We establish sample complexity results for stochastic optimization over the integers, especially with a view to understand the complexity with respect to the corresponding continuous optimization problem. We show that integer optimization can sometimes require strictly more samples and sometimes strictly smaller number of samples, depending on the structure of the objective and constraints. 1. For Lipschitz objectives over subsets of the ℓ_∞ ball, the statistical complexity of general stochastic mixed-integer, nonlinear, nonconvex optimization is exactly the same as stochastic linear optimization with just bound constraints. 2. For Lipschitz objectives over subsets of the ℓ_2 ball, we show that integer optimization can require strictly *smaller* sample size compared to the continuous setting in a certain regime. To get to this result, we also establish tight sample complexity results for nonconvex continuous stochastic optimization which, to the best of our knowledge, do not appear in prior work. 3. For strongly convex, smooth objectives, integer optimization has high statistical complexity compared to the continuous setting. In particular, we show that integer optimization requires Ω(1/ε^2) samples to report an ε-approximate solution, compared to the well-known O(1/ε) sample complexity from the continuous optimization literature.

This project will explore designs for a simple ExecutionPlanner prototype that is capable of executing caesar source extractor tasks and using this to enable the caesar-rest system to make use of remote compute platforms managed by other projects.

Two-stage stochastic integer programs provide a powerful framework for modeling decision-making under uncertainty, but they are notoriously difficult to solve at scale due to their high dimensionality and intrinsic nonconvexity. Decomposition-based algorithms such as Benders methods and Branch-and-Price (related dual decomposition methods) have become standard computational approaches for such problems and demonstrate excellent empirical performance in practice. Despite their widespread use, however, existing theoretical guarantees are almost exclusively based on worst-case analyses, which predict exponential convergence behavior in the problem dimension and fail to explain the strong performance observed in practice. In this paper, we present the first average-case analysis of Branch-and-Price for a broad class of two-stage stochastic binary integer programs. We study a stochastic-input model in which objective coefficients and constraint matrices are drawn at random and right-hand-side vectors scale with the decision dimension, while the number of constraints per scenario is fixed. Under this model, we prove that, with high probability, Branch-and-Price explores at most n^O(log s)nodes, yielding a quasi-polynomial bound on the size of the search tree in typical instances, where n denotes the decision dimension and s the number of scenarios. A key ingredient of our analysis is an average-case bound on the integrality gap of the natural linear programming (LP) relaxation. We show that this gap shrinks at rate O((logs log^2 n)/n)with high probability. This result is of independent interest, as it implies that the integrality gap grows only logarithmically with the number of scenarios on average.

The Astronomy Open Science Competence Centre Pilot (Astro-CC) is an ESCAPE-cluster related project meant to enable the astronomy research communities to accelerate their use of Open Science by supporting the implementation of FAIR principles. The Astro-CC project aims at expanding the use of Virtual Observatory standards by astronomy-focused ESFRIs, RIs, and data-producing projects of all scales, enabling the astronomy research communities to accelerate their use of Open Science by supporting the implementation of FAIR principles. It will run community events engaging experts in astronomical data service interoperability to prepare and define the scope of a Community Competence Center. The project will support the community development of the Virtual Observatory interoperability framework and its integration into EOSC, building on the progress made in the ESCAPE Science Cluster project. It aims at contributing to the vision of EOSC as a federation, providing feedback on the practical implementation of Open Science to the EOSC governance.

Competitive analysis is central to the study of online algorithms, but upper bounds are often highly problem-specific. We develop a more unifying methodology via the minimax viewpoint. Guided by Yao's principle, we reduce worst-case competitive analysis to Bayesian online design under an arbitrary correlated prior over arrival sequences. For such a prior, let X^* be the hindsight-optimal fractional solution for the realized instance, and let X^(t)=𝔼[X^*|ℱ_t] be its posterior process. Our guiding rule is posterior matching: at each time t, choose the feasible online action that tracks the current posterior X^(t) as closely as the online constraints permit. We show that this single principle yields optimal or near-optimal guarantees for several classical online fractional problems, including set cover, load balancing, matching and more general resource-allocation problems, recovering or improving state-of-the-art bounds in these settings with norm/concave objectives. Via known rounding reductions, it also yields randomized integral guarantees for weighted paging, MTS on star metrics, and ski-rental. At a technical level, our analysis reduces competitive guarantees to key probabilistic inequalities for the vector martingales generated by the posterior of the offline optimum. The resulting framework gives a reusable route from Bayesian online design under arbitrary correlated priors to information-theoretic worst-case competitive guarantees.

