the latter distribution is known. However, this is not always the case, certainly when this proportion is the target variable. In this paper a maximum likelihood estimator for the true proportion of positives in data sets is suggested and tested on synthetic and real world data.

PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, when applied to some family of deterministic models such as neural networks, they require a loose and costly derandomization step. As an alternative to this step, we introduce three new PAC-Bayesian generalization bounds that have the originality to be pointwise, meaning that they provide guarantees over one single hypothesis instead of the usual averaged analysis. Our bounds are rather general, potentially parameterizable, and provide novel insights for various machine learning settings that rely on randomized algorithms. We illustrate the interest of our theoretical result for the analysis of neural network training.