In this paper, we study learning-augmented algorithms for the Bahncard problem.

The online caching problem aims to minimize cache misses when serving a sequence of requests under a limited cache size. While naive learning-augmented caching algorithms achieve ideal $1$-consistency, they lack robustness guarantees. Existing robustification methods either sacrifice $1$-consistency or introduce excessive computational overhead. In this paper, we introduce Guard, a lightweight robustification framework that enhances the robustness of a broad class of learning-augmented caching algorithms to $2H_{k-1} + 2$, while preserving their $1$-consistency. Guard achieves the current best-known trade-off between consistency and robustness, with only O(1) additional per-request overhead, thereby maintaining the original time complexity of the base algorithm. Extensive experiments across multiple real-world datasets and prediction models validate the effectiveness of Guard in practice.

Since some of the data sets will naturally be imbalanced (e.g., if we train

Modern deep learning systems require huge data sets to achieve impressive performance, but there is little guidance on how much or what kind of data to collect. Over-collecting data incurs unnecessary present costs, while under-collecting may incur future costs and delay workflows.

We illustrate the online optimization process of RCL in Figure 1. We set b = 10 and A = I for the cost function in Eqn. The testing process is almost instant and takes less than 1 second. It does not use robustification during online optimization. By Theorem 4.1, there is a trade-off (governed by ML predictions for those problem instances that are adversarial to ROBD.

In this paper, we study learning-augmented algorithms for the Bahncard problem.

Large language models (LLMs) demonstrate remarkable performance across diverse tasks, yet their effectiveness frequently depends on costly commercial APIs or cloud services. Model selection thus entails a critical trade-off between performance and cost: high-performing LLMs typically incur substantial expenses, whereas budget-friendly small language models (SLMs) are constrained by limited capabilities. Current research primarily proposes two routing strategies: pre-generation routing and cascade routing. Both approaches have distinct characteristics, with cascade routing typically offering superior cost-effectiveness and accuracy despite its higher latency. To further address the limitations of both approaches, we introduce SATER, a dual-mode compatible approach that fine-tunes models through shortest-response preference optimization and a confidence-aware rejection mechanism. SATER significantly reduces redundant outputs and response times, while improving both the performance of pre-generation routing and the efficiency of cascade routing. Experiments across three SLMs and six datasets, varying in type and complexity, demonstrate that SATER achieves comparable performance while consistently reducing computational costs by over 50\% and cascade latency by over 80\%.

Optimizing Data Collection for Machine Learning

Optimizing Data Collection for Machine Learning