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Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques usually incur overhead by having to train multiple model instances or do not produce very diverse predictions. This comprehensive and extensive survey aims to familiarize the reader with an alternative class of models based on the concept of Evidential Deep Learning: For unfamiliar data, they aim to admit "what they don't know", and fall back onto a prior belief. Furthermore, they allow uncertainty estimation in a single model and forward pass by parameterizing distributions over distributions. This survey recapitulates existing works, focusing on the implementation in a classification setting, before surveying the application of the same paradigm to regression. We also reflect on the strengths and weaknesses compared to other existing methods and provide the most fundamental derivations using a unified notation to aid future research.

This paper studies the communication complexity of convex risk-averse optimization over a network. The problem generalizes the well-studied risk-neutral finite-sum distributed optimization problem and its importance stems from the need to handle risk in an uncertain environment. For algorithms in the literature, there exists a gap in communication complexities for solving risk-averse and risk-neutral problems. We propose two distributed algorithms, namely the distributed risk averse optimization (DRAO) method and the distributed risk averse optimization with sliding (DRAO-S) method, to close the gap. Specifically, the DRAO method achieves the optimal communication complexity by assuming a certain saddle point subproblem can be easily solved in the server node. The DRAO-S method removes the strong assumption by introducing a novel saddle point sliding subroutine which only requires the projection over the ambiguity set $P$. We observe that the number of $P$-projections performed by DRAO-S is optimal. Moreover, we develop matching lower complexity bounds to show the communication complexities of both DRAO and DRAO-S to be improvable. Numerical experiments are conducted to demonstrate the encouraging empirical performance of the DRAO-S method.

We consider the problem of learning a control policy that is robust against the parameter mismatches between the training environment and testing environment. We formulate this as a distributionally robust reinforcement learning (DR-RL) problem where the objective is to learn the policy which maximizes the value function against the worst possible stochastic model of the environment in an uncertainty set. We focus on the tabular episodic learning setting where the algorithm has access to a generative model of the nominal (training) environment around which the uncertainty set is defined. We propose the Robust Phased Value Learning (RPVL) algorithm to solve this problem for the uncertainty sets specified by four different divergences: total variation, chi-square, Kullback-Leibler, and Wasserstein. We show that our algorithm achieves $\tilde{\mathcal{O}}(|\mathcal{S}||\mathcal{A}| H^{5})$ sample complexity, which is uniformly better than the existing results by a factor of $|\mathcal{S}|$, where $|\mathcal{S}|$ is number of states, $|\mathcal{A}|$ is the number of actions, and $H$ is the horizon length. We also provide the first-ever sample complexity result for the Wasserstein uncertainty set. Finally, we demonstrate the performance of our algorithm using simulation experiments.

Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. Recently proposed evidential neural networks explicitly account for different uncertainties by treating the network's outputs as evidence to parameterize the Dirichlet distribution, and achieve impressive performance in uncertainty estimation. However, for high data uncertainty samples but annotated with the one-hot label, the evidence-learning process for those mislabeled classes is over-penalized and remains hindered. To address this problem, we propose a novel method, \textit{Fisher Information-based Evidential Deep Learning} ($\mathcal{I}$-EDL). In particular, we introduce Fisher Information Matrix (FIM) to measure the informativeness of evidence carried by each sample, according to which we can dynamically reweight the objective loss terms to make the network more focus on the representation learning of uncertain classes. The generalization ability of our network is further improved by optimizing the PAC-Bayesian bound. As demonstrated empirically, our proposed method consistently outperforms traditional EDL-related algorithms in multiple uncertainty estimation tasks, especially in the more challenging few-shot classification settings.