In the random-order online set cover problem, the instance with m sets and n elements is chosen in a worst-case fashion, but then the elements arrive in a uniformly random order. Can this random-order model allow us to circumvent the bound of O(log m log n)-competitiveness for the adversarial arrival order model? This long-standing question was recently resolved by Gupta et al. (2021), who gave an algorithm that achieved an O(log mn)-competitive ratio. While their LearnOrCover was inspired by ideas in online learning (and specifically the multiplicative weights update method), the analysis proceeded by showing progress from first principles. In this work, we show a concrete connection between random-order set cover and stochastic mirror-descent/online convex optimization. In particular, we show how additive/multiplicative regret bounds for the latter translate into competitiveness for the former. Indeed, we give a clean recipe for this translation, allowing us to extend our results to covering integer programs, set multicover, and non-metric facility location in the random order model, matching (and giving simpler proofs of) the previous applications of the LearnOrCover framework.

Mathematical programming – the task of expressing operations and decision-making problems in precise mathematical language – is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise. Recent advances in large language models for complex reasoning have spurred interest in automating this task, translating natural language into executable optimization models. Current approaches, however, achieve limited accuracy, hindered by scarce and noisy training data without leveraging domain knowledge. In this work, we systematically integrate optimization expertise to improve formulation accuracy for mixed-integer linear programming, a key family of mathematical programs. Our OptiMind framework leverages semi-automated, class-based error analysis to guide both training and inference, explicitly preventing common mistakes within each optimization class. Our resulting fine-tuned LLM significantly improves formulation accuracy by 20.7

The EU ESCAPE project (European Science Cluster of Astronomy & Particle Physics ESFRI) is developing ESAP, the ESFRI Scientific Analysis Platform, as an API gateway that enables the seamless integration of independent services accessing distributed data and computing resources. In ESCAPE we are exploring the possibility of exploiting EGI's OpenStack cloud computing services through ESAP. ESFRI (European Strategy Forum on Research Infrastructures) are unique facilities, resources, or services identified by European research communities to conduct and to support top-level research activities in their domains. The ESFRI projects are in their preparation phase and have been selected for the excellence of their scientific cases and for their maturity, according to a sound expectation that the projects will enter the implementation phase in a fixed period of time. EGI is a federation of computing and storage resource providers delivering open solutions for advanced computing and data analytics to support research and development. In this contribution we briefly describe ESCAPE and ESAP, the use cases, the work done to automate a virtual machine creation in EGI's OpenStack cloud computing, drawbacks and possible solutions.

We establish new lower-bounds for the information complexity of mixed-integer convex optimization under two "bit-wise" oracles. The first oracle provides bits of first-order information in the standard coordinate model, and the second oracle answers whether the inner product of a specified vector with the gradient of the function at a point or the normal vector of a separating hyperplane for the feasible region is positive or non-positive, thus also providing one bit of first-order information. The new contribution is that under such oracles, the complexity is quadratic in the number of continuous decision variables, which was not known before even for continuous convex optimization. These new lower-bounds are tight (up to a logarithmic term), matched by a natural discretization of standard cutting-plane methods for convex optimization. These reveal that using a standard bit-representation of the first-order information is, in general, the best one can do with respect to the number of bits of information needed to solve constrained convex optimization problems.

