In digital health, the strategy of allocating a limited treatment budget across available risk times is crucial to reduce user fatigue. This strategy, however, encounters a significant obstacle due to the unknown actual number of risk times, a factor not adequately addressed by existing methods lacking theoretical guarantees. This paper introduces, for the first time, the online uniform risk times sampling problem within the approximation algorithm framework. We propose two online approximation algorithms for this problem, one with and one without learning augmentation, and provide rigorous theoretical performance guarantees for them using competitive ratio analysis. We assess the performance of our algorithms using both synthetic experiments and a real-world case study on HeartSteps mobile applications.

In this study, we introduce an optimization framework aimed at enhancing the efficiency of motion priority design in scenarios involving automated and teleoperated robots within an industrial recovery context. The escalating utilization of industrial robots at manufacturing sites has been instrumental in mitigating human workload. Nevertheless, the challenge persists in achieving effective human-robot collaboration/cooperation where human workers and robots share a workspace for collaborative tasks. In the event of an industrial robot encountering a failure, it necessitates the suspension of the corresponding factory cell for safe recovery. Given the limited capacity of pre-programmed robots to rectify such failures, human intervention becomes imperative, requiring entry into the robot workspace to address the dropped object while the robot system is halted. This non-continuous manufacturing process results in productivity loss. Robotic teleoperation has emerged as a promising technology enabling human workers to undertake high-risk tasks remotely and safely. Our study advocates for the incorporation of robotic teleoperation in the recovery process during manufacturing failure scenarios, which is referred to as "Cooperative Tele-Recovery". Our proposed approach involves the formulation of priority rules designed to facilitate collision avoidance between manufacturing and recovery robots. This, in turn, ensures a continuous manufacturing process with minimal production loss within a configurable risk limitation. We present a comprehensive motion priority optimization framework, encompassing an HRC simulator-based priority optimization and a cooperative multi-robot controller, to identify optimal parameters for the priority function. The framework dynamically adjusts the allocation of motion priorities for manufacturing and recovery robots while adhering to predefined risk limitations.