In this paper, we investigate the optimal robot path planning problem for high-level specifications described by co-safe linear temporal logic (LTL) formulae. We consider the scenario where the map geometry of the workspace is partially-known. Specifically, we assume that there are some unknown regions, for which the robot does not know their successor regions a priori unless it reaches these regions physically. In contrast to the standard game-based approach that optimizes the worst-case cost, in the paper, we propose to use regret as a new metric for planning in such a partially-known environment. The regret of a plan under a fixed but unknown environment is the difference between the actual cost incurred and the best-response cost the robot could have achieved if it realizes the actual environment with hindsight. We provide an effective algorithm for finding an optimal plan that satisfies the LTL specification while minimizing its regret. A case study on firefighting robots is provided to illustrate the proposed framework. We argue that the new metric is more suitable for the scenario of partially-known environment since it captures the trade-off between the actual cost spent and the potential benefit one may obtain for exploring an unknown region.
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The original formulation of de Finetti's theorem says that an exchangeable sequence of Bernoulli random variables is a mixture of iid sequences of random variables. Following the work of Hewitt and Savage, this theorem was previously known for several classes of exchangeable random variables (for instance, for Baire measurable random variables taking values in a compact Hausdorff space, and for Borel measurable random variables taking values in a Polish space). Under an assumption of the underlying common distribution being Radon, we show that de Finetti's theorem holds for a sequence of Borel measurable exchangeable random variables taking values in any Hausdorff space. This includes and generalizes the previously known versions of de Finetti's theorem. Furthermore, it shows that the theorem is explainable as a consequence of the nature of the distribution of the exchangeable random variables as opposed to the topological nature of their state space, which do not play a key role. Using known relative consistency results from set theory, this also shows that it is consistent with the axioms of ZFC that de Finetti's theorem holds for all sequences of exchangeable random variables taking values in any complete metric space. We use nonstandard analysis to first study the empirical measures induced by hyperfinitely many identically distributed random variables, which leads to a proof of de Finetti's theorem in great generality while retaining the combinatorial intuition of proofs of simpler versions of de Finetti's theorem. An overview of the requisite tools from nonstandard measure theory and topological meeasure theory is provided, with some new perspectives built at the interface between these fields as part of that overview. One highlight of this development is a new generalization of Prokhorov's theorem.
This paper is concerned with offline reinforcement learning (RL), which learns using pre-collected data without further exploration. Effective offline RL would be able to accommodate distribution shift and limited data coverage. However, prior algorithms or analyses either suffer from suboptimal sample complexities or incur high burn-in cost to reach sample optimality, thus posing an impediment to efficient offline RL in sample-starved applications. We demonstrate that the model-based (or "plug-in") approach achieves minimax-optimal sample complexity without burn-in cost for tabular Markov decision processes (MDPs). Concretely, consider a finite-horizon (resp. $\gamma$-discounted infinite-horizon) MDP with $S$ states and horizon $H$ (resp. effective horizon $\frac{1}{1-\gamma}$), and suppose the distribution shift of data is reflected by some single-policy clipped concentrability coefficient $C^{\star}_{\text{clipped}}$. We prove that model-based offline RL yields $\varepsilon$-accuracy with a sample complexity of \[ \begin{cases} \frac{H^{4}SC_{\text{clipped}}^{\star}}{\varepsilon^{2}} & (\text{finite-horizon MDPs}) \frac{SC_{\text{clipped}}^{\star}}{(1-\gamma)^{3}\varepsilon^{2}} & (\text{infinite-horizon MDPs}) \end{cases} \] up to log factor, which is minimax optimal for the entire $\varepsilon$-range. The proposed algorithms are ``pessimistic'' variants of value iteration with Bernstein-style penalties, and do not require sophisticated variance reduction. Our analysis framework is established upon delicate leave-one-out decoupling arguments in conjunction with careful self-bounding techniques tailored to MDPs.
Compared to mean regression and quantile regression, the literature on modal regression is very sparse. We propose a unified framework for Bayesian modal regression based on a family of unimodal distributions indexed by the mode along with other parameters that allow for flexible shapes and tail behaviors. Following prior elicitation, we carry out regression analysis of simulated data and datasets from several real-life applications. Besides drawing inference for covariate effects that are easy to interpret, we consider prediction and model selection under the proposed Bayesian modal regression framework. Evidence from these analyses suggest that the proposed inference procedures are very robust to outliers, enabling one to discover interesting covariate effects missed by mean or median regression, and to construct much tighter prediction intervals than those from mean or median regression. Computer programs for implementing the proposed Bayesian modal regression are available at //github.com/rh8liuqy/Bayesian_modal_regression.
Deep learning-based grasp prediction models have become an industry standard for robotic bin-picking systems. To maximize pick success, production environments are often equipped with several end-effector tools that can be swapped on-the-fly, based on the target object. Tool-change, however, takes time. Choosing the order of grasps to perform, and corresponding tool-change actions, can improve system throughput; this is the topic of our work. The main challenge in planning tool change is uncertainty - we typically cannot see objects in the bin that are currently occluded. Inspired by queuing and admission control problems, we model the problem as a Markov Decision Process (MDP), where the goal is to maximize expected throughput, and we pursue an approximate solution based on model predictive control, where at each time step we plan based only on the currently visible objects. Special to our method is the idea of void zones, which are geometrical boundaries in which an unknown object will be present, and therefore cannot be accounted for during planning. Our planning problem can be solved using integer linear programming (ILP). However, we find that an approximate solution based on sparse tree search yields near optimal performance at a fraction of the time. Another question that we explore is how to measure the performance of tool-change planning: we find that throughput alone can fail to capture delicate and smooth behavior, and propose a principled alternative. Finally, we demonstrate our algorithms on both synthetic and real world bin picking tasks.