Online Set Cover and Load Balancing are central problems in online optimization, and there is a long line of work focusing on developing algorithms for these problems with convex objectives. Although we know optimal online algorithms with l(p)-norm objectives, recent developments for general norms and convex objectives that rely on the online primal-dual framework apply only to fractional settings due to large integrality gaps. Our work focuses on directly designing integral online algorithms for Set Cover and Load Balancing with convex objectives, bypassing the convex-relaxation and the primal-dual technique. Some of the main implications of our approach are: 1) For Online Set Cover, we can extend the results of [1] for convex objectives and of [2] for symmetric norms from fractional to integral settings. 2) Our results for convex objectives and symmetric norms even apply to the Online Generalized Scheduling Problem, which generalizes both Set Cover and Load Balancing. Previous works could only handle the offline version of this problem with norm objectives [3]. 3) Our approach easily extends to settings involving disjoint-composition of norms. This allows us to recover or improve the norm-composition results of [4], [2] and extend our results to a large class of norms beyond the symmetric setting. Our approach involves first reducing these online problems to online packing problems, and to then design good approximation algorithms for the latter. To solve these packing problem, we use two key ideas. First, we decouple the global packing problem into a series of local packing problems on different machines. Second, we choose random activation thresholds for machines such that conditional on a machine being activated the expected number of jobs it covers is high compared to its cost. This approach may be of independent interest and could find applications to other online problems.

This paper optimizes the configuration of large-scale data centers toward cost-effective, reliable and sustainable cloud supply chains. The problem involves placing incoming racks of servers within a data center to maximize demand coverage given space, power and cooling restrictions. We formulate an online integer optimization model to support rack placement decisions. We propose a tractable online sampling optimization (OSO) approach to multi-stage stochastic optimization, which approximates unknown parameters with a sample path and re-optimizes decisions dynamically. We prove that OSO achieves a strong competitive ratio in canonical online resource allocation problems and sublinear regret in the online batched bin packing problem. Theoretical and computational results show it can outperform mean-based certainty-equivalent resolving heuristics. Our algorithm has been packaged into a software solution deployed across Microsoft's data centers, contributing an interactive decision-making process at the human-machine interface. Using deployment data, econometric tests suggest that adoption of the solution has a negative and statistically significant impact on power stranding, estimated at 1-3 percentage point. At the scale of cloud computing, these improvements in data center performance result in significant cost savings and environmental benefits.

CAESAR (Comprehensive Space Weather Studies for the ASPIS Prototype Realisation) is a project funded by ASI (Italian Space Agency) and INAF (Italian National Institute for Astrophysics) for the development of the prototype of ASPIS (ASI SPace weather InfraStructure). We report here design considerations, challenges and final status of the creation of a database for the ASPIS prototype, which will allow for the study of the chain of phenomena from the Sun to Earth and planetary environments. The database is aimed at handling the heterogeneity of metadata and data while storing and managing the interconnections of various Space Weather events. On top of the database, interfaces for users, including a graphical web interface and an advanced Python module (ASPIS.py), have been developed to facilitate data discovery, access, and analysis. The high-level metadata, to inform the discovery phase in the database, have been collected using an internally developed tool, ProSpecT (Product Specification Template). This tool utilises JSON Schema and JSONForms to create a web interface to guide the data providers in describing their "Products" and generate a JSON object with the necessary metadata. The metadata structure starts from the IVOA VOResource standard, tailored to suit the CAESAR project's requirements. At present, approximately 100 product descriptions in JSON format have been collected and used to create wiki-like documentation pages besides helping in examining formats and metadata details for the implementation of the database prototype. The graphical web interface helps the users discover, filter, and access the database content, while ASPIS.py also provides more advanced analysis tooling. Moreover, ASPIS.py sits on top of commonly used Python packages like SunPy, scikit-learn, matplotlib to help integrate research analysis with other tools and research domains. The database has been built keeping in mind adherence to FAIR principles and with the idea to make it easily interoperable with other research data infrastructures in the Space Weather or sibling research domains.

The goal of this software is to computationally ascertain how common it is for the strong branching rule to exhibit non-monotonicity in practice. We do so by applying cover cuts on randomly generated multi-dimensional knapsacks as well as by considering cuts applied by SCIP on MIPLIB 2017 benchmark set. Our main insight from these experiments is that if the gap closed by cuts is small, change in tree size is difficult to predict, and often increases, possibly due to inherent non-monotonicity. However, when a sufficiently large gap is closed, a significant decrease in tree size may be expected.

