arXiv subjects

Marco Molinaro

Publications and source records attributed to Marco Molinaro.

At least 19 recordsLinked to original sources

arXiv2026

Online Algorithms via Minimax and Posterior Matching

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 $X^{(t)}=\mathbb E[X^*\mid \mathcal F_t]$ 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.

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arXiv2026

Astronomy Open Science Competence Centre in Europe

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.

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arXiv2026

Sample Complexity of Stochastic Optimization with Integer Variables

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 $\ell_\infty$ 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 $\ell_2$ 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 $\Omega(1/\epsilon^2)$ samples to report an $\epsilon$-approximate solution, compared to the well-known $O(1/\epsilon)$ sample complexity from the continuous optimization literature.

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arXiv2026

Probabilistic analysis of dual decomposition on two-stage stochastic integer programs

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.

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arXiv2025

A Learning Perspective on Random-Order Covering Problems

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.

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arXiv2025

Tight Lower Bounds for Binary First-Order Oracles for Convex Optimization

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.

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arXiv2025

Encapsulating Textual Contents into a MOC data Structure for Advanced Applications

Context. The Multi-Order Coverage map (MOC) is a widely adopted standard promoted by the International Virtual Observatory Alliance (IVOA) to support data sharing and interoperability within the Virtual Observatory (VO) ecosystem. This hierarchical data structure efficiently encodes and visualizes irregularly shaped regions of the sky, enabling applications such as cross-matching large astronomical catalogs. Aims. This study aims to explore potential enhancements to the MOC data structure by encapsulating textual descriptions and semantic embeddings into sky regions. Specifically, we introduce "Textual MOCs", in which textual content is encapsulated, and "Semantic MOCs" that transform textual content into semantic embeddings. These enhancements are designed to enable advanced operations such as similarity searches and complex queries and to integrate with generative artificial intelligence (GenAI) tools. Method. We experimented with Textual MOCs by annotating detailed descriptions directly into the MOC sky regions, enriching the maps with contextual information suitable for interactive learning tools. For Semantic MOCs, we converted the textual content into semantic embeddings, numerical representations capturing textual meanings in multidimensional spaces, and stored them in high-dimensional vector databases optimized for efficient retrieval. Results. The implementation of Textual MOCs enhances user engagement by providing meaningful descriptions within sky regions. Semantic MOCs enable sophisticated query capabilities, such as similarity-based searches and context-aware data retrieval. Integration with multimodal generative AI systems allows for more accurate and contextually relevant interactions supporting both spatial, semantic and visual operations for advancing astronomical data analysis capabilities.

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arXiv2025

OptiMind: Teaching LLMs to Think Like Optimization Experts

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% across multiple optimization benchmarks, with consistent gains under test-time scaling methods such as self-consistency and multi-turn feedback, enabling further progress toward robust LLM-assisted optimization formulation.

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arXiv2025

Integral Online Algorithms for Set Cover and Load Balancing with Convex Objectives

Online Set Cover and Load Balancing are central problems in online optimization, and there is a long line of work on developing algorithms for these problems with convex objectives. Although we know optimal online algorithms with $\ell_p$-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 are: 1. For Online Set Cover, we can extend the results of Azar et. al. (2016) for convex objectives and of Kesselheim, Molinaro, and Singla (2024) 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 (Deng, Li, and Rabani 2023). 3. Our methods easily extend to settings with disjoint-composition of norms. This allows us to recover or improve the norm-composition results of Nagarajan and Shen (2020), and Kesselheim, Molinaro, and Singla (2024), and to extend our results to a large class of norms beyond symmetric. Our approach is to first reduce these problems to online packing problems, and then to design good approximation algorithms for the latter. To solve these packing problems, we use two key ideas. First, we decouple the global packing problem into a series of local packing problems on different machines. Next, 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.

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arXiv2025

Exo-MerCat v2.0.0: updates and open-source release of the Exoplanet Merged Catalog software

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.

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arXiv2025

Online Scheduling for LLM Inference with KV Cache Constraints

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.

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arXiv2025

Online Rack Placement in Large-Scale Data Centers: Online Sampling Optimization and Deployment

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.

