arXiv subjects

Jiheng Zhang

Publications and source records attributed to Jiheng Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Efficient Parameter-Free First-Order Methods for Nonsmooth Composite Minimax Optimization

In this paper we propose first-order methods for a class of nonsmooth composite strongly convex--strongly concave and nonconvex--concave minimax optimization. We first develop an inexact proximal method and an accumulative regularizated method for strongly convex--strongly concave problems. The latter achieves the optimal dependence on the curvature parameters and places the smaller curvature inside the accuracy logarithm. Using this method as a subsolver, we propose a proximal point method for nonconvex--concave problems. Under suitable assumptions, it finds an $ε$-stationary point with an operation complexity of $O(ε^{-5/2})$, which improves the best-known $O(ε^{-5/2}\log(1/ε))$ bounds by removing the logarithmic factor. We further develop parameter-free variants for both problem classes, and achieve the same complexity without knowledge of any problem constants. All proposed methods are equipped with verifiable termination criteria.

math.OC↗

arXiv2026

When to Screen, When to Bypass: LLM-Judges in Resource-Scarce AI-Human Workflow

AI systems can generate outputs at scale, but most outputs require human approval before release. This creates a bottleneck: humans cannot keep pace with AI-generated volume. A natural response is to insert an LLM-judge that screens outputs before they reach humans, filtering errors and amplifying effective review capacity. But judges are imperfect. False rejections send correct outputs back for unnecessary rework; false acceptances consume judge capacity without relieving humans. When should outputs be routed through the judge, and when should they bypass it directly to human review? We model this workflow as a queueing network with three resource pools and use a fluid approximation to characterize optimal judge allocation. The analysis reveals that optimal allocation depends critically on which resource is the current bottleneck: screening amplifies human capacity when reviewers are scarce, yet generates a rework trap that crowds out new production when workers are stretched thin. For heterogeneous task classes with different error profiles, optimal priority can reverse across operating regimes, and classes with complementary error structures can be mixed to achieve throughput that neither class attains alone. We propose a policy that uses the fluid-optimal allocation fractions for routing and the fluid-optimal service levels for admission control, and establish its asymptotic optimality as system scale grows. Extensions incorporate human feedback that improves rework quality and joint capacity planning under budget constraints. Numerical experiments confirm rapid convergence to the fluid optimum and demonstrate that the policy significantly outperforms benchmarks that either always screen or never screen.

math.OC↗

arXiv2026

Quality-Constrained Routing over a Fixed Pool of Quantized Mixture-of-Experts Instances

Quantized Mixture-of-Experts (MoE) services can hold several pre-materialized instances of one base model, but quantization damage varies sharply across requests and bitwidths. Because instance materialization and replica counts consume memory and require slow reconfiguration, we treat them as upstream provisioning decisions and study routing within a fixed resident pool. Within this fixed-pool boundary, we route each request to maximize modeled throughput under a class-level expected quality-degradation budget and measured instance capacities. To predict this request-specific risk, we introduce FWP (Fragility-Weighted Perplexity), computed from prompt tokens on a reference-instance prefill and calibrated to candidate-instance degradation. Underlying FWP is an exact two-expert affinity--fragility decomposition and a conditional multi-layer top-$k$ expansion whose bias, interaction, route-change, separability, and higher-order terms remain explicit. Using these calibrated risks, a window-level linear program yields a signed reduced-reward score that is KKT-consistent with the LP optimum under optimal prices and primal-feasible tie allocation. On 88 extended Qwen prompts, complete W2, W3, and W4 instances quantizing all 6,144 expert blocks incur mean $Δ$NLL of $0.9437$, $0.1832$, and $0.0513$. Under the same population and $τ=0.1513$, FWP allocation reaches a $1.284\times$ offline model-based multiplier versus $1.253\times$ for request-agnostic mixing and $1.000\times$ for static W4, an incremental $2.5\%$ relative FWP gain.

cs.LG↗

arXiv2026

Learning to Price and Stock Under Contextual and Censored Demand

To make optimal joint pricing and inventory control decisions is a critical challenge for modern retailers. In practice, retailers face changing market conditions where demands are influenced by various contextual factors, while simultaneously dealing with the difficulty of lost sales that obscure true demand information. However, existing approaches often fail to account for both contextual information and censored demand observations. We address this gap by presenting a framework where we model demand as a linear combination of basis functions with unknown coefficients, allowing for adaptive pricing and inventory decisions that respond to changing contexts. We propose an efficient algorithm to achieve regret bound $\mathcal{O}(K\sqrt{T}\log T)$ under concave revenue conditions and $\mathcal{O}(K^{2/3}T^{2/3}(\log T)^{1/2})$ for the general case, with matching lower bounds confirming optimality. Extensive numerical experiments across diverse scenarios demonstrate our algorithm's effectiveness.

