We present a distribution optimization framework that significantly improves confidence bounds for various risk measures compared to previous methods. Our framework encompasses popular risk measures such as the entropic risk measure, conditional value at risk (CVaR), spectral risk measure, distortion risk measure, equivalent certainty, and rank-dependent expected utility, which are well established in risk-sensitive decision-making literature. To achieve this, we introduce two estimation schemes based on concentration bounds derived from the empirical distribution, specifically using either the Wasserstein distance or the supremum distance. Unlike traditional approaches that add or subtract a confidence radius from the empirical risk measures, our proposed schemes evaluate a specific transformation of the empirical distribution based on the distance. Consequently, our confidence bounds consistently yield tighter results compared to previous methods. We further verify the efficacy of the proposed framework by providing tighter problem-dependent regret bound for the CVaR bandit.

The efficient computation of viewpoints under consideration of various system and process constraints is a common challenge that any robot vision system is confronted with when trying to execute a vision task. Although fundamental research has provided solid and sound solutions for tackling this problem, a holistic framework that poses its formal description, considers the heterogeneity of robot vision systems, and offers an integrated solution remains unaddressed. Hence, this publication outlines the generation of viewpoints as a geometrical problem and introduces a generalized theoretical framework based on Feature-Based Constrained Spaces ($\mathcal{C}$-spaces) as the backbone for solving it. A $\mathcal{C}$-space can be understood as the topological space that a viewpoint constraint spans, where the sensor can be positioned for acquiring a feature while fulfilling the regarded constraint. The present study demonstrates that many viewpoint constraints can be efficiently formulated as $\mathcal{C}$-spaces providing geometric, deterministic, and closed solutions. The introduced $\mathcal{C}$-spaces are characterized based on generic domain and viewpoint constraints models to ease the transferability of the present framework to different applications and robot vision systems. The effectiveness and efficiency of the concepts introduced are verified on a simulation-based scenario and validated on a real robot vision system comprising two different sensors.

Planning multi-contact motions in a receding horizon fashion requires a value function to guide the planning with respect to the future, e.g., building momentum to traverse large obstacles. Traditionally, the value function is approximated by computing trajectories in a prediction horizon (never executed) that foresees the future beyond the execution horizon. However, given the non-convex dynamics of multi-contact motions, this approach is computationally expensive. To enable online Receding Horizon Planning (RHP) of multi-contact motions, we find efficient approximations of the value function. Specifically, we propose a trajectory-based and a learning-based approach. In the former, namely RHP with Multiple Levels of Model Fidelity, we approximate the value function by computing the prediction horizon with a convex relaxed model. In the latter, namely Locally-Guided RHP, we learn an oracle to predict local objectives for locomotion tasks, and we use these local objectives to construct local value functions for guiding a short-horizon RHP. We evaluate both approaches in simulation by planning centroidal trajectories of a humanoid robot walking on moderate slopes, and on large slopes where the robot cannot maintain static balance. Our results show that locally-guided RHP achieves the best computation efficiency (95\%-98.6\% cycles converge online). This computation advantage enables us to demonstrate online receding horizon planning of our real-world humanoid robot Talos walking in dynamic environments that change on-the-fly.

We consider a general online resource allocation model with bandit feedback and time-varying demands. While online resource allocation has been well studied in the literature, most existing works make the strong assumption that the demand arrival process is stationary. In practical applications, such as online advertisement and revenue management, however, this process may be exogenous and non-stationary, like the constantly changing internet traffic. Motivated by the recent Online Algorithms with Advice framework [Mitazenmacher and Vassilvitskii, \emph{Commun. ACM} 2022], we explore how online advice can inform policy design. We establish an impossibility result that any algorithm perform poorly in terms of regret without any advice in our setting. In contrast, we design an robust online algorithm that leverages the online predictions on the total demand volumes. Empowered with online advice, our proposed algorithm is shown to have both theoretical performance and promising numerical results compared with other algorithms in literature. We also provide two explicit examples for the time-varying demand scenarios and derive corresponding theoretical performance guarantees. Finally, we adapt our model to a network revenue management problem, and numerically demonstrate that our algorithm can still performs competitively compared to existing baselines.

In robotics, optimizing controller parameters under safety constraints is an important challenge. Safe Bayesian optimization (BO) quantifies uncertainty in the objective and constraints to safely guide exploration in such settings. Hand-designing a suitable probabilistic model can be challenging, however. In the presence of unknown safety constraints, it is crucial to choose reliable model hyper-parameters to avoid safety violations. Here, we propose a data-driven approach to this problem by meta-learning priors for safe BO from offline data. We build on a meta-learning algorithm, F-PACOH, capable of providing reliable uncertainty quantification in settings of data scarcity. As core contribution, we develop a novel framework for choosing safety-compliant priors in a data-riven manner via empirical uncertainty metrics and a frontier search algorithm. On benchmark functions and a high-precision motion system, we demonstrate that our meta-learned priors accelerate the convergence of safe BO approaches while maintaining safety.

