arXiv subjects

Maxime Bouscary

Publications and source records attributed to Maxime Bouscary.

4 recordsLinked to original sources

arXiv2026

Budget-Efficient Automatic Algorithm Design via Code Graph

Large language models (LLMs) have emerged as powerful tools for automatic algorithm design (AAD). However, existing pipelines remain inefficient. They operate at the granularity of full algorithms, redundantly rewriting recurring substructures and discarding low-fitness candidates that may contain valuable algorithmic features. We formalize budget-efficient automatic algorithm design, wherein the search policy maximizes realized fitness subject to limited computational cost. We propose a directed acyclic graph representation of algorithms and build a search framework that fully exploits the LLM's output. Instead of querying the LLM for full algorithms, we use it to obtain corrections: compact operators that add, replace, or remove code blocks. Each correction augments the graph, yielding new algorithms that compose with prior corrections. This graph structure decomposes algorithms into sets of corrections, enabling correction-level credit assignment that informs subsequent queries. We complement this framework with theoretical insights into the ideal balance between search depth and breadth at different budget levels. We validate our method empirically on three combinatorial optimization problems, demonstrating consistent superiority of our graph-based search over full-algorithm search at equal token budget. Finally, our experiments suggest that rich contexts help only when the LLM's prior knowledge is shallow, and can hinder performance otherwise.

cs.AI↗

arXiv2025

OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling

LLM-based solvers have emerged as a promising means of automating problem modeling and solving. However, they remain unreliable and often depend on iterative repair loops that result in significant latency. We introduce OptiHive, a framework that enhances any solver-generation pipeline to produce higher-quality solvers from natural-language descriptions of optimization problems. OptiHive uses a single batched generation to produce diverse components (solvers, problem instances, and validation tests) and filters out erroneous components to ensure fully interpretable outputs. Accounting for the imperfection of the generated components, we employ a statistical model to infer their true performance, enabling principled uncertainty quantification and solver selection. On tasks ranging from traditional optimization problems to challenging variants of the Multi-Depot Vehicle Routing Problem, OptiHive significantly outperforms baselines, increasing the optimality rate from 5% to 92% on the most complex problems.

cs.AI↗

arXiv2025

Reducing Contextual Stochastic Bilevel Optimization via Structured Function Approximation

Contextual Stochastic Bilevel Optimization (CSBO) extends standard stochastic bilevel optimization (SBO) by incorporating context-dependent lower-level problems. CSBO problems are generally intractable since existing methods require solving a distinct lower-level problem for each sampled context, resulting in prohibitive sample and computational complexity, in addition to relying on impractical conditional sampling oracles. We propose a reduction framework that approximates the lower-level solutions using expressive basis functions, thereby decoupling the lower-level dependence on context and transforming CSBO into a standard SBO problem solvable using only joint samples from the context and noise distribution. First, we show that this reduction preserves hypergradient accuracy and yields an $\epsilon$-stationary solution to CSBO. Then, we relate the sample complexity of the reduced problem to simple metrics of the basis. This establishes sufficient criteria for a basis to yield $\epsilon$-stationary solutions with a near-optimal complexity of $\widetilde{O}(\epsilon^{-3})$, matching the best-known rate for standard SBO up to logarithmic factors. Moreover, we show that Chebyshev polynomials provide a concrete and efficient choice of basis that satisfies these criteria for a broad class of problems. Empirical results on inverse and hyperparameter optimization demonstrate that our approach outperforms CSBO baselines in convergence, sample efficiency, and memory usage.

math.OC↗

arXiv2024

Integrated Bundling and Pricing of Unique Items

Retailers have significant potential to improve recommendations through strategic bundling and pricing. By taking into account different types of customers and their purchasing decisions, retailers can better accommodate customer preferences and increase revenues while reducing unsold items. We consider a retailer seeking to maximize its expected revenue by selling unique and non-replenishable items over a finite horizon. The retailer may offer each item individually or as part of a bundle. Our approach provides tractable bounds on expected revenue that are tailored to unique items and suitable for a rich class of choice models. We leverage these bounds to propose a bundling algorithm that efficiently selects bundles in a column-generation fashion. Under the multinomial logit model, our bounds are asymptotically optimal as the expected number of arrivals $\lambda$ grows, yielding a performance bound in $O(1/\lambda)$. In contrast, we show that both the static and fluid approximations are not asymptotically optimal. Moreover, we propose a greedy algorithm that allows for tractable dynamic bundling. We show through numerical experiments that third-party logistics providers (3PL) in particular can benefit from improved load recommendations and pricing decisions. By not only minimizing shipping costs, but also reducing empty miles and suggesting options that better match carrier preferences, our methodology benefits digital brokerage platforms while contributing to the transportation industry's sustainability efforts. In a Texas Triangle simulation powered by Uber Freight data, dynamic bundling and pricing reduces costs by 6%, empty miles by 25%, and more than halves the number of unmatched loads over dynamic pricing alone.

math.OC↗