ICML 2026 Papers

We present **NEMO**, a system that translates **N**atural-language descriptions of decision problems into formal **E**xecutable **M**athematical **O**ptimization implementations using autonomous coding agents (ACAs). Existing approaches rely on specialized large language models (LLMs) or bespoke task-specific agents that are often brittle and frequently generate syntactically invalid or non-executable code. NEMO instead treats ACAs as a first-class abstraction analogous to API-based interaction with LLMs; their sandboxed execution guarantees code is executable by construction and supports automated validation and repair. We introduce novel coordination patterns including asymmetric validation loops between independently generated optimizer and simulator implementations, external memory for experience reuse, and robustness enhancements via minimum Bayes risk (MBR) decoding and self-consistency. Across nine established optimization benchmarks, NEMO achieves state-of-the-art performance on the majority of tasks with substantial margins on several datasets, demonstrating the power of execution-aware agentic architectures for automated optimization modeling.

We study simultaneous confidence bounds for aggregated effects over downward-closed subset families of independent statistical tests. The bounds are obtained by bootstrap calibration of the maximum normalized aggregated effect over the relevant subset family, yielding valid post-hoc inference for data-selected subsets and tighter bounds than classical methods that protect all linear contrasts. A central challenge is that the required maximization is a nonlinear combinatorial optimization problem. We cast it as a weighted densest-subgraph problem and derive exact linear and mixed integer linear program reformulations, and we further develop a fully polynomial-time approximation scheme that exploits the rank-1 structure of the objective to scale to large families. On the statistical side, we establish a finite-sample coverage guarantee with a lighter dependence on the subset family size than high-dimensional central limit theorems provide. We illustrate the method on synthetic and real machine learning applications.

For communication-efficient decentralized learning, advanced network (NW) topologies, such as exponential and 1-peer exponential graphs, have been studied under homogeneous communication delays. However, real-world NWs exhibit heterogeneous communication delays, making node assignment optimization crucial for minimizing the Bottleneck Communication Delay (BCD). We propose BTSP-MSR, an approximate method for minimizing BCD on circulant digraphs, including exponential and 1-peer exponential graphs. Leveraging the fact that circulant digraphs can be viewed as a union of (directed) ring graphs, we derive an upper bound on the BCD by combining the ring-graph BCD (BTSP) with a deviation term (MSR). We then construct a solver that sequentially minimizes these two terms. Numerical experiments show that BTSP-MSR consistently reduces BCD across several circulant digraphs with large numbers of nodes. Notably, incorporating the exponential or 1-peer exponential graph enables communication-efficient decentralized learning under heterogeneous delay settings.

This paper studies optimization for a family of problems termed **compositional entropic risk minimization**, in which each data's loss is formulated as a Log-Expectation-Exponential (Log-E-Exp) function. The Log-E-Exp formulation serves as an abstraction of the Log-Sum-Exponential (LogSumExp) function when the explicit summation inside the logarithm is taken over a gigantic number of items and is therefore expensive to evaluate. While entropic risk objectives of this form arise in many machine learning problems, existing optimization algorithms suffer from several fundamental limitations including non-convergence, numerical instability, and slow convergence rates. To address these limitations, we propose a geometry-aware stochastic algorithm, termed **SCENT**, for the dual formulation of entropic risk minimization cast as a min--min optimization problem. The key to our design is a **stochastic proximal mirror descent (SPMD)** update for the dual variable, equipped with a Bregman divergence induced by a negative exponential function that faithfully captures the geometry of the objective. Our main contributions are threefold: (i) we establish an $O(1/\sqrt{T})$ convergence rate of the proposed SCENT algorithm for convex problems; (ii) we theoretically characterize the advantages of SPMD over standard SGD update for optimizing the dual variable; and (iii) we demonstrate the empirical effectiveness of SCENT on extreme classification, partial AUC maximization, contrastive learning and distributionally robust optimization, where it consistently outperforms existing baselines.

The proliferation of Large Language Models (LLMs) has shifted serving systems from processing isolated requests to orchestrating high-concurrency, multi-tenant agentic workflows. However, existing solutions typically prioritize intra-workflow optimization, largely neglecting the significant potential for inter-workflow optimization. In this paper, we propose HeraSys, an LLM serving system designed to optimize the end-to-end performance of concurrent workflows. Through fine-grained orchestration, HeraSys eliminates cross-workflow computational redundancy via structural node merging and reuse. Furthermore, HeraSys introduces a load-aware joint scheduling policy that dynamically manages execution order by evaluating both inter- and intra-query priorities. By integrating a resource skewing mechanism with adaptive batching and pipeline decomposition, HeraSys effectively mitigates tail latency while maintaining low average latency, thereby substantially improving system throughput. Extensive experiments demonstrate that HeraSys reduces P99 latency by up to 2.17$\times$ and increases serving throughput by up to 1.85$\times$ under strict latency guarantees.