Entropy regularized Markov decision processes have been widely used in reinforcement learning. This paper is concerned with the primal-dual formulation of the entropy regularized problems. Standard first-order methods suffer from slow convergence due to the lack of strict convexity and concavity. To address this issue, we first introduce a new quadratically convexified primal-dual formulation. The natural gradient ascent descent of the new formulation enjoys a global convergence guarantee and exponential convergence rate. We also propose a new interpolating metric that further accelerates the convergence significantly. Numerical results are provided to demonstrate the performance of the proposed methods under multiple settings.

Learning optimal control policies directly on physical systems is challenging since even a single failure can lead to costly hardware damage. Most existing model-free learning methods that guarantee safety, i.e., no failures, during exploration are limited to local optima. A notable exception is the GoSafe algorithm, which, unfortunately, cannot handle high-dimensional systems and hence cannot be applied to most real-world dynamical systems. This work proposes GoSafeOpt as the first algorithm that can safely discover globally optimal policies for high-dimensional systems while giving safety and optimality guarantees. We demonstrate the superiority of GoSafeOpt over competing model-free safe learning methods on a robot arm that would be prohibitive for GoSafe.

Line coverage is the task of servicing a given set of one-dimensional features in an environment. It is important for the inspection of linear infrastructure such as road networks, power lines, and oil and gas pipelines. This paper addresses the single robot line coverage problem for aerial and ground robots by modeling it as an optimization problem on a graph. The problem belongs to the broad class of arc routing problems and is closely related to the rural postman problem (RPP) on asymmetric graphs. The paper presents an integer linear programming formulation with proofs of correctness. Using the minimum cost flow problem, we develop approximation algorithms with guarantees on the solution quality. These guarantees also improve the existing results for the asymmetric RPP. The main algorithm partitions the problem into three cases based on the structure of the required graph, i.e., the graph induced by the features that require servicing. We evaluate our algorithms on road networks from the 50 most populous cities in the world, consisting of up to 730 road segments. The algorithms, augmented with improvement heuristics, run within 3s and generate solutions that are within 10% of the optimum. We experimentally demonstrate our algorithms with commercial UAVs.

Social media platforms are essential outlets for expressing opinions, providing a valuable resource for capturing public viewpoints via text analytics. However, for many users, passive browsing is their preferred mode of interaction, leading to their perspectives being overlooked by text analytics methods. Meanwhile, social media polls have emerged as a practical feature for gathering public opinions, allowing post authors to pose questions with pre-defined answer options for readers to vote on. To broaden the benefits of polls for posts without them, this article explores the automatic generation of a poll from a social media post by leveraging cutting-edge natural language generation (NLG) techniques. However, existing NLG techniques, primarily developed for general-domain texts, may be ineffective when applied to noisy social media data, which often feature implicit context-question-answer relations. To tackle these challenges, we enrich a post context with its comments and propose a novel unified poll generation framework called UniPoll. It employs prompt tuning with multi-objective optimization to bolster the connection exploration between contexts (posts and comments) and polls (questions and answers). Experimental comparisons on a large-scale Chinese Weibo dataset show that UniPoll significantly outperforms T5, the state-of-the-art NLG model, which generates question and answer separately. Comprehensive qualitative and quantitative analyses further underscore the superiority of UniPoll through various evaluation lenses.

Gaussian process (GP) based Bayesian optimization (BO) is a powerful method for optimizing black-box functions efficiently. The practical performance and theoretical guarantees associated with this approach depend on having the correct GP hyperparameter values, which are usually unknown in advance and need to be estimated from the observed data. However, in practice, these estimations could be incorrect due to biased data sampling strategies commonly used in BO. This can lead to degraded performance and break the sub-linear global convergence guarantee of BO. To address this issue, we propose a new BO method that can sub-linearly converge to the global optimum of the objective function even when the true GP hyperparameters are unknown in advance and need to be estimated from the observed data. Our method uses a multi-armed bandit technique (EXP3) to add random data points to the BO process, and employs a novel training loss function for the GP hyperparameter estimation process that ensures unbiased estimation from the observed data. We further provide theoretical analysis of our proposed method. Finally, we demonstrate empirically that our method outperforms existing approaches on various synthetic and real-world problems.