Mapping the surrounding environment is essential for the successful operation of autonomous robots. While extensive research has focused on mapping geometric structures and static objects, the environment is also influenced by the movement of dynamic objects. Incorporating information about spatial motion patterns can allow mobile robots to navigate and operate successfully in populated areas. In this paper, we propose a deep state-space model that learns the map representations of spatial motion patterns and how they change over time at a certain place. To evaluate our methods, we use two different datasets: one generated dataset with specific motion patterns and another with real-world pedestrian data. We test the performance of our model by evaluating its learning ability, mapping quality, and application to downstream tasks. The results demonstrate that our model can effectively learn the corresponding motion pattern, and has the potential to be applied to robotic application tasks.

A Markov decision process can be parameterized by a transition kernel and a reward function. Both play essential roles in the study of reinforcement learning as evidenced by their presence in the Bellman equations. In our inquiry of various kinds of "costs" associated with reinforcement learning inspired by the demands in robotic applications, rewards are central to understanding the structure of a Markov decision process and reward-centric notions can elucidate important concepts in reinforcement learning. Specifically, we study the sample complexity of policy evaluation and develop a novel estimator with an instance-specific error bound of $\tilde{O}(\sqrt{\frac{\tau_s}{n}})$ for estimating a single state value. Under the online regret minimization setting, we refine the transition-based MDP constant, diameter, into a reward-based constant, maximum expected hitting cost, and with it, provide a theoretical explanation for how a well-known technique, potential-based reward shaping, could accelerate learning with expert knowledge. In an attempt to study safe reinforcement learning, we model hazardous environments with irrecoverability and proposed a quantitative notion of safe learning via reset efficiency. In this setting, we modify a classic algorithm to account for resets achieving promising preliminary numerical results. Lastly, for MDPs with multiple reward functions, we develop a planning algorithm that computationally efficiently finds Pareto-optimal stochastic policies.

This paper presents a hidden Markov model designed to investigate the complex nature of earnings persistence. The proposed model assumes that the residuals of log-earnings consist of a persistent component and a transitory component, both following general Markov processes. Nonparametric identification is achieved through spectral decomposition of linear operators, and a modified stochastic EM algorithm is introduced for model estimation. Applying the framework to the Panel Study of Income Dynamics (PSID) dataset, we find that the earnings process displays nonlinear persistence, conditional skewness, and conditional kurtosis. Additionally, the transitory component is found to possess non-Gaussian properties, resulting in a significantly asymmetric distributional impact when high-earning households face negative shocks or low-earning households encounter positive shocks. Our empirical findings also reveal the presence of ARCH effects in earnings at horizons ranging from 2 to 8 years, further highlighting the complex dynamics of earnings persistence.

In this paper, we propose a new way of remembering by introducing a memory influence mechanism for the least squares support vector machine (LSSVM). Without changing the equation constraints of the original LSSVM, this mechanism, allows an accurate partitioning of the training set without overfitting. The maximum memory impact model (MIMM) and the weighted impact memory model (WIMM) are then proposed. It is demonstrated that these models can be degraded to the LSSVM. Furthermore, we propose some different memory impact functions for the MIMM and WIMM. The experimental results show that that our MIMM and WIMM have better generalization performance compared to the LSSVM and significant advantage in time cost compared to other memory models.

Learning strategic robot behavior -- like that required in pursuit-evasion interactions -- under real-world constraints is extremely challenging. It requires exploiting the dynamics of the interaction, and planning through both physical state and latent intent uncertainty. In this paper, we transform this intractable problem into a supervised learning problem, where a fully-observable robot policy generates supervision for a partially-observable one. We find that the quality of the supervision signal for the partially-observable pursuer policy depends on two key factors: the balance of diversity and optimality of the evader's behavior and the strength of the modeling assumptions in the fully-observable policy. We deploy our policy on a physical quadruped robot with an RGB-D camera on pursuit-evasion interactions in the wild. Despite all the challenges, the sensing constraints bring about creativity: the robot is pushed to gather information when uncertain, predict intent from noisy measurements, and anticipate in order to intercept. Project webpage: https://abajcsy.github.io/vision-based-pursuit/

Computational agents support humans in many areas of life and are therefore found in heterogeneous contexts. This means they operate in rapidly changing environments and can be confronted with huge state and action spaces. In order to perform services and carry out activities in a goal-oriented manner, agents require prior knowledge and therefore have to develop and pursue context-dependent policies. However, prescribing policies in advance is limited and inflexible, especially in dynamically changing environments. Moreover, the context of an agent determines its choice of actions. Since the environments can be stochastic and complex in terms of the number of states and feasible actions, activities are usually modelled in a simplified way by Markov decision processes so that, e.g., agents with reinforcement learning are able to learn policies, that help to capture the context and act accordingly to optimally perform activities. However, training policies for all possible contexts using reinforcement learning is time-consuming. A requirement and challenge for agents is to learn strategies quickly and respond immediately in cross-context environments and applications, e.g., the Internet, service robotics, cyber-physical systems. In this work, we propose a novel simulation-based approach that enables a) the representation of heterogeneous contexts through knowledge graphs and entity embeddings and b) the context-aware composition of policies on demand by ensembles of agents running in parallel. The evaluation we conducted with the "Virtual Home" dataset indicates that agents with a need to switch seamlessly between different contexts, can request on-demand composed policies that lead to the successful completion of context-appropriate activities without having to learn these policies in lengthy training steps and episodes, in contrast to agents that use reinforcement learning.

