We study non-parametric estimation of the value function of an infinite-horizon $\gamma$-discounted Markov reward process (MRP) using observations from a single trajectory. We provide non-asymptotic guarantees for a general family of kernel-based multi-step temporal difference (TD) estimates, including canonical $K$-step look-ahead TD for $K = 1, 2, \ldots$ and the TD$(\lambda)$ family for $\lambda \in [0,1)$ as special cases. Our bounds capture its dependence on Bellman fluctuations, mixing time of the Markov chain, any mis-specification in the model, as well as the choice of weight function defining the estimator itself, and reveal some delicate interactions between mixing time and model mis-specification. For a given TD method applied to a well-specified model, its statistical error under trajectory data is similar to that of i.i.d. sample transition pairs, whereas under mis-specification, temporal dependence in data inflates the statistical error. However, any such deterioration can be mitigated by increased look-ahead. We complement our upper bounds by proving minimax lower bounds that establish optimality of TD-based methods with appropriately chosen look-ahead and weighting, and reveal some fundamental differences between value function estimation and ordinary non-parametric regression.

Humans demonstrate a variety of interesting behavioral characteristics when performing tasks, such as selecting between seemingly equivalent optimal actions, performing recovery actions when deviating from the optimal trajectory, or moderating actions in response to sensed risks. However, imitation learning, which attempts to teach robots to perform these same tasks from observations of human demonstrations, often fails to capture such behavior. Specifically, commonly used learning algorithms embody inherent contradictions between the learning assumptions (e.g., single optimal action) and actual human behavior (e.g., multiple optimal actions), thereby limiting robot generalizability, applicability, and demonstration feasibility. To address this, this paper proposes designing imitation learning algorithms with a focus on utilizing human behavioral characteristics, thereby embodying principles for capturing and exploiting actual demonstrator behavioral characteristics. This paper presents the first imitation learning framework, Bayesian Disturbance Injection (BDI), that typifies human behavioral characteristics by incorporating model flexibility, robustification, and risk sensitivity. Bayesian inference is used to learn flexible non-parametric multi-action policies, while simultaneously robustifying policies by injecting risk-sensitive disturbances to induce human recovery action and ensuring demonstration feasibility. Our method is evaluated through risk-sensitive simulations and real-robot experiments (e.g., table-sweep task, shaft-reach task and shaft-insertion task) using the UR5e 6-DOF robotic arm, to demonstrate the improved characterisation of behavior. Results show significant improvement in task performance, through improved flexibility, robustness as well as demonstration feasibility.

Although numerous algorithms have been proposed to solve the categorical data clustering problem, how to access the statistical significance of a set of categorical clusters remains unaddressed. To fulfill this void, we employ the likelihood ratio test to derive a test statistic that can serve as a significance-based objective function in categorical data clustering. Consequently, a new clustering algorithm is proposed in which the significance-based objective function is optimized via a Monte Carlo search procedure. As a by-product, we can further calculate an empirical $p$-value to assess the statistical significance of a set of clusters and develop an improved gap statistic for estimating the cluster number. Extensive experimental studies suggest that our method is able to achieve comparable performance to state-of-the-art categorical data clustering algorithms. Moreover, the effectiveness of such a significance-based formulation on statistical cluster validation and cluster number estimation is demonstrated through comprehensive empirical results.

Cross entropy loss has served as the main objective function for classification-based tasks. Widely deployed for learning neural network classifiers, it shows both effectiveness and a probabilistic interpretation. Recently, after the success of self supervised contrastive representation learning methods, supervised contrastive methods have been proposed to learn representations and have shown superior and more robust performance, compared to solely training with cross entropy loss. However, cross entropy loss is still needed to train the final classification layer. In this work, we investigate the possibility of learning both the representation and the classifier using one objective function that combines the robustness of contrastive learning and the probabilistic interpretation of cross entropy loss. First, we revisit a previously proposed contrastive-based objective function that approximates cross entropy loss and present a simple extension to learn the classifier jointly. Second, we propose a new version of the supervised contrastive training that learns jointly the parameters of the classifier and the backbone of the network. We empirically show that our proposed objective functions show a significant improvement over the standard cross entropy loss with more training stability and robustness in various challenging settings.

We focus on causal discovery in the presence of measurement error in linear systems where the mixing matrix, i.e., the matrix indicating the independent exogenous noise terms pertaining to the observed variables, is identified up to permutation and scaling of the columns. We demonstrate a somewhat surprising connection between this problem and causal discovery in the presence of unobserved parentless causes, in the sense that there is a mapping, given by the mixing matrix, between the underlying models to be inferred in these problems. Consequently, any identifiability result based on the mixing matrix for one model translates to an identifiability result for the other model. We characterize to what extent the causal models can be identified under a two-part faithfulness assumption. Under only the first part of the assumption (corresponding to the conventional definition of faithfulness), the structure can be learned up to the causal ordering among an ordered grouping of the variables but not all the edges across the groups can be identified. We further show that if both parts of the faithfulness assumption are imposed, the structure can be learned up to a more refined ordered grouping. As a result of this refinement, for the latent variable model with unobserved parentless causes, the structure can be identified. Based on our theoretical results, we propose causal structure learning methods for both models, and evaluate their performance on synthetic data.

