Beyond the worst-case analysis of algorithms, the learning-augmented framework considers that an algorithm can leverage possibly imperfect predictions about the unknown variables to have guarantees tied to the prediction quality. We consider online non-clairvoyant scheduling to minimize the max-stretch under this framework, where the scheduler can access job size predictions. We present a family of algorithms: Relaxed-Greedy (RG) with an $O(\eta^3 \cdot \sqrt{P})$ competitive ratio, where $\eta$ denotes the prediction error for job sizes and $P$ the maximum job size ratio; Adaptive Relaxed-Greedy with an $O(\lambda^{0.5} \cdot \eta^{2.5} \cdot \sqrt{P})$ competitive ratio, where $\lambda$ denotes the error for the minimum job size; Predictive Relaxed-Greedy with an $O(\lambda^{0.5} \cdot \varphi^{0.5} \cdot \eta \cdot \max \\\{ \eta, \varphi \\\} \cdot \sqrt{P})$ competitive ratio, where $\varphi$ denotes the error for the maximum job size. We also present *${RG}^x$*, an algorithm that represents a trade-off between consistency and smoothness, with an $O(\eta^{2+2x} \cdot P^{1-x})$ competitive ratio. We introduce a general method using resource augmentation to bound robustness, resulting in *RR*-augmented *RG*, with a $(1 + \epsilon)$-speed $O(\min \\\{ \eta^3 \sqrt{P}, \frac{n}{\epsilon} \\\})$ competitive ratio. Finally, we conduct simulations on synthetic and real-world datasets to evaluate the practical performance of these algorithms.

Online portfolio selection seeks to determine a sequence of allocations to maximize capital growth. Classical universal strategies asymptotically match the best constant-rebalanced portfolio but ignore potential forecasts, whereas heuristic methods often collapse when belief fails. We formalize this tension in a learning-augmented setting in which an investor observes (possibly erroneous) predictions prior to each decision moment, and we introduce the Rebalanced Arithmetic Mean portfolio with predictions (RAM). Under arbitrary return sequences, we prove that RAM captures at least a constant fraction of the hindsight-optimal wealth when forecasts are perfect while still exceeding the geometric mean of the sequence even when the predictions are adversarial. Comprehensive experiments on large-scale equity data strengthen our theory, spanning both synthetic prediction streams and production-grade machine-learning models. RAM advantages over universal-portfolio variants equipped with side information across various regimes. These results demonstrate that modest predictive power can be reliably converted into tangible gains without sacrificing worst-case guarantees.

The recent revival in learning theory gives us improved capabilities for accurate predictions and increased opportunities for performance enhancement. This work extends the research agenda of augmenting algorithms with predictions to one of the central scheduling problems – soft real-time scheduling on single and parallel machines to minimize the mean response time. We design an algorithm, PEDRMLF (Predictions Enhanced Dynamic Randomized MultiLevel Feedback), that incorporates job size predictions, achieving an optimal competitive ratio under perfect predictions and the best-known competitive ratio under any predictions. PEDRMLF is the first algorithm that simultaneously achieves optimal consistency and bounded robustness. Simulations show that the proposed algorithm performs close to the theoretically optimal bound while consistently outperforming state-of-the-art benchmarks.

We consider the problem of non-clairvoyant scheduling on single machine to minimize the total flow time with job size predictions. The existing algorithm achieves 2-consistency to predictions, but no algorithm can simultaneously attain bounded robustness. This work finds a sufficient condition for any algorithm to achieve optimal O(P)-robustness, where P is the maximum ratio of any two job sizes. We give the first algorithm that achieves optimal robustness up to a constant multiplicative factor and optimal consistency using this condition. Finally, for addressing small prediction errors, we present an algorithm that we conjecture to achieve the optimal O(η^2) competitive ratio, where η is the prediction error. Proving the claimed bound is our ongoing work.

The increasing use of renewable energy sources and electrical energy storage systems creates a new energy paradigm for residential houses and buildings. Such design reduces carbon footprint, but it also introduces a new challenge for minimizing the electricity bill while still meeting users’ needs. This challenge is often accompanied by deep uncertainty in user load demands, electricity tariffs, and renewable energy generations. To address this challenge, we propose an online algorithm, Virtual Algorithm-based Lightweight Online Scheduling (VALOS), to manage electricity purchasing and battery operations. Our solution does not use any prediction components in dealing with uncertainties. Instead, our algorithm employs a lightweight routine, Virtual Algorithm (VA), for making critical decisions to manage uncertainty. We prove that VA achieves an expected probability of 1/e for choosing the optimal purchasing timing online and incurs only a logarithmic computational cost. With VA, VALOS decides how the energy storage reacts to the load demands, which incurs only a linear-logarithmic online computational cost while achieving optimal performance under the specified conditions. Finally, we conduct extensive trace-driven simulations on real-world datasets to confirm the theoretical results and demonstrate the potential of VALOS.

Only when we understand how hackers think, can we defend against their attacks. Towards this end, this paper studies the cyber-attacks that aim to remove nodes or links from network topologies. We particularly focus on one type of such attacks called Maximum Vertex Coverage Attacks under Knapsack constraint (MVCAK), in which a hacker has a fixed budget to remove nodes from a network with the nodes involving different costs for removal, and the hacker's goal is to maximize the number of links incident to the nodes removed. Since the MVCAK problem is NP-hard, we firstly propose an optimal solution by Integer Linear Program formulation. Secondly, we give an approximate solution by Linear Programming relaxation that achieves an approximation ratio of 3/4, outperforming the existing 1 - 1/sqrt(e) (about 0.39). Thirdly, since the straightforward implementation of our approximate solution has a high time complexity, we propose two heuristics to significantly reduce its complexity while preserving the approximation ratio. We formally prove the correctness and the effectiveness of these two heuristics. Finally, we conduct extensive experiments on both artificial and real-world networks, showing that our approximate solution produces almost the same results as the optimal solution in practice and has an acceptable running time.