LLM routing aims to select the most appropriate model for each query, balancing competing performance metrics such as accuracy and cost across a pool of language models. Prior approaches typically adopt a decoupled strategy, where the metrics are first predicted and the model is then selected based on these estimates. This setup is prone to compounding errors and often relies on full-feedback data, where each query is evaluated by all candidate models, which is costly to obtain and maintain in practice. In contrast, we learn from observational data, which records only the outcome of the model actually deployed. We propose a causal end-to-end framework that learns routing policies by minimizing decision-making regret from observational data. To enable efficient optimization, we introduce two theoretically grounded surrogate objectives: a classification-based upper bound, and a softmax-weighted regret approximation shown to recover the optimal policy at convergence. We further extend our framework to handle heterogeneous cost preferences via an interval-conditioned architecture. Experiments on public benchmarks show that our method outperforms existing baselines, achieving state-of-the-art performance across different embedding models.

We study the problem of finding optimal manifold-aligned counterfactual explanations for neural networks. Existing approaches that involve solving a complex mixed-integer optimization (MIP) problem frequently suffer from scalability issues, limiting their practical usefulness. Furthermore, the solutions are not guaranteed to follow the data manifold, resulting in unrealistic counterfactual explanations. To address these challenges, we first present a MIP formulation where we explicitly enforce manifold alignment by reformulating the highly nonlinear Local Outlier Factor (LOF) metric as mixed-integer constraints. To address the computational challenge, we leverage the geometry of a trained neural network and propose an efficient decomposition scheme that reduces the initial large, hard-to-solve optimization problem into a series of significantly smaller, easier-to-solve problems by constraining the search space to “live” polytopes, i.e., regions that contain at least one actual data point. Experiments on real-world datasets demonstrate the efficacy of our approach in producing both optimal and realistic counterfactual explanations, and computational traceability.

Hierarchical time series forecasting requires not only prediction accuracy but also coherency, i.e., forecasts add up appropriately across the hierarchy. Recent literature has shown that reconciliation via projection outperforms prior methods such as top-down or bottom-up approaches. Unlike existing work that pre-specifies a projection matrix (e.g., orthogonal), we study the problem of learning the optimal oblique projection from data for coherent forecasting of hierarchical time series. In addition to the unbiasedness-preserving property, oblique projection implicitly accounts for the hierarchy structure and assigns different weights to individual time series, providing significant adaptability over orthogonal projection which treats base forecast errors equally. We examine two broad classes of projections, namely Euclidean projection and general oblique projections. We propose to model the reconciliation step as a learnable, structured, projection layer in the neural forecaster architecture. The proposed approach allows for the efficient learning of the optimal projection in an end-to-end framework where both the neural forecaster and the projection layer are learned simultaneously. An empirical evaluation of real-world hierarchical time series datasets demonstrates the superior performance of the proposed method over existing state-of-the-art approaches.

We study the problem of obtaining optimal and realistic prescriptions when using ReLU networks for data-driven decision-making. In this setting, the network is used to predict a quantity of interest and then is optimized to retrieve the decisions that maximize the quantity (e.g. find the best prices that maximize revenue). However, optimizing over-parameterized models often produces unrealistic prescriptions, far from the data manifold. This phenomenon is known as the Optimizer's Curse. To tackle this problem, we model the requirement for the resulting decisions to align with the data manifold as a tractable optimization constraint. This is achieved by reformulating the highly nonlinear Local Outlier Factor (LOF) metric as a single linear or quadratic constraint. To solve the problem efficiently for large networks, we propose an adaptive sampling algorithm that reduces the initial hard-to-solve optimization problem into a small number of significantly easier-to-solve problems by restricting the decision space to realistic polytopes, i.e. polytopes of the decision space that contain at least one realistic data point. Experiments on publicly available networks demonstrate the efficacy and scalability of our approach.

We study the problem of learning optimal policy from a set of discrete treatment options using observational data. We propose a piecewise linear neural network model that can balance strong prescriptive performance and interpretability, which we refer to as the prescriptive ReLU network, or P-ReLU. We show analytically that this model (i) partitions the input space into disjoint polyhedra, where all instances that belong to the same partition receive the same treatment, and (ii) can be converted into an equivalent prescriptive tree with hyperplane splits for interpretability. We demonstrate the flexibility of the P-ReLU network as constraints can be easily incorporated with minor modifications to the architecture. Through experiments, we validate the superior prescriptive accuracy of P-ReLU against competing benchmarks. Lastly, we present examples of prescriptive trees extracted from trained P-ReLUs using a real-world dataset, for both the unconstrained and constrained scenarios.

Modern large-scale computing deployments consist of complex elastic applications running over machine clusters. A current trend adopted by providers is to set unused virtual machines, or else spot instances, in low prices to take advantage of spare capacity. In this paper we present a group of efficient allocation and pricing policies that can be used by vendors for their spot price mechanisms. We model the procedure of acquiring virtual machines as a truthful knapsack auction and we deploy dynamic allocation and pricing rules that achieve near-optimal revenue and social welfare. As the problem is NP-hard our solutions are based on approximate algorithms. First, we propose two solutions that do not use prior knowledge. Then, we enhance them with three learning algorithms. We evaluate them with simulations on the Google Cluster dataset and we benchmark them against the Uniform Price, the Optimal Single Price and the Ex-CORE mechanisms. Our proposed dynamic mechanism is robust, achieves revenue up to 89% of the Optimal Single Price auction, and computes the allocation in polynomial time making our contribution computationally tractable in realtime scenarios.

Mobile Network Operators develop new technologies, as the 5G network, to handle the constantly increasing network traffic, while they put less effort on optimizing their operations. However, more energy efficient approaches are essential for cost reduction and compliance with energy footprint principles. Network usage and IoT data produced in the base stations can be used to develop such approaches. Considering the above, the BigOptiBase platform has been designed. Through this platform we will offer a big data analytics subsystem developed to provide elastic energy efficient solutions for the base stations using data analytics and machine learning technologies.