Learning from humans allows non-experts to program robots with ease, lowering the resources required to build complex robotic solutions. Nevertheless, such data-driven approaches often lack the ability to provide guarantees regarding their learned behaviors, which is critical for avoiding failures and/or accidents. In this work, we focus on reaching/point-to-point motions, where robots must always reach their goal, independently of their initial state. This can be achieved by modeling motions as dynamical systems and ensuring that they are globally asymptotically stable. Hence, we introduce a novel Contrastive Learning loss for training Deep Neural Networks (DNN) that, when used together with an Imitation Learning loss, enforces the aforementioned stability in the learned motions. Differently from previous work, our method does not restrict the structure of its function approximator, enabling its use with arbitrary DNNs and allowing it to learn complex motions with high accuracy. We validate it using datasets and a real robot. In the former case, motions are 2 and 4 dimensional, modeled as first- and second-order dynamical systems. In the latter, motions are 3, 4, and 6 dimensional, of first and second order, and are used to control a 7DoF robot manipulator in its end effector space and joint space. More details regarding the real-world experiments are presented in: \url{https://youtu.be/OM-2edHBRfc}.

This paper addresses a novel multi-agent deep reinforcement learning (MADRL)-based positioning algorithm for multiple unmanned aerial vehicles (UAVs) collaboration (i.e., UAVs work as mobile base stations). The primary objective of the proposed algorithm is to establish dependable mobile access networks for cellular vehicle-to-everything (C-V2X) communication, thereby facilitating the realization of high-quality intelligent transportation systems (ITS). The reliable mobile access services can be achieved in following two ways, i.e., i) energy-efficient UAV operation and ii) reliable wireless communication services. For energy-efficient UAV operation, the reward of our proposed MADRL algorithm contains the features for UAV energy consumption models in order to realize efficient operations. Furthermore, for reliable wireless communication services, the quality of service (QoS) requirements of individual users are considered as a part of rewards and 60GHz mmWave radio is used for mobile access. This paper considers the 60GHz mmWave access for utilizing the benefits of i) ultra-wide-bandwidth for multi-Gbps high-speed communications and ii) high-directional communications for spatial reuse that is obviously good for densely deployed users. Lastly, the comprehensive and data-intensive performance evaluation of the proposed MADRL-based algorithm for multi-UAV positioning is conducted in this paper. The results of these evaluations demonstrate that the proposed algorithm outperforms other existing algorithms.

Notwithstanding its difficulty, forecasting of the development of intricate non-linear dynamical systems has been in a spotlight of various scientific fields (Strogatz, 2001; Jackson and Radunskaya, 2015). A plausible approach to forecasting the development is to isolate the non-linear estimation problem into (i) learning non-linear representations by applying highly non-linear functions such as deep neural networks (Goodfellow et al., 2016), and (ii) estimating its development with simple linear models. An example is a reservoir computing (RC; Jaeger, 2001, 2002). RC first randomly specifies a state in the reservoir layer in recurrent neural network (Rumelhart et al., 1986), and optimizes the weights only in the output layer; RC corresponds to non-linearly transform its input (in the reservoir layer) and trains a simple linear prediction model (in the output layer). It has been reported that such a simple combination of the non-linear representation learning and the linear estimation is effective to forecasting the intricate dynamical systems (Tanaka et al., 2019). Effectiveness of the simple combination is not limited to RC; applying a linear model to the non-linear representation in more general deep neural network is also regarded as a solid forecasting strategy (Lusch et al., 2018). Unfortunately, however, partial degrees of freedom corresponding to several state variables are not observed in some practical situations (Lucor et al., 2022; Cheng et al., 2023). There could be a variety of reasons for missing observations: it would be caused by the difficulty of measurement, it would be caused by the immature understanding of the system of interest, and so forth.

