We survey in this article the connections between Machine Learning and Control Theory. Control Theory provide useful concepts and tools for Machine Learning. Conversely Machine Learning can be used to solve large control problems. In the first part of the paper, we develop the connections between reinforcement learning and Markov Decision Processes, which are discrete time control problems. In the second part, we review the concept of supervised learning and the relation with static optimization. Deep learning which extends supervised learning, can be viewed as a control problem. In the third part, we present the links between stochastic gradient descent and mean-field theory. Conversely, in the fourth and fifth parts, we review machine learning approaches to stochastic control problems, and focus on the deterministic case, to explain, more easily, the numerical algorithms.

With the development of Internet of Things (IoT), IoT intelligence becomes emerging technology. "Curse of Dimensionality" is the barrier of data fusion in edge devices for the success of IoT intelligence. A Linguistic Attribute Hierarchy (LAH), embedded with Linguistic Decision Trees (LDTs), can represent a new attribute deep learning. In contrast to the conventional deep learning, an LAH could overcome the shortcoming of missing interpretation by providing transparent information propagation through the rules, produced by LDTs in the LAH. Similar to the conventional deep learning, the computing complexity of optimising LAHs blocks the applications of LAHs. In this paper, we propose a heuristic approach to constructing an LAH, embedded with LDTs for decision making or classification by utilising the distance correlations between attributes and between attributes and the goal variable. The set of attributes is divided to some attribute clusters, and then they are heuristically organised to form a linguistic attribute hierarchy. The proposed approach was validated with some benchmark decision making or classification problems from the UCI machine learning repository. The experimental results show that the proposed self-organisation algorithm can construct an effective and efficient linguistic attribute hierarchy. Such a self-organised linguistic attribute hierarchy embedded with LDTs can not only efficiently tackle "curse of dimensionality" in a single LDT for data fusion with massive attributes, but also achieve better or comparable performance on decision making or classification, compared to the single LDT for the problem to be solved. The self-organisation algorithm is much efficient than the Genetic Algorithm in Wrapper for the optimisation of LAHs. This makes it feasible to embed the self-organisation algorithm in edge devices for IoT intelligence.

We present an approach to classify user validity in survey responses by using a machine learning techniques. The approach is based on collecting user mouse activity on web-surveys and fast predicting validity of the survey in general without analysis of specific answers. Rule based approach, LSTM and HMM models are considered. The approach might be used in web-survey applications to detect suspicious users behaviour and request from them proper answering instead of false data recording.

Survival models are a popular tool for the analysis of time to event data with applications in medicine, engineering, economics and many more. Advances like the Cox proportional hazard model have enabled researchers to better describe hazard rates for the occurrence of single fatal events, but are limited by modeling assumptions, like proportionality of hazard rates and linear effects. Moreover, common phenomena are often better described through multiple states, for example, the progress of a disease might be modeled as healthy, sick and dead instead of healthy and dead, where the competing nature of death and disease has to be taken into account. Also, individual characteristics can vary significantly between observational units, like patients, resulting in idiosyncratic hazard rates and different disease trajectories. These considerations require flexible modeling assumptions. Current standard models, however, are often ill-suited for such an analysis. To overcome these issues, we propose the use of neural ordinary differential equations as a flexible and general method for estimating multi-state survival models by directly solving the Kolmogorov forward equations. To quantify the uncertainty in the resulting individual cause-specific hazard rates, we further introduce a variational latent variable model. We show that our model exhibits state-of-the-art performance on popular survival data sets and demonstrate its efficacy in a multi-state setting.

We consider the problem of reinforcement learning (RL) with unbounded state space motivated by the classical problem of scheduling in a queueing network. Traditional policies as well as error metric that are designed for finite, bounded or compact state space, require infinite samples for providing any meaningful performance guarantee (e.g. $\ell_\infty$ error) for unbounded state space. That is, we need a new notion of performance metric. As the main contribution of this work, inspired by the literature in queuing systems and control theory, we propose stability as the notion of "goodness": the state dynamics under the policy should remain in a bounded region with high probability. As a proof of concept, we propose an RL policy using Sparse-Sampling-based Monte Carlo Oracle and argue that it satisfies the stability property as long as the system dynamics under the optimal policy respects a Lyapunov function. The assumption of existence of a Lyapunov function is not restrictive as it is equivalent to the positive recurrence or stability property of any Markov chain, i.e., if there is any policy that can stabilize the system then it must possess a Lyapunov function. And, our policy does not utilize the knowledge of the specific Lyapunov function. To make our method sample efficient, we provide an improved, sample efficient Sparse-Sampling-based Monte Carlo Oracle with Lipschitz value function that may be of interest in its own right. Furthermore, we design an adaptive version of the algorithm, based on carefully constructed statistical tests, which finds the correct tuning parameter automatically.