cs.LG↗

arXiv2026

Nonparametric Contextual Pricing and Inventory Learning under Censored Demand

In online retailing, when a product sells out, a retailer often sees only the units sold, not how many customers would have bought it had inventory been available. However, the inventory level determines how much demand is revealed, and this information can influence subsequent decisions and future profits. We study an online selling problem in which, in each round, the seller observes a market context and then makes pricing and stocking decisions based on censored sales data from previous rounds. The challenge is to learn a context-dependent pricing and stocking policy without assuming a particular formula for demand or observing realized profit. To overcome this difficulty, we propose a Mean-Calibrated Kernel UCB (MCK-UCB) algorithm that turns each incomplete sales record into a reliable guide for both inventory and price decisions, using data from past rounds with similar market conditions. This design allows us to learn while serving customers, without a separate exploration phase or the need to recover all demand hidden by stockouts. We prove the minimax optimality of the proposed algorithm, with strictly faster rates when expected profit varies more smoothly with price. Comprehensive numerical experiments have been conducted to confirm the effectiveness of the proposed algorithm.

cs.LG↗

arXiv2026

Learning to Bid with Unknown Private Values in Budget-Constrained First-Price Auctions

We study the operational problem of automated bidding in repeated first-price auctions under budget and return-on-spend (RoS) constraints. In this setting, an auto-bidder must translate advertiser goals and constraints into real-time bids while learning two latent objects: the causal uplift value of each ad impression and the highest competing bid (HoB) needed to win it. We model uplift values and HoBs through a shared-context Linear Treatment Effect (LTE) structure and analyze both full-information and binary HoB feedback. We develop Dual-LTE, a dual-aware online learning framework that coordinates value estimation, HoB estimation, and budget/RoS control through confidence-guided exploration. We prove regret and constraint-violation guarantees that scale as $\widetilde{O}(\sqrt{T})$ under full-information HoB feedback and $\widetilde{O}(T^{2/3})$ under binary win/loss feedback, where $\widetilde{O}(\cdot)$ hides problem-dependent and logarithmic factors. Semi-synthetic experiments using real auction covariates show that Dual-LTE achieves lower regret than the baselines across budget and RoS settings, while illustrating the tradeoff between regret and constraint violation. Our results provide operational guidance for DSPs and platform auto-bidders that manage advertiser budgets or seek to meet ROAS targets. When impression values must be learned, value estimation should be coordinated with budget or ROAS control: the auto-bidder should follow the Lagrangian bidding rule only when value estimates are sufficiently accurate given the current constraint pressure and should otherwise use controlled exploration.

cs.LG↗

arXiv2026

Minimax-Optimal Semiparametric Contextual Dynamic Pricing with Multimodal Revenue

We study contextual dynamic pricing with arbitrary covariate sequences and bounded, possibly nonbinary purchase quantities. Demand follows a semiparametric surplus-index model with an unknown linear valuation parameter and an unknown Hölder-smooth response. We impose neither concavity nor strong unimodality on revenue and allow nonunique optimal prices. We develop a pilot-corrected layered decision-partitioning policy that combines directional pilot estimation, local polynomial learning, predictable data assignment, and global action elimination. Pilot correction removes the first-order effect of valuation-parameter error, while permanent labels enable concentration under adaptive sampling. The policy attains the minimax smoothness-dependent horizon rate up to logarithmic factors; a matching lower bound already holds for a constant-context binary-demand subclass.

stat.ML↗

arXiv2026

A Distinct Covering System with Minimum Modulus 7 and Minimal Least Common Multiple 10080

We determine the minimum possible least common multiple of a distinct covering system whose minimum modulus is $7$. Klein previously constructed such a system with least common multiple $15120$ and conjectured that this value was minimal. We give a construction with least common multiple $10080$, and we prove that no smaller least common multiple can occur. The proof is organized as a successive filtering argument. Starting from the possible multiples of $7$ below $10080$, we first apply a reciprocal-sum filter, then a divisor-completed integer-programming filter, then a stronger partial-sum filter. The few remaining hard cases are finally certified by complete Gurobi computations.