Modern mixed-integer programming solvers use the branch-and-cut framework, where cutting planes are added to improve the tightness of the linear programming (LP) relaxation, with the expectation that the tighter formulation would produce smaller branch-and-bound trees. In this work, we consider the question of whether adding cuts will always lead to smaller trees for a given fixed branching rule. We formally call such a property of a branching rule monotonicity. We prove that any branching rule which exclusively branches on fractional variables in the LP solution is non-monotonic. Moreover, we present a family of instances where adding a single cut leads to an exponential increase in the size of full strong branching trees, despite improving the LP bound. Finally, we empirically attempt to estimate the prevalence of non-monotonicity in practice while using full strong branching. We consider randomly generated multi-dimensional knapsacks tightened by cover cuts as well as instances from the MIPLIB 2017 benchmark set for the computational experiments. Our main insight from these experiments is that if the gap closed by cuts is small, change in tree size is difficult to predict, and often increases, possibly due to inherent non-monotonicity. However, when a sufficiently large gap is closed, a significant decrease in tree size may be expected.

Exoplanet research is at the forefront of contemporary astronomy recommendations. As more and more exoplanets are discovered and vetted, databases and catalogs are built to collect information. Various resources are available to scientists for this purpose, though every one of them has different scopes and notations. In Alei et al. (2020) we described Exo-MerCat, a script that collects information from multiple sources and creates a homogenized table. In this manuscript, we announce the release of the Exo-MerCat v2.0.0 script as an upgraded, tested, documented and open-source software to produce catalogs. The main upgrades on the script concern: 1) the addition of the TESS Input Catalog and the K2 Input Catalog as input sources; 2) the optimization of the main identifier queries; 3) a more complex merging of the entries from the input sources into the final catalog; 4) some quality-of-life improvements such as informative flags, more user-friendly column headers, and log files; 5) the refactoring of the code in modules. We compare the performance of Exo-MerCat v2.0.0 with the previous version and notice a substantial improvement in the completeness of the sample, thanks to the addition of new input sources, and its accuracy, because of the optimization of the script.

Large Language Model (LLM) inference, where a trained model generates text one word at a time in response to user prompts, is a computationally intensive process requiring efficient scheduling to optimize latency and resource utilization. A key challenge in LLM inference is the management of the Key-Value (KV) cache, which reduces redundant computations but introduces memory constraints. In this work, we model LLM inference with KV cache constraints theoretically and propose a novel batching and scheduling algorithm that minimizes inference latency while effectively managing the KV cache's memory. More specifically, we make the following contributions. First, to evaluate the performance of online algorithms for scheduling in LLM inference, we introduce a hindsight optimal benchmark, formulated as an integer program that computes the minimum total inference latency under full future information. Second, we prove that no deterministic online algorithm can achieve a constant competitive ratio when the arrival process is arbitrary. Third, motivated by the computational intractability of solving the integer program at scale, we propose a polynomial-time online scheduling algorithm and show that under certain conditions it can achieve a constant competitive ratio. We also demonstrate our algorithm's strong empirical performance by comparing it to the hindsight optimal in a synthetic dataset. Finally, we conduct empirical evaluations on a real-world public LLM inference dataset, simulating the Llama2-70B model on A100 GPUs, and show that our algorithm significantly outperforms the benchmark algorithms. Overall, our results offer a path toward more sustainable and cost-effective LLM deployment.

Many classical problems in theoretical computer science involve norms, even if implicitly; for example, both XOS functions and downward-closed sets are equivalent to some norms. The last decade has seen a lot of interest in designing algorithms beyond the standard ℓp norms ||· ||p. Despite notable advancements, many existing methods remain tailored to specific problems, leaving a broader applicability to general norms less understood. This paper investigates the intrinsic properties of ℓp norms that facilitate their widespread use and seeks to abstract these qualities to a more general setting. We identify supermodularity—often reserved for combinatorial set functions and characterized by monotone gradients—as a defining feature beneficial for ||·||pp. We introduce the notion of p-supermodularity for norms, asserting that a norm is p-supermodular if its pth power function exhibits supermodularity. The association of supermodularity with norms offers a new lens through which to view and construct algorithms. Our work demonstrates that for a large class of problems p-supermodularity is a sufficient criterion for developing good algorithms. This is either by reframing existing algorithms for problems like Online Load-Balancing and Bandits with Knapsacks through a supermodular lens, or by introducing novel analyses for problems such as Online Covering, Online Packing, and Stochastic Probing. Moreover, we prove that every symmetric norm can be approximated by a p-supermodular norm. Together, these recover and extend several existing results, and support p-supermodularity as a unified theoretical framework for optimization challenges centered around norm-related problems.