In recent years, the intelligence of various parts of the home has become one of the essential features of any modern home. One of these parts is the intelligence lighting system that personalizes the light for each person. This paper proposes an intelligent system based on machine learning that personalizes lighting in the instant future location of a recognized user, inferred by trajectory prediction. Our proposed system consists of the following modules: (I) human detection to detect and localize the person in each given video frame, (II) face recognition to identify the detected person, (III) human tracking to track the person in the sequence of video frames and (IV) trajectory prediction to forecast the future location of the user in the environment using Inverse Reinforcement Learning. The proposed method provides a unique profile for each person, including specifications, face images, and custom lighting settings. This profile is used in the lighting adjustment process. Unlike other methods that consider constant lighting for every person, our system can apply each 'person's desired lighting in terms of color and light intensity without direct user intervention. Therefore, the lighting is adjusted with higher speed and better efficiency. In addition, the predicted trajectory path makes the proposed system apply the desired lighting, creating more pleasant and comfortable conditions for the home residents. In the experimental results, the system applied the desired lighting in an average time of 1.4 seconds from the moment of entry, as well as a performance of 22.1mAp in human detection, 95.12% accuracy in face recognition, 93.3% MDP in human tracking, and 10.80 MinADE20, 18.55 MinFDE20, 15.8 MinADE5 and 30.50 MinFDE5 in trajectory prediction.

Probability and moment inequalities for sums of random variables are of paramount importance in the complexity analysis of numerous stochastic approximation algorithms or finite-time analysis of Monte Carlo estimators; see [20], [10], and references therein. The main focus in this area has been on concentration inequalities for independent random variable sums or martingale difference sequences; see e.g. in [4, 36]. However, the study of concentration inequalities for additive Markov chain functions is still relatively underdeveloped. For the technically simple case of uniformly ergodic Markov chains, there is extensive work on Hoeffding-and Bernstein-like inequalities as found in [23, 34, 20, 38]. Nevertheless, the application of these results may be difficult due to a lack of quantitative data or the substitution of asymptotic variance of the chain by surrogates; see Section 2.1 for relevant definitions. The present work aims to fill this gap by extending Rosenthal-and Bernstein-type inequalities to Markov chains which converge geometrically fast to a unique invariant distribution, with an explicit emphasis on the mixing time of the underlying Markov chain. An important tool for establishing deviation bounds for sums of random variables is based on moment inequalities.

For min-max optimization and variational inequalities problems (VIP) encountered in diverse machine learning tasks, Stochastic Extragradient (SEG) and Stochastic Gradient Descent Ascent (SGDA) have emerged as preeminent algorithms. Constant step-size variants of SEG/SGDA have gained popularity, with appealing benefits such as easy tuning and rapid forgiveness of initial conditions, but their convergence behaviors are more complicated even in rudimentary bilinear models. Our work endeavors to elucidate and quantify the probabilistic structures intrinsic to these algorithms. By recasting the constant step-size SEG/SGDA as time-homogeneous Markov Chains, we establish a first-of-its-kind Law of Large Numbers and a Central Limit Theorem, demonstrating that the average iterate is asymptotically normal with a unique invariant distribution for an extensive range of monotone and non-monotone VIPs. Specializing to convex-concave min-max optimization, we characterize the relationship between the step-size and the induced bias with respect to the Von-Neumann's value. Finally, we establish that Richardson-Romberg extrapolation can improve proximity of the average iterate to the global solution for VIPs. Our probabilistic analysis, underpinned by experiments corroborating our theoretical discoveries, harnesses techniques from optimization, Markov chains, and operator theory.

