The interaction and collaboration between humans and multiple robots represent a novel field of research known as human multi-robot systems. Adequately designed systems within this field allow teams composed of both humans and robots to work together effectively on tasks such as monitoring, exploration, and search and rescue operations. This paper presents a deep reinforcement learning-based affective workload allocation controller specifically for multi-human multi-robot teams. The proposed controller can dynamically reallocate workloads based on the performance of the operators during collaborative missions with multi-robot systems. The operators' performances are evaluated through the scores of a self-reported questionnaire (i.e., subjective measurement) and the results of a deep learning-based cognitive workload prediction algorithm that uses physiological and behavioral data (i.e., objective measurement). To evaluate the effectiveness of the proposed controller, we use a multi-human multi-robot CCTV monitoring task as an example and carry out comprehensive real-world experiments with 32 human subjects for both quantitative measurement and qualitative analysis. Our results demonstrate the performance and effectiveness of the proposed controller and highlight the importance of incorporating both subjective and objective measurements of the operators' cognitive workload as well as seeking consent for workload transitions, to enhance the performance of multi-human multi-robot teams.

Stochastic optimal control and games have found a wide range of applications, from finance and economics to social sciences, robotics and energy management. Many real-world applications involve complex models which have driven the development of sophisticated numerical methods. Recently, computational methods based on machine learning have been developed for stochastic control problems and games. We review such methods, with a focus on deep learning algorithms that have unlocked the possibility to solve such problems even when the dimension is high or when the structure is very complex, beyond what is feasible with traditional numerical methods. Here, we consider mostly the continuous time and continuous space setting. Many of the new approaches build on recent neural-network based methods for high-dimensional partial differential equations or backward stochastic differential equations, or on model-free reinforcement learning for Markov decision processes that have led to breakthrough results. In this paper we provide an introduction to these methods and summarize state-of-the-art works on machine learning for stochastic control and games.

We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the planning phase, the agent is given a reward function and is expected to find a near-optimal policy based on samples collected in the exploration phase. The sample complexities of existing reward-free algorithms have a polynomial dependence on the planning horizon, which makes them intractable for long planning horizon RL problems. In this paper, we propose a new reward-free algorithm for learning linear mixture Markov decision processes (MDPs), where the transition probability can be parameterized as a linear combination of known feature mappings. At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and a high-order moment estimator for the aleatoric and epistemic uncertainties. When the total reward is bounded by $1$, we show that our algorithm only needs to explore $\tilde O( d^2\varepsilon^{-2})$ episodes to find an $\varepsilon$-optimal policy, where $d$ is the dimension of the feature mapping. The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is ``horizon-free''. In addition, we provide an $\Omega(d^2\varepsilon^{-2})$ sample complexity lower bound, which matches the sample complexity of our algorithm up to logarithmic factors, suggesting that our algorithm is optimal.

We introduce a new optimization algorithm, termed contrastive adjustment, for learning Markov transition kernels whose stationary distribution matches the data distribution. Contrastive adjustment is not restricted to a particular family of transition distributions and can be used to model data in both continuous and discrete state spaces. Inspired by recent work on noise-annealed sampling, we propose a particular transition operator, the noise kernel, that can trade mixing speed for sample fidelity. We show that contrastive adjustment is highly valuable in humancomputer design processes, as the stationarity of the learned Markov chain enables local exploration of the data manifold and makes it possible to iteratively refine outputs by human feedback. We compare the performance of noise kernels trained with contrastive adjustment to current state-of-the-art generative models and demonstrate promising results on a variety of image synthesis tasks. Figure 1: Unconditional samples from noise kernels trained with contrastive adjustment.

We study learning in periodic Markov Decision Process (MDP), a special type of non-stationary MDP where both the state transition probabilities and reward functions vary periodically, under the average reward maximization setting. We formulate the problem as a stationary MDP by augmenting the state space with the period index, and propose a periodic upper confidence bound reinforcement learning-2 (PUCRL2) algorithm. We show that the regret of PUCRL2 varies linearly with the period $N$ and as $\mathcal{O}(\sqrt{Tlog T})$ with the horizon length $T$. Utilizing the information about the sparsity of transition matrix of augmented MDP, we propose another algorithm PUCRLB which enhances upon PUCRL2, both in terms of regret ($O(\sqrt{N})$ dependency on period) and empirical performance. Finally, we propose two other algorithms U-PUCRL2 and U-PUCRLB for extended uncertainty in the environment in which the period is unknown but a set of candidate periods are known. Numerical results demonstrate the efficacy of all the algorithms.

