arXiv subjects

Changkun Guan

Publications and source records attributed to Changkun Guan.

10 recordsLinked to original sources

arXiv2026

DecompGym: Benchmarking LLM Agents on Designing Decomposition Algorithms

Benders decomposition and column generation solve large optimization problems by passing cuts, columns, and dual values between a master problem and subproblems, and are hard to implement correctly. Large language models now automate parts of algorithm design, which points toward agents that build decomposition solvers for new problems. As a first step toward such agents, we study how well current coding agents design and implement these two algorithms, and how they fail. We introduce DecompGym, 81 instances from nine problem families (five Benders, four column generation), in which an agent writes a solver for a prescribed method. Each solver must meet three criteria: execution within a 60-second time limit; numerical feasibility together with a method audit, in which an LLM judge reads the solver's code; and an objective within 1% of the stored optimal objective. We evaluate 12 GPT, Claude, and Gemini models running in coding-agent tools. Over up to ten attempts, we compare independent regeneration with reflection, which first diagnoses the failure. On the first attempt, two models solve every instance and seven solve more than 90%. Most Benders failures (48 of 62) are missing or suboptimal solutions. The most common column-generation failure is a method-audit rejection. Output checks alone would accept 93 of the 108 attempts that fail the method audit. The most common rejection, an optimalif, occurs 96 times, 92 of them in one model.Reflection turns 66% of retries into successes, compared with 39% for regeneration, and it repairs method-audit failures, for which the judge names the defecective gaps. Agents for decomposition therefore need checks on how a solver reaches its answer and feedback that locates the error. The benchmark is available at https://github.com/SIKAI-C/DecompGym.

cs.AI↗

arXiv2026

Match the Canvas, Not Just the Answer: Predictability-Aware SFT for Diffusion Language Models

Diffusion language models (DLMs) enable flexible parallel generation by resolving tokens according to the model's evolving predictability rather than a fixed left-to-right order. This flexibility, however, introduces training choices absent from standard autoregressive teacher forcing: which reference tokens are visible when a target is supervised and how much generation space is allocated. Standard supervised fine-tuning (SFT) typically makes these choices through random masking, independently of inference. Our analysis shows how this training-inference mismatch can misdirect supervision. Random masking can conceal prediction errors or penalize uncertainty that decoding would otherwise resolve, while the attention-visible input length can change which response formulations the model favors, even when the underlying solution is unchanged. Motivated by these findings, we propose Predictability-Aware Canvas Selection and Supervision (PACS), an SFT method. PACS uses the model's own predictability to select each example's attention-visible input length and supervises reference tokens immediately before their confidence-guided revelation. Across reasoning and code-generation benchmarks, PACS consistently achieves the highest mean accuracy among the compared SFT methods, with gains of up to 12.84 percentage points over vanilla SFT on individual benchmarks. Code will be released upon publication.

cs.LG↗

arXiv2026

The Role of Coordinates in Pareto Regret for Adversarial Multi-Objective Bandits

Adversarial multi-objective bandits hold the potential to help us optimize choices (arms) whose reward is a multidimensional vector chosen by an adversary and whose performance is measured by Pareto regret. We define loss as one minus reward and measure the easiness of a coordinate by the smallest cumulative loss of the arms on it, and call the coordinate easier when this quantity is smaller. Existing work suggests that in theory an easier coordinate may reduce Pareto regret. However, in practice, one may not know which coordinate is easier. On the negative side, we show that this lack of information eliminates the possibility: a smaller cumulative loss does not improve the worst-case order of Pareto regret. Precisely, let $L_d$ be the smallest cumulative loss along coordinate $d$ over $T$ rounds. For $K\ge4$ arms, $T\ge6$ rounds, and at least 2 coordinates, we prove that the minimax expected Pareto regret is $Ω(\min\{T-L_0,\sqrt{K(T-L_0)}\})$. It is monotonically decreasing in $L_0$, even when $L_0=\min_d L_d$ itself is known. On the positive side, this result motivates the possibility that other coordinates, not just the easy one, may suffice to attain the optimal rate of Pareto regret. When $L_0$ is known, we apply Poly-INF to a fixed coordinate and obtain an upper bound on Pareto regret that exhibits the same order and thus matches the lower bound. Without such knowledge, we develop a reward-doubling version of Poly-INF that adapts to this unknown quantity while still attaining the matching minimax rate. Another implication is that it has no extra $\log T$ factor and is independent of the number of coordinates.