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arXiv2024

The Power of Migrations in Dynamic Bin Packing

In the Dynamic Bin Packing problem, $n$ items arrive and depart the system in an online manner, and the goal is to maintain a good packing throughout. We consider the objective of minimizing the total active time, i.e., the sum of the number of open bins over all times. An important tool for maintaining an efficient packing in many applications is the use of migrations; e.g., transferring computing jobs across different machines. However, there are large gaps in our understanding of the approximability of dynamic bin packing with migrations. Prior work has covered the power of no migrations and $> n$ migrations, but we ask the question: What is the power of limited ($\leq n$) migrations? Our first result is a dichotomy between no migrations and linear migrations: Using a sublinear number of migrations is asymptotically equivalent to doing zero migrations, where the competitive ratio grows with $\mu$, the ratio of the largest to smallest item duration. On the other hand, we prove that for every $\alpha \in (0,1]$, there is an algorithm that does $\approx \alpha n$ migrations and achieves competitive ratio $\approx 1/\alpha$ (in particular, independent of $\mu$); we also show that this tradeoff is essentially best possible. This fills in the gap between zero migrations and $> n$ migrations in Dynamic Bin Packing. Finally, in light of the above impossibility results, we introduce a new model that more directly captures the impact of migrations. Instead of limiting the number of migrations, each migration adds a delay of $C$ time units to the item's duration; this commonly appears in settings where a blackout or set-up time is required before the item can restart its execution in the new bin. In this new model, we prove a $O(\min (\sqrt{C}, \mu))$-approximation, and an almost matching lower bound.

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arXiv2024

Supermodular Approximation of Norms and Applications

Many classical problems in theoretical computer science involve norm, 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 $\ell_p$ norms $\|\cdot \|_p$. 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 $\ell_p$ 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 $ \|\cdot\|_p^p$. We introduce the notion of $p$-supermodularity for norms, asserting that a norm is $p$-supermodular if its $p^{th}$ 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 results from the literature, and support $p$-supermodularity as a unified theoretical framework for optimization challenges centered around norm-related problems.

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arXiv2024

A Universal Transfer Theorem for Convex Optimization Algorithms Using Inexact First-order Oracles

Given any algorithm for convex optimization that uses exact first-order information (i.e., function values and subgradients), we show how to use such an algorithm to solve the problem with access to inexact first-order information. This is done in a ``black-box'' manner without knowledge of the internal workings of the algorithm. This complements previous work that considers the performance of specific algorithms like (accelerated) gradient descent with inexact information. In particular, our results apply to a wider range of algorithms beyond variants of gradient descent, e.g., projection-free methods, cutting-plane methods, or any other first-order methods formulated in the future. Further, they also apply to algorithms that handle structured nonconvexities like mixed-integer decision variables.

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arXiv2024

Non-Monotonicity of Branching Rules with respect to Linear Relaxations

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.

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arXiv2023

CAESAR: Space Weather archive prototype for ASPIS

The project CAESAR (Comprehensive spAce wEather Studies for the ASPIS prototype Realization) is aimed to tackle all the relevant aspects of Space Weather (SWE) and realize the prototype of the scientific data centre for Space Weather of the Italian Space Agency (ASI) called ASPIS (ASI SPace Weather InfraStructure). This contribution is meant to bring attention upon the first steps in the development of the CAESAR prototype for ASPIS and will focus on the activities of the Node 2000 of CAESAR, the set of Work Packages dedicated to the technical design and implementation of the CAESAR ASPIS archive prototype. The product specifications of the intended resources that will form the archive, functional and system requirements gathered as first steps to seed the design of the prototype infrastructure, and evaluation of existing frameworks, tools and standards, will be presented as well as the status of the project in its initial stage.

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arXiv2023

Information Complexity of Mixed-integer Convex Optimization

We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This leaves only a lower order linear term (in the dimension) as the gap between the lower and upper bounds. This is derived as a corollary of a more fundamental ``transfer" result that shows how lower bounds on information complexity of continuous convex optimization under different oracles can be transferred to the mixed-integer setting in a black-box manner. Further, we (to the best of our knowledge) initiate the study of, and obtain the first set of results on, information complexity under oracles that only reveal \emph{partial} first-order information, e.g., where one can only make a binary query over the function value or subgradient at a given point. We give algorithms for (mixed-integer) convex optimization that work under these less informative oracles. We also give lower bounds showing that, for some of these oracles, every algorithm requires more iterations to achieve a target error compared to when complete first-order information is available. That is, these oracles are provably less informative than full first-order oracles for the purpose of optimization.

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