Human and robot partners increasingly need to work together to perform tasks as a team. Robots designed for such collaboration must reason about how their task-completion strategies interplay with the behavior and skills of their human team members as they coordinate on achieving joint goals. Our goal in this work is to develop a computational framework for robot adaptation to human partners in human-robot team collaborations. We first present an algorithm for autonomously recognizing available task-completion strategies by observing human-human teams performing a collaborative task. By transforming team actions into low dimensional representations using hidden Markov models, we can identify strategies without prior knowledge. Robot policies are learned on each of the identified strategies to construct a Mixture-of-Experts model that adapts to the task strategies of unseen human partners. We evaluate our model on a collaborative cooking task using an Overcooked simulator. Results of an online user study with 125 participants demonstrate that our framework improves the task performance and collaborative fluency of human-agent teams, as compared to state of the art reinforcement learning methods.

Influence Maximization (IM) is a classical combinatorial optimization problem, which can be widely used in mobile networks, social computing, and recommendation systems. It aims at selecting a small number of users such that maximizing the influence spread across the online social network. Because of its potential commercial and academic value, there are a lot of researchers focusing on studying the IM problem from different perspectives. The main challenge comes from the NP-hardness of the IM problem and \#P-hardness of estimating the influence spread, thus traditional algorithms for overcoming them can be categorized into two classes: heuristic algorithms and approximation algorithms. However, there is no theoretical guarantee for heuristic algorithms, and the theoretical design is close to the limit. Therefore, it is almost impossible to further optimize and improve their performance. With the rapid development of artificial intelligence, the technology based on Machine Learning (ML) has achieved remarkable achievements in many fields. In view of this, in recent years, a number of new methods have emerged to solve combinatorial optimization problems by using ML-based techniques. These methods have the advantages of fast solving speed and strong generalization ability to unknown graphs, which provide a brand-new direction for solving combinatorial optimization problems. Therefore, we abandon the traditional algorithms based on iterative search and review the recent development of ML-based methods, especially Deep Reinforcement Learning, to solve the IM problem and other variants in social networks. We focus on summarizing the relevant background knowledge, basic principles, common methods, and applied research. Finally, the challenges that need to be solved urgently in future IM research are pointed out.

While deep reinforcement learning has proven to be successful in solving control tasks, the "black-box" nature of an agent has received increasing concerns. We propose a prototype-based post-hoc policy explainer, ProtoX, that explains a blackbox agent by prototyping the agent's behaviors into scenarios, each represented by a prototypical state. When learning prototypes, ProtoX considers both visual similarity and scenario similarity. The latter is unique to the reinforcement learning context, since it explains why the same action is taken in visually different states. To teach ProtoX about visual similarity, we pre-train an encoder using contrastive learning via self-supervised learning to recognize states as similar if they occur close together in time and receive the same action from the black-box agent. We then add an isometry layer to allow ProtoX to adapt scenario similarity to the downstream task. ProtoX is trained via imitation learning using behavior cloning, and thus requires no access to the environment or agent. In addition to explanation fidelity, we design different prototype shaping terms in the objective function to encourage better interpretability. We conduct various experiments to test ProtoX. Results show that ProtoX achieved high fidelity to the original black-box agent while providing meaningful and understandable explanations.

PV power forecasting models are predominantly based on machine learning algorithms which do not provide any insight into or explanation about their predictions (black boxes). Therefore, their direct implementation in environments where transparency is required, and the trust associated with their predictions may be questioned. To this end, we propose a two stage probabilistic forecasting framework able to generate highly accurate, reliable, and sharp forecasts yet offering full transparency on both the point forecasts and the prediction intervals (PIs). In the first stage, we exploit natural gradient boosting (NGBoost) for yielding probabilistic forecasts, while in the second stage, we calculate the Shapley additive explanation (SHAP) values in order to fully comprehend why a prediction was made. To highlight the performance and the applicability of the proposed framework, real data from two PV parks located in Southern Germany are employed. Comparative results with two state-of-the-art algorithms, namely Gaussian process and lower upper bound estimation, manifest a significant increase in the point forecast accuracy and in the overall probabilistic performance. Most importantly, a detailed analysis of the model's complex nonlinear relationships and interaction effects between the various features is presented. This allows interpreting the model, identifying some learned physical properties, explaining individual predictions, reducing the computational requirements for the training without jeopardizing the model accuracy, detecting possible bugs, and gaining trust in the model. Finally, we conclude that the model was able to develop complex nonlinear relationships which follow known physical properties as well as human logic and intuition.

The study of decentralized learning or independent learning in cooperative multi-agent reinforcement learning has a history of decades. Recently empirical studies show that independent PPO (IPPO) can obtain good performance, close to or even better than the methods of centralized training with decentralized execution, in several benchmarks. However, decentralized actor-critic with convergence guarantee is still open. In this paper, we propose \textit{decentralized policy optimization} (DPO), a decentralized actor-critic algorithm with monotonic improvement and convergence guarantee. We derive a novel decentralized surrogate for policy optimization such that the monotonic improvement of joint policy can be guaranteed by each agent \textit{independently} optimizing the surrogate. In practice, this decentralized surrogate can be realized by two adaptive coefficients for policy optimization at each agent. Empirically, we compare DPO with IPPO in a variety of cooperative multi-agent tasks, covering discrete and continuous action spaces, and fully and partially observable environments. The results show DPO outperforms IPPO in most tasks, which can be the evidence for our theoretical results.