The upper confidence reinforcement learning (UCRL2) strategy introduced in (Jaksch et al., 2010) is a popular method to perform regret minimization in unknown discrete Markov Decision Processes under the average-reward criterion. Despite its nice and generic theoretical regret guarantees, this strategy and its variants have remained until now mostly theoretical as numerical experiments on simple environments exhibit long burn-in phases before the learning takes place. Motivated by practical efficiency, we present UCRL3, following the lines of UCRL2, but with two key modifications: First, it uses state-of-the-art time-uniform concentration inequalities, to compute confidence sets on the reward and transition distributions for each state-action pair. To further tighten exploration, we introduce an adaptive computation of the support of each transition distributions. This enables to revisit the extended value iteration procedure to optimize over distributions with reduced support by disregarding low probability transitions, while still ensuring near-optimism. We demonstrate, through numerical experiments on standard environments, that reducing exploration this way yields a substantial numerical improvement compared to UCRL2 and its variants. On the theoretical side, these key modifications enable to derive a regret bound for UCRL3 improving on UCRL2, that for the first time makes appear a notion of local diameter and effective support, thanks to variance-aware concentration bounds.

Active inference offers a first principle account of sentient behaviour, from which special and important cases can be derived, e.g., reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design, etc. Active inference resolves the exploitation-exploration dilemma in relation to prior preferences, by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this paper, we consider a sophisticated kind of active inference, using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about "what would happen if I did that" to "what would I believe about what would happen if I did that". The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states, as opposed to states per se. We illustrate the competence of this scheme, using numerical simulations of deep decision problems.

Recent work in the behavioural sciences has begun to overturn the long-held belief that human decision making is irrational, suboptimal and subject to biases. This turn to the rational suggests that human decision making may be a better source of ideas for constraining how machine learning problems are defined than would otherwise be the case. One promising idea concerns human decision making that is dependent on apparently irrelevant aspects of the choice context. Previous work has shown that by taking into account choice context and making relational observations, people can maximize expected value. Other work has shown that Partially observable Markov decision processes (POMDPs) are a useful way to formulate human-like decision problems. Here, we propose a novel POMDP model for contextual choice tasks and show that, despite the apparent irrationalities, a reinforcement learner can take advantage of the way that humans make decisions. We suggest that human irrationalities may offer a productive source of inspiration for improving the design of AI architectures and machine learning methods.

Real world multi-agent tasks often involve varying types and quantities of agents and non-agent entities. Agents frequently do not know a priori how many other agents and non-agent entities they will need to interact with in order to complete a given task, requiring agents to generalize across a combinatorial number of task configurations with each potentially requiring different strategies. In this work, we tackle the problem of multi-agent reinforcement learning (MARL) in such dynamic scenarios. We hypothesize that, while the optimal behaviors in these scenarios with varying quantities and types of agents/entities are diverse, they may share common patterns within sub-teams of agents that are combined to form team behavior. As such, we propose a method that can learn these subgroup relationships and how they can be combined, ultimately improving knowledge sharing and generalization across scenarios. This method, Attentive-Imaginative QMIX, extends QMIX for dynamic MARL in two ways: 1) an attention mechanism that enables model sharing across variable sized scenarios and 2) a training objective that improves learning across scenarios with varying combinations of agent/entity types by factoring the value function into imagined sub-scenarios. We validate our approach on both a novel grid-world task as well as a version of the StarCraft Multi-Agent Challenge [28] minimally modified for the dynamic scenario setting.

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD) reinforcement learning methods can be formally derived, not by starting from their original objective functions, as previously attempted, but rather from a primal-dual saddle-point objective function. We also conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Previous analyses of this class of algorithms use stochastic approximation techniques to prove asymptotic convergence, and do not provide any finite-sample analysis. We also propose an accelerated algorithm, called GTD2-MP, that uses proximal ``mirror maps'' to yield an improved convergence rate. The results of our theoretical analysis imply that the GTD family of algorithms are comparable and may indeed be preferred over existing least squares TD methods for off-policy learning, due to their linear complexity. We provide experimental results showing the improved performance of our accelerated gradient TD methods.