cs.LG↗

arXiv2026

Optimal Combinatorial Testing with Constraints: The Balancing Act

Imagine that you are in front of a cockpit with several on-off buttons. If you were to thoroughly test it, you would need to try a prohibitive number of configurations. But since most bugs in practice can be isolated to interactions among few components, having tests that cover every possible pairwise configuration is a good start. However, this is a problem that goes from easy to NP-hard as soon as some pairwise configurations are forbidden. In this paper, we revisit unconstrained combinatorial testing with pairwise coverage on binary parameters and contrast it with the constrained case, showing and conjecturing properties that either are upheld or change from one to the other. In particular, we discuss the extent to which it remains a good idea -- and sometimes indeed optimal -- to have every button almost as many times on as off to minimize testing. We propose the first exact algorithm based on integer programming and a faster heuristic that often produces optimal solutions, both outperforming or competitive with their baselines.

math.OC↗

arXiv2026

End-to-End Supply Chain Planning in the Paper Industry Via Column Generation and Benders Decomposition

Problem definition: The paper studies an integrated end-to-end planning problem in large-scale paper manufacturing, where production scheduling, trimming decisions, vehicle loading, and multi-period fulfillment of make-to-order and make-to-stock demand must be coordinated over time. In practice, these decisions are often optimized sequentially, leading to material waste, inefficient transportation, and degraded service levels. Solving the fully integrated problem at industrial scale remains computationally challenging due to its combinatorial structure. Methodology/results: A key structural feature of the problem is that downstream fulfillment decisions depend on upstream production and logistics choices only through aggregate supply availability over time. By exploiting this structure, the paper develops an exact mathematical formulation and proposes a two-phase hybrid framework (BDCG-DP) that integrates column generation (CG) using exact dynamic-programming (DP) for supply-side decisions with Benders decomposition (BD) for downstream fulfillment. Computational experiments on proprietary instances from a major North American paper manufacturer show that BDCG-DP lowers total costs by 24.4% compared to a traditional CG-DP on challenging eight-week planning problems. Median runtime for four-week planning problems decreases from over five hours using CG-DP to under one hour using BDCG-DP. Managerial implications: This paper provides the first exact model that integrates production, trimming, load planning, and multi-period fulfillment at an industrial scale. The proposed approach returns integer-feasible plans within 2.3 to 6 hours for the most complex planning problems, enabling planners to access high-quality implementable schedules within hours, a capability that was previously unavailable in practice.

math.OC↗

arXiv2026

Learning Optimization Proxies for Sequential Contextual Stochastic Programs: An Order Fulfillment Application

Sequential contextual stochastic programs model real-time decision systems in which each time epoch commits to an action under uncertainty whose consequences propagate into future decisions. In many practical contexts, these programs require obtaining solutions rapidly as new information becomes available. These problems can be represented through scenario approximations to be solved by off-the-shelf optimization solvers, which achieve high decision quality offline but typically run in seconds to minutes per instance, falling short of the sub-second responses that peak periods of planning require. This paper develops a learning-based optimization proxy: a scenario-embedded neural network trained offline on solver-generated labels, paired online with a decoder that enforces feasibility, replacing the per-epoch solve with a single forward pass. The framework is specialized to omnichannel order fulfillment, where each arriving order requires a sub-second assignment of products to distribution centers and carrier services under stochastic delivery times and future demand. A two-stage contextual stochastic program is introduced to formulate this problem, and its contextual sample average approximation (C-SAA) supplies the offline labels, while a composite training loss combines label imitation, a constraint-violation penalty, and self-supervised cost alignment. In a calibrated simulator built from JD.com transactional records, a detailed computational study is provided. The proxy reduces decision latency by roughly 2800x relative to the online finite-sample C-SAA reference and improves over it by 3.3% in realized fulfillment cost. Relative to established fulfillment policies, the proxy lowers total realized cost by at least 10.7% and roughly halves the late-delivery rate.