The atmospheric characterisation of hot and warm Neptune-size exoplanets is challenging due to their small radius and atmospheric scale height. The warm-Neptune HAT-P-11b is a remarkable target for such characterisation due to the large brightness of its host star (V=9.46 mag; H=7.13 mag). The aims of this work are to review the main physical and architectural properties of the HAT-P-11 planetary system, and to probe the presence of 8 molecular species in the atmosphere of HAT-P-11b at high spectral resolution in the near-infrared. The planetary system was reviewed by analysing transits and occultations of HAT-P-11b from the Kepler data set as well as HIRES at Keck archival radial-velocity (RV) data. We modelled the latter with Gaussian-process regression and a combined quasi-periodic and squared-exponential kernel to account for stellar variations on both (short-term) rotation and (long-term) activity-cycle timescales. In order to probe the atmospheric composition of HAT-P-11b, we observed 4 transits of this target with GIANO-B at TNG. We find that the long-period ($P\sim9.3$ years) RV signal previously attributed to planet HAT-P-11c is more likely due to the stellar magnetic activity cycle. Nonetheless, the Hipparcos-Gaia difference in the proper-motion anomaly suggests that an outer-bound companion might still exist. For HAT-P-11b, we measure a radius $R_{\rm p}=0.4466\pm0.0059\,R_{\rm J}$, a mass $M_{\rm p}=0.0787\pm0.0048\,M_{\rm J}$, and an eccentricity $e=0.2577^{+0.0033}_{-0.0025}$, in accordance with values in the literature. Probing its atmosphere, we detect $NH_3$ (S/N$=5.3$, significance$=5.0\sigma$) and confirm the presence of $H_2O$ (S/N$=5.1$, significance$=3.4\sigma$). We also tentatively detect the signal of $CO_2$ (S/N$=3.0$, significance$=3.2\sigma$) and $CH_4$ (S/N$=4.8$, significance$=2.6\sigma$), whose presence need to be confirmed by further observations.

Context. Due to observational biases, a large fraction of known exoplanets are short-period objects. However, the search for planets began more than 20 yr ago, and so it is already possible - with the use of a suitable dataset - to begin exploring a wider range of the parameter space, such as that encompassing long-period planets. Aims. The aim of this paper is to investigate the presence of long-period giant companions in two systems where one or more planets are already known and for which a long-term trend in the radial velocities (RVs) was noted in previous works. Methods. Over the last 11 yr, we have collected 122 spectra of HD 75898 and 72 spectra of HD 11506 with the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) in the framework of the Global Architecture of Planetary Systems (GAPS) project, from which we derived precise RV and activity indicator measurements. Additional RV data from the High-Resolution Echelle Spectrometer (HIRES) are also used here to increase the total time span. For our RV analysis, we used PyORBIT, an advanced Python tool for the simultaneous Bayesian analysis of RVs and stellar activity indicators. In addition, we used astrometric (Gaia DR3) and imaging archive data to complete our analysis. In particular, we combined RVs and astrometry to better constrain the mass and period of the new long-period companions. Results. We find evidence for one additional long-period companion (gas giant planet or brown dwarf) in both systems considered. The new candidate for HD 75898 has a period of roughly 18 yr and a true mass of around 8.5 M-j. For HD 11506, we confirm the new object (planet d) recently announced using HIRES data but we find that the period and true mass are both almost double the values based on HIRES results (P-d similar to 72 yr, M-d similar to 13 Mj). In addition, for HD 75898, we also find evidence of an activity cycle affecting RVs with a period of one order of magnitude lower than found in the literature.