Reinforcement learning (RL) has recently proven great success in various domains. Yet, the design of the reward function requires detailed domain expertise and tedious fine-tuning to ensure that agents are able to learn the desired behaviour. Using a sparse reward conveniently mitigates these challenges. However, the sparse reward represents a challenge on its own, often resulting in unsuccessful training of the agent. In this paper, we therefore address the sparse reward problem in RL. Our goal is to find an effective alternative to reward shaping, without using costly human demonstrations, that would also be applicable to a wide range of domains. Hence, we propose to use model predictive control~(MPC) as an experience source for training RL agents in sparse reward environments. Without the need for reward shaping, we successfully apply our approach in the field of mobile robot navigation both in simulation and real-world experiments with a Kuboki Turtlebot 2. We furthermore demonstrate great improvement over pure RL algorithms in terms of success rate as well as number of collisions and timeouts. Our experiments show that MPC as an experience source improves the agent's learning process for a given task in the case of sparse rewards.

The Teacher-Student Framework (TSF) is a reinforcement learning setting where a teacher agent guards the training of a student agent by intervening and providing online demonstrations. Assuming optimal, the teacher policy has the perfect timing and capability to intervene in the learning process of the student agent, providing safety guarantee and exploration guidance. Nevertheless, in many real-world settings it is expensive or even impossible to obtain a well-performing teacher policy. In this work, we relax the assumption of a well-performing teacher and develop a new method that can incorporate arbitrary teacher policies with modest or inferior performance. We instantiate an Off-Policy Reinforcement Learning algorithm, termed Teacher-Student Shared Control (TS2C), which incorporates teacher intervention based on trajectory-based value estimation. Theoretical analysis validates that the proposed TS2C algorithm attains efficient exploration and substantial safety guarantee without being affected by the teacher's own performance. Experiments on various continuous control tasks show that our method can exploit teacher policies at different performance levels while maintaining a low training cost. Moreover, the student policy surpasses the imperfect teacher policy in terms of higher accumulated reward in held-out testing environments. Code is available at //metadriverse.github.io/TS2C.

In this paper, we consider the closed-loop control problem of nonlinear robotic systems in the presence of probabilistic uncertainties and disturbances. More precisely, we design a state feedback controller that minimizes deviations of the states of the system from the nominal state trajectories due to uncertainties and disturbances. Existing approaches to address the control problem of probabilistic systems are limited to particular classes of uncertainties and systems such as Gaussian uncertainties and processes and linearized systems. We present an approach that deals with nonlinear dynamics models and arbitrary known probabilistic uncertainties. We formulate the controller design problem as an optimization problem in terms of statistics of the probability distributions including moments and characteristic functions. In particular, in the provided optimization problem, we use moments and characteristic functions to propagate uncertainties throughout the nonlinear motion model of robotic systems. In order to reduce the tracking deviations, we minimize the uncertainty of the probabilistic states around the nominal trajectory by minimizing the trace and the determinant of the covariance matrix of the probabilistic states. To obtain the state feedback gains, we solve deterministic optimization problems in terms of moments, characteristic functions, and state feedback gains using off-the-shelf interior-point optimization solvers. To illustrate the performance of the proposed method, we compare our method with existing probabilistic control methods.

This paper is proposed to efficiently provide a convex approximation for the probabilistic reachable set of a dynamic system in the face of uncertainties. When the uncertainties are not limited to bounded ones, it may be impossible to find a bounded reachable set of the system. Instead, we turn to find a probabilistic reachable set that bounds system states with confidence. A data-driven approach of Kernel Density Estimator (KDE) accelerated by Fast Fourier Transform (FFT) is customized to model the uncertainties and obtain the probabilistic reachable set efficiently. However, the irregular or non-convex shape of the probabilistic reachable set refrains it from practice. For the sake of real applications, we formulate an optimization problem as Mixed Integer Nonlinear Programming (MINLP) whose solution accounts for an optimal $n$-sided convex polygon to approximate the probabilistic reachable set. A heuristic algorithm is then developed to solve the MINLP efficiently while ensuring accuracy. The results of comprehensive case studies demonstrate the near-optimality, accuracy, efficiency, and robustness enjoyed by the proposed algorithm. The benefits of this work pave the way for its promising applications to safety-critical real-time motion planning of uncertain systems.

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.