Deterministic methods for motion planning guarantee safety amidst uncertainty in obstacle locations by trying to restrict the robot from operating in any possible location that an obstacle could be in. Unfortunately, this can result in overly conservative behavior. Chance-constrained optimization can be applied to improve the performance of motion planning algorithms by allowing for a user-specified amount of bounded constraint violation. However, state-of-the-art methods rely either on moment-based inequalities, which can be overly conservative, or make it difficult to satisfy assumptions about the class of probability distributions used to model uncertainty. To address these challenges, this work proposes a real-time, risk-aware reachability based motion planning framework called RADIUS. The method first generates a reachable set of parameterized trajectories for the robot offline. At run time, RADIUS computes a closed-form over-approximation of the risk of a collision with an obstacle. This is done without restricting the probability distribution used to model uncertainty to a simple class (e.g., Gaussian). Then, RADIUS performs real-time optimization to construct a trajectory that can be followed by the robot in a manner that is certified to have a risk of collision that is less than or equal to a user-specified threshold. The proposed algorithm is compared to several state-of-the-art chance-constrained and deterministic methods in simulation, and is shown to consistently outperform them in a variety of driving scenarios. A demonstration of the proposed framework on hardware is also provided.
Deep Reinforcement Learning (DRL) policies have been shown to be vulnerable to small adversarial noise in observations. Such adversarial noise can have disastrous consequences in safety-critical environments. For instance, a self-driving car receiving adversarially perturbed sensory observations about nearby signs (e.g., a stop sign physically altered to be perceived as a speed limit sign) or objects (e.g., cars altered to be recognized as trees) can be fatal. Existing approaches for making RL algorithms robust to an observation-perturbing adversary have focused on reactive approaches that iteratively improve against adversarial examples generated at each iteration. While such approaches have been shown to provide improvements over regular RL methods, they are reactive and can fare significantly worse if certain categories of adversarial examples are not generated during training. To that end, we pursue a more proactive approach that relies on directly optimizing a well-studied robustness measure, regret instead of expected value. We provide a principled approach that minimizes maximum regret over a "neighborhood" of observations to the received "observation". Our regret criterion can be used to modify existing value- and policy-based Deep RL methods. We demonstrate that our approaches provide a significant improvement in performance across a wide variety of benchmarks against leading approaches for robust Deep RL.
A deep reinforcement learning technique is presented for task offloading decision-making algorithms for a multi-access edge computing (MEC) assisted unmanned aerial vehicle (UAV) network in a smart farm Internet of Things (IoT) environment. The task offloading technique uses financial concepts such as cost functions and conditional variable at risk (CVaR) in order to quantify the damage that may be caused by each risky action. The approach was able to quantify potential risks to train the reinforcement learning agent to avoid risky behaviors that will lead to irreversible consequences for the farm. Such consequences include an undetected fire, pest infestation, or a UAV being unusable. The proposed CVaR-based technique was compared to other deep reinforcement learning techniques and two fixed rule-based techniques. The simulation results show that the CVaR-based risk quantifying method eliminated the most dangerous risk, which was exceeding the deadline for a fire detection task. As a result, it reduced the total number of deadline violations with a negligible increase in energy consumption.
Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation monitoring. However, there are also limitations; satellites are difficult to manufacture, expensive to maintain, and tricky to launch into orbit. Therefore, it is critical that satellites are employed efficiently. This poses a challenge known as the satellite mission planning problem, which could be computationally prohibitive to solve on large scales. However, close-to-optimal algorithms can often provide satisfactory resolutions, such as greedy reinforcement learning, and optimization algorithms. This paper introduces a set of quantum algorithms to solve the mission planning problem and demonstrate an advantage over the classical algorithms implemented thus far. The problem is formulated as maximizing the number of high-priority tasks completed on real datasets containing thousands of tasks and multiple satellites. This work demonstrates that through solution-chaining and clustering, optimization and machine learning algorithms offer the greatest potential for optimal solutions. Most notably, this paper illustrates that a hybridized quantum-enhanced reinforcement learning agent can achieve a completion percentage of 98.5% over high-priority tasks, which is a significant improvement over the baseline greedy methods with a completion rate of 63.6%. The results presented in this work pave the way to quantum-enabled solutions in the space industry and, more generally, future mission planning problems across industries.
This paper investigates a new approach to model-based reinforcement learning using background planning: mixing (approximate) dynamic programming updates and model-free updates, similar to the Dyna architecture. Background planning with learned models is often worse than model-free alternatives, such as Double DQN, even though the former uses significantly more memory and computation. The fundamental problem is that learned models can be inaccurate and often generate invalid states, especially when iterated many steps. In this paper, we avoid this limitation by constraining background planning to a set of (abstract) subgoals and learning only local, subgoal-conditioned models. This goal-space planning (GSP) approach is more computationally efficient, naturally incorporates temporal abstraction for faster long-horizon planning and avoids learning the transition dynamics entirely. We show that our GSP algorithm can learn significantly faster than a Double DQN baseline in a variety of situations.
Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.
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