Various probabilistic time series forecasting models have sprung up and shown remarkably good performance. However, the choice of model highly relies on the characteristics of the input time series and the fixed distribution that the model is based on. Due to the fact that the probability distributions cannot be averaged over different models straightforwardly, the current time series model ensemble methods cannot be directly applied to improve the robustness and accuracy of forecasting. To address this issue, we propose pTSE, a multi-model distribution ensemble method for probabilistic forecasting based on Hidden Markov Model (HMM). pTSE only takes off-the-shelf outputs from member models without requiring further information about each model. Besides, we provide a complete theoretical analysis of pTSE to prove that the empirical distribution of time series subject to an HMM will converge to the stationary distribution almost surely. Experiments on benchmarks show the superiority of pTSE overall member models and competitive ensemble methods.

Constrained Markov Decision Processes (CMDPs) are one of the common ways to model safe reinforcement learning problems, where constraint functions model the safety objectives. Lagrangian-based dual or primal-dual algorithms provide efficient methods for learning in CMDPs. For these algorithms, the currently known regret bounds in the finite-horizon setting allow for a "cancellation of errors"; one can compensate for a constraint violation in one episode with a strict constraint satisfaction in another. However, we do not consider such a behavior safe in practical applications. In this paper, we overcome this weakness by proposing a novel model-based dual algorithm OptAug-CMDP for tabular finite-horizon CMDPs. Our algorithm is motivated by the augmented Lagrangian method and can be performed efficiently. We show that during $K$ episodes of exploring the CMDP, our algorithm obtains a regret of $\tilde{O}(\sqrt{K})$ for both the objective and the constraint violation. Unlike existing Lagrangian approaches, our algorithm achieves this regret without the need for the cancellation of errors.

Mathematical methods are developed to characterize the asymptotics of recurrent neural networks (RNN) as the number of hidden units, data samples in the sequence, hidden state updates, and training steps simultaneously grow to infinity. In the case of an RNN with a simplified weight matrix, we prove the convergence of the RNN to the solution of an infinite-dimensional ODE coupled with the fixed point of a random algebraic equation. The analysis requires addressing several challenges which are unique to RNNs. In typical mean-field applications (e.g., feedforward neural networks), discrete updates are of magnitude $\mathcal{O}(\frac{1}{N})$ and the number of updates is $\mathcal{O}(N)$. Therefore, the system can be represented as an Euler approximation of an appropriate ODE/PDE, which it will converge to as $N \rightarrow \infty$. However, the RNN hidden layer updates are $\mathcal{O}(1)$. Therefore, RNNs cannot be represented as a discretization of an ODE/PDE and standard mean-field techniques cannot be applied. Instead, we develop a fixed point analysis for the evolution of the RNN memory states, with convergence estimates in terms of the number of update steps and the number of hidden units. The RNN hidden layer is studied as a function in a Sobolev space, whose evolution is governed by the data sequence (a Markov chain), the parameter updates, and its dependence on the RNN hidden layer at the previous time step. Due to the strong correlation between updates, a Poisson equation must be used to bound the fluctuations of the RNN around its limit equation. These mathematical methods give rise to the neural tangent kernel (NTK) limits for RNNs trained on data sequences as the number of data samples and size of the neural network grow to infinity.

Deep reinforcement learning (DRL) has seen remarkable success in the control of single robots. However, applying DRL to robot swarms presents significant challenges. A critical challenge is non-stationarity, which occurs when two or more robots update individual or shared policies concurrently, thereby engaging in an interdependent training process with no guarantees of convergence. Circumventing non-stationarity typically involves training the robots with global information about other agents' states and/or actions. In contrast, in this paper we explore how to remove the need for global information. We pose our problem as a Partially Observable Markov Decision Process, due to the absence of global knowledge on other agents. Using collective transport as a testbed scenario, we study two approaches to multi-agent training. In the first, the robots exchange no messages, and are trained to rely on implicit communication through push-and-pull on the object to transport. In the second approach, we introduce Global State Prediction (GSP), a network trained to forma a belief over the swarm as a whole and predict its future states. We provide a comprehensive study over four well-known deep reinforcement learning algorithms in environments with obstacles, measuring performance as the successful transport of the object to the goal within a desired time-frame. Through an ablation study, we show that including GSP boosts performance and increases robustness when compared with methods that use global knowledge.