We develop several provably efficient model-free reinforcement learning (RL) algorithms for infinite-horizon average-reward Markov Decision Processes (MDPs). We consider both online setting and the setting with access to a simulator. In the online setting, we propose model-free RL algorithms based on reference-advantage decomposition. Our algorithm achieves $\widetilde{O}(S^5A^2\mathrm{sp}(h^*)\sqrt{T})$ regret after $T$ steps, where $S\times A$ is the size of state-action space, and $\mathrm{sp}(h^*)$ the span of the optimal bias function. Our results are the first to achieve optimal dependence in $T$ for weakly communicating MDPs. In the simulator setting, we propose a model-free RL algorithm that finds an $\epsilon$-optimal policy using $\widetilde{O} \left(\frac{SA\mathrm{sp}^2(h^*)}{\epsilon^2}+\frac{S^2A\mathrm{sp}(h^*)}{\epsilon} \right)$ samples, whereas the minimax lower bound is $\Omega\left(\frac{SA\mathrm{sp}(h^*)}{\epsilon^2}\right)$. Our results are based on two new techniques that are unique in the average-reward setting: 1) better discounted approximation by value-difference estimation; 2) efficient construction of confidence region for the optimal bias function with space complexity $O(SA)$.

Reinforcement Learning (RL) has made promising progress in planning and decision-making for Autonomous Vehicles (AVs) in simple driving scenarios. However, existing RL algorithms for AVs fail to learn critical driving skills in complex urban scenarios. First, urban driving scenarios require AVs to handle multiple driving tasks of which conventional RL algorithms are incapable. Second, the presence of other vehicles in urban scenarios results in a dynamically changing environment, which challenges RL algorithms to plan the action and trajectory of the AV. In this work, we propose an action and trajectory planner using Hierarchical Reinforcement Learning (atHRL) method, which models the agent behavior in a hierarchical model by using the perception of the lidar and birdeye view. The proposed atHRL method learns to make decisions about the agent's future trajectory and computes target waypoints under continuous settings based on a hierarchical DDPG algorithm. The waypoints planned by the atHRL model are then sent to a low-level controller to generate the steering and throttle commands required for the vehicle maneuver. We empirically verify the efficacy of atHRL through extensive experiments in complex urban driving scenarios that compose multiple tasks with the presence of other vehicles in the CARLA simulator. The experimental results suggest a significant performance improvement compared to the state-of-the-art RL methods.

Multi-task Imitation Learning (MIL) aims to train a policy capable of performing a distribution of tasks based on multi-task expert demonstrations, which is essential for general-purpose robots. Existing MIL algorithms suffer from low data efficiency and poor performance on complex long-horizontal tasks. We develop Multi-task Hierarchical Adversarial Inverse Reinforcement Learning (MH-AIRL) to learn hierarchically-structured multi-task policies, which is more beneficial for compositional tasks with long horizons and has higher expert data efficiency through identifying and transferring reusable basic skills across tasks. To realize this, MH-AIRL effectively synthesizes context-based multi-task learning, AIRL (an IL approach), and hierarchical policy learning. Further, MH-AIRL can be adopted to demonstrations without the task or skill annotations (i.e., state-action pairs only) which are more accessible in practice. Theoretical justifications are provided for each module of MH-AIRL, and evaluations on challenging multi-task settings demonstrate superior performance and transferability of the multi-task policies learned with MH-AIRL as compared to SOTA MIL baselines.

Various methods for Multi-Agent Reinforcement Learning (MARL) have been developed with the assumption that agents' policies are based on accurate state information. However, policies learned through Deep Reinforcement Learning (DRL) are susceptible to adversarial state perturbation attacks. In this work, we propose a State-Adversarial Markov Game (SAMG) and make the first attempt to investigate the fundamental properties of MARL under state uncertainties. Our analysis shows that the commonly used solution concepts of optimal agent policy and robust Nash equilibrium do not always exist in SAMGs. To circumvent this difficulty, we consider a new solution concept called robust agent policy, where agents aim to maximize the worst-case expected state value. We prove the existence of robust agent policy for finite state and finite action SAMGs. Additionally, we propose a Robust Multi-Agent Adversarial Actor-Critic (RMA3C) algorithm to learn robust policies for MARL agents under state uncertainties. Our experiments demonstrate that our algorithm outperforms existing methods when faced with state perturbations and greatly improves the robustness of MARL policies. Our code is public on https://songyanghan.github.io/what_is_solution/.