In this paper, we study the two-level ski-rental problem,where a user needs to fulfill a sequence of demands for multiple items by choosing one of the three payment options: paying for the on-demand usage (i.e., rent), buying individual items (i.e., single purchase), and buying all the items (i.e., combo purchase). Without knowing future demands, the user aims to minimize the total cost (i.e., the sum of the rental, single purchase, and combo purchase costs) by balancing the trade-off between the expensive upfront costs (for purchase) and the potential future expenses (for rent). We first design a robust online algorithm (RDTSR) that offers a worst-case performance guarantee. While online algorithms are robust against the worst-case scenarios, they are often overly cautious and thus suffer a poor average performance in typical scenarios. On the other hand, Machine Learning (ML) algorithms typically show promising average performance in various applications but lack worst-case performance guarantees. To harness the benefits of both methods, we develop a learning-augmented algorithm (LADTSR) by integrating ML predictions into the robust online algorithm, which outperforms the robust online algorithm under accurate predictions while ensuring worst-case performance guarantees even when predictions are inaccurate. Finally, we conduct numerical experiments on both synthetic and real-world trace data to corroborate the effectiveness of our approach.

This paper proposes regenerative particle Thompson sampling (RPTS), a flexible variation of Thompson sampling. Thompson sampling itself is a Bayesian heuristic for solving stochastic bandit problems, but it is hard to implement in practice due to the intractability of maintaining a continuous posterior distribution. Particle Thompson sampling (PTS) is an approximation of Thompson sampling obtained by simply replacing the continuous distribution by a discrete distribution supported at a set of weighted static particles. We observe that in PTS, the weights of all but a few fit particles converge to zero. RPTS is based on the heuristic: delete the decaying unfit particles and regenerate new particles in the vicinity of fit surviving particles. Empirical evidence shows uniform improvement from PTS to RPTS and flexibility and efficacy of RPTS across a set of representative bandit problems, including an application to 5G network slicing.

Network slicing achieves cost-efficient slice customization to support heterogeneous applications and services. Configuring cross-domain resources to end-to-end slices based on service-level agreements, however, is challenging, due to the complicated underlying correlations and the simulation-to-reality discrepancy between simulators and real networks. In this paper, we propose Atlas, an online network slicing system, which automates the service configuration of slices via safe and sample-efficient learn-to-configure approaches in three interrelated stages. First, we design a learning-based simulator to reduce the sim-to-real discrepancy, which is accomplished by a new parameter searching method based on Bayesian optimization. Second, we offline train the policy in the augmented simulator via a novel offline algorithm with a Bayesian neural network and parallel Thompson sampling. Third, we online learn the policy in real networks with a novel online algorithm with safe exploration and Gaussian process regression. We implement Atlas on an end-to-end network prototype based on OpenAirInterface RAN, OpenDayLight SDN transport, OpenAir-CN core network, and Docker-based edge server. Experimental results show that, compared to state-of-the-art solutions, Atlas achieves 63.9% and 85.7% regret reduction on resource usage and slice quality of experience during the online learning stage, respectively.