Prescriptive Process Monitoring is a prominent problem in Process Mining, which consists in identifying a set of actions to be recommended with the goal of optimising a target measure of interest or Key Performance Indicator (KPI). One challenge that makes this problem difficult is the need to provide Prescriptive Process Monitoring techniques only based on temporally annotated (process) execution data, stored in, so-called execution logs, due to the lack of well crafted and human validated explicit models. In this paper we aim at proposing an AI based approach that learns, by means of Reinforcement Learning (RL), an optimal policy (almost) only from the observation of past executions and recommends the best activities to carry on for optimizing a KPI of interest. This is achieved first by learning a Markov Decision Process for the specific KPIs from data, and then by using RL training to learn the optimal policy. The approach is validated on real and synthetic datasets and compared with off-policy Deep RL approaches. The ability of our approach to compare with, and often overcome, Deep RL approaches provides a contribution towards the exploitation of white box RL techniques in scenarios where only temporal execution data are available.

Partially Observable Monte Carlo Planning (POMCP) is an efficient solver for Partially Observable Markov Decision Processes (POMDPs). It allows scaling to large state spaces by computing an approximation of the optimal policy locally and online, using a Monte Carlo Tree Search based strategy. However, POMCP suffers from sparse reward function, namely, rewards achieved only when the final goal is reached, particularly in environments with large state spaces and long horizons. Recently, logic specifications have been integrated into POMCP to guide exploration and to satisfy safety requirements. However, such policy-related rules require manual definition by domain experts, especially in real-world scenarios. In this paper, we use inductive logic programming to learn logic specifications from traces of POMCP executions, i.e., sets of belief-action pairs generated by the planner. Specifically, we learn rules expressed in the paradigm of answer set programming. We then integrate them inside POMCP to provide soft policy bias toward promising actions. In the context of two benchmark scenarios, rocksample and battery, we show that the integration of learned rules from small task instances can improve performance with fewer Monte Carlo simulations and in larger task instances. We make our modified version of POMCP publicly available at https://github.com/GiuMaz/pomcp_clingo.git.

Concept bottleneck model (CBM) is a ubiquitous method that can interpret neural networks using concepts. In CBM, concepts are inserted between the output layer and the last intermediate layer as observable values. This helps in understanding the reason behind the outputs generated by the neural networks: the weights corresponding to the concepts from the last hidden layer to the output layer. However, it has not yet been possible to understand the behavior of the generalization error in CBM since a neural network is a singular statistical model in general. When the model is singular, a one to one map from the parameters to probability distributions cannot be created. This non-identifiability makes it difficult to analyze the generalization performance. In this study, we mathematically clarify the Bayesian generalization error and free energy of CBM when its architecture is three-layered linear neural networks. We also consider a multitask problem where the neural network outputs not only the original output but also the concepts. The results show that CBM drastically changes the behavior of the parameter region and the Bayesian generalization error in three-layered linear neural networks as compared with the standard version, whereas the multitask formulation does not.

Continuous-time Markov decision processes (CTMDPs) are canonical models to express sequential decision-making under dense-time and stochastic environments. When the stochastic evolution of the environment is only available via sampling, model-free reinforcement learning (RL) is the algorithm-of-choice to compute optimal decision sequence. RL, on the other hand, requires the learning objective to be encoded as scalar reward signals. Since doing such translations manually is both tedious and error-prone, a number of techniques have been proposed to translate high-level objectives (expressed in logic or automata formalism) to scalar rewards for discrete-time Markov decision processes (MDPs). Unfortunately, no automatic translation exists for CTMDPs. We consider CTMDP environments against the learning objectives expressed as omega-regular languages. Omega-regular languages generalize regular languages to infinite-horizon specifications and can express properties given in popular linear-time logic LTL. To accommodate the dense-time nature of CTMDPs, we consider two different semantics of omega-regular objectives: 1) satisfaction semantics where the goal of the learner is to maximize the probability of spending positive time in the good states, and 2) expectation semantics where the goal of the learner is to optimize the long-run expected average time spent in the ``good states" of the automaton. We present an approach enabling correct translation to scalar reward signals that can be readily used by off-the-shelf RL algorithms for CTMDPs. We demonstrate the effectiveness of the proposed algorithms by evaluating it on some popular CTMDP benchmarks with omega-regular objectives.

Multi-agent reinforcement learning (MARL) is the study of the learning dynamics of strategic agents that coexist in a shared environment, and is one of the important frontiers of machine learning and control. In this paper, we study MARL in stochastic games, also known as Markov games, a multi-agent generalization of Markov decision problems (MDPs) in which the cost-relevant history of the system is summarized by a state variable Shapley [1953]. Due to its ability to model both dynamic inter-temporal choice as well as strategic interaction, the stochastic games model has long been a popular framework for studying multi-agent learning Littman [1994]. In comparison to single-agent reinforcement learning, analysis of MARL is difficult due to several challenges inherent to multi-agent systems, including non-stationarity, conflicting interests, and decentralized information. As a result, fundamental understanding of multi-agent reinforcement learning theory has lagged behind its single-agent counterpart Zhang et al. [2021].