math.OC↗

arXiv2026

SkillsBench: Benchmarking How Well Agent Skills Work Across Diverse Tasks

Agent Skills are structured packages of procedural knowledge that augment large language model (LLM) agents at inference time. Despite rapid adoption, there is no standard way to measure whether they actually help. We present SkillsBench, a benchmark whose current inventory contains 87 tasks across 8 domains paired with curated Skills and deterministic verifiers. Our latest aggregate evaluation runs the 87-task benchmark under matched no-Skills and curated-Skills conditions for 18 model-harness configurations. Curated Skills raise the average pass rate from 33.9% to 50.5% (+16.6 percentage points; 25.5% normalized gain), with configuration-level gains ranging from +4.1 to +25.7 pp. Focused Skills with at most three modules outperform larger or exhaustive bundles, and smaller models with Skills can match larger models without them. SkillsBench establishes paired evaluation as the foundation for rigorous measurement of Skill efficacy on agentic, expertise-heavy work.

cs.AI↗

arXiv2026

The Proxy Benders Decomposition

Benders decomposition is a fundamental framework for solving large-scale mixed-integer optimization problems with complicating variables that, when fixed, yield significantly easier subproblems. However, classical Benders decomposition repeatedly solves highly similar subproblems and often exhibits zigzagging behavior across iterations, leading to slow convergence in large-scale settings. Motivated by the repetitive structure and parametric nature of Benders subproblems, this paper introduces the proxy Benders decomposition (Proxy-BD), a new decomposition framework in which subproblem optimization is replaced by certified optimization proxies rather than repeated exact solves. The proposed proxy follows a self-supervised predict-project-and-complete mechanism that produces dual-feasible solutions for generating provably valid Benders cuts. The framework preserves the theoretical validity of the decomposition independently of prediction quality through a projection-and-completion certification layer. A formal characterization of proxy-induced cuts is established, and the framework naturally extends to modern decomposition schemes, including branch-and-Benders-cut algorithms. Computational experiments on large-scale facility location and network design problems demonstrate that Proxy-BD substantially reduces the computational effort of subproblems while maintaining near-optimal solution quality. On large-scale uncapacitated facility location instances up to 2000x2000, Proxy-BD achieves median optimality gaps below 0.5%, yields up to 161x median speedups, and reduces the number of generated cuts by more than 240x on the largest instances. The computational gains consistently increase with recourse complexity, indicating that proxy-based inference scales substantially more favorably than repeated exact subproblem optimization in large-scale decomposition settings.

math.OC↗

arXiv2026

Are Stochastic Multi-objective Bandits Harder than Single-objective Bandits?

Multi-objective bandits have attracted increasing attention for their broad applicability, with $d$-dimensional reward vectors inducing Pareto regret. There has been a subtle debate over whether this added structure makes the problem fundamentally harder than single-objective bandits. We answer this by showing that, in terms of Pareto regret, it is surprisingly no harder: Pareto regret scales inversely with $g^\dagger$, the largest objective-wise suboptimality gap, and thus matches the smallest objective-wise classical regret. We formalize this idea via a novel method with upper and lower confidence-bound estimators for every arm-objective pair. It uses top-two races to compare arms within each objective and an uncertainty-greedy rule to allocate exploration toward the largest objective-wise gap $g^\dagger$, until the corresponding Pareto-optimal arm is committed to. We prove that it achieves Pareto regret of $O(\nicefrac{\log T}{g^\dagger})$, where $T$ is the horizon, with \emph{no dependence on $d$}. A matching lower bound of $Ω(\nicefrac{\log T}{g^\dagger})$ implies optimality. We evaluate the method on synthetic and real-world datasets, confirming the theory and achieving order-of-magnitude reductions in Pareto regret over baselines. Real-world results further show that our method commits to a Pareto optimal arm, possibly at the cost of empirical fairness, suggesting a potential hardness absent in single-objective bandits.

cs.LG↗

arXiv2023

Crouzeix's conjecture, compressions of shifts, and classes of nilpotent matrices

This paper studies the level set Crouzeix conjecture, which is a weak version of Crouzeix's conjecture that applies to finite compressions of the shift. Amongst other results, this paper establishes the level set Crouzeix conjecture for several classes of $3\times3$, $4\times4$, and $5\times5$ matrices associated to compressions of the shift via a geometric analysis of their numerical ranges. This paper also establishes Crouzeix's conjecture for several classes of nilpotent matrices whose studies are motivated by related compressions of shifts.

math.FA↗