math.NT↗

arXiv2026

When to Match: A Cost-Balancing Principle for Dynamic Markets

Platforms in ridesharing, food delivery, and online gaming must decide not only whom to match but when: immediate matching cuts waiting, while delay thickens the market and improves match quality. Because demand is hard to forecast, the right waiting window shifts continuously. Fixed-window industry rules are simple but fragile, while forecast-based optimization models are brittle when assumptions fail. This paper develops a matching rule that is as simple as industry practice yet carries a guarantee requiring no forecasts. We study a model in which agents of several types are matched in groups drawing one agent from each type, waiting is costly, and matching costs fall as queues grow. We propose the Cost-Balancing (CB) rule: match as soon as the waiting cost accumulated since the last match reaches a calibrated proportion of the current matching cost. On any finite arrival stream delivering equal numbers of each type, CB calibrated for the worst case incurs at most twice the cost of an optimal clairvoyant policy that knows all future arrivals. No deterministic online rule can guarantee a smaller factor, so CB is worst-case optimal, while greedy and fixed-threshold policies can perform arbitrarily worse than this benchmark. The guarantee extends to matches with fixed heterogeneous consumption requirements. In a game-matching experiment, CB reduces total cost by 3--8\% versus the industry-standard heuristic; in a food-delivery experiment, it reduces average delay by 14.5\% versus the best fixed-rule benchmark. Platforms can manage match timing with Cost-Balancing, a simple, efficient, and robust rule. Its worst-case guarantee provides a safety net even in volatile conditions where fixed rules break down. Responding to realized costs, the rule matches faster during surges and waits longer during lulls, without forecasts or retuning.

math.OC↗

arXiv2026

Dynamic Regret for Non-Stationary Linear Bandits via Misspecification Reductions

Many online decision-making problems involve both round-specific feasible actions and drifting reward models: eligible ad impressions, feasible prices, and available treatments can change over time, while user preferences, demand curves, and patient responses may evolve. Motivated by these applications, we study non-stationary linear bandits with round-specific feasible decision sets. Existing methods that obtain the optimal $\widetilde O(T^{2/3}P_T^{1/3})$ dependence, where $P_T$ is the path length of the reward-parameter sequence, impose an orthogonal-structure assumption on round-specific decision sets, which can be restrictive in contextual applications. We address this gap through a unified misspecification-reduction viewpoint: after partitioning the horizon into blocks, we relate each block's dynamic regret to regret against a fixed-parameter linear bandit benchmark, with the within-block parameter drift entering as bounded misspecification. Restarting algorithms with misspecification-dependent regret guarantees then yields the optimal $T^{2/3}P_T^{1/3}$ dynamic-regret dependence for both linear bandits with general compact decision sets and $K$-armed contextual linear bandits.

cs.LG↗

arXiv2026

Large-Scale LLM Inference with Heterogeneous Workloads: Prefill-Decode Contention and Asymptotically Optimal Control

Large Language Models (LLMs) are rapidly becoming critical infrastructure for enterprise applications, driving unprecedented demand for GPU-based inference services. A key operational challenge arises from the two-phase nature of LLM inference: a compute-intensive \emph{prefill} phase that processes user input, followed by a memory-bound \emph{decode} phase that generates output tokens. When these phases share GPU resources, prefill tasks throttle the processing speed of concurrent decodes, creating state-dependent contention. This contention is further complicated by workload heterogeneity, as different applications exhibit vastly different input and output lengths. We develop a stochastic control framework for scheduling heterogeneous LLM workloads across large GPU clusters. We formulate LLM inference as a multiclass many-server queueing network with state-dependent service rates, grounded in empirical iteration-time measurements. We analyze the fluid approximation of this system and solve steady-state linear programs that characterize optimal resource allocation. We design gate-and-route policies that regulate prefill admission and decode routing, and prove that they are asymptotically optimal in the many-GPU limit under both bundled and separate token-pricing schemes. We further extend the framework to incorporate Service Level Indicators (SLIs) such as latency and fairness, providing a general approach to constrained scheduling. Numerical experiments calibrated to empirical iteration-time data demonstrate that our policies outperform standard serving heuristics.

cs.DC↗

arXiv2026

Direction-Aware Offline-to-Online Learning in Linear Contextual Bandits

Many bandit systems are deployed with offline historical data, such as past logs from earlier policies. Using these data can reduce early online exploration when they remain informative for the online problem. When the offline and online environments differ, such data can be biased for the online problem. For linear (contextual) bandits, this bias is directional: offline data may be informative in some feature directions and misleading in others. However, prior work typically controls this gap through a known Euclidean bound on the model parameters, which we prove is too coarse: even with the offline parameter known, bias in a single unknown direction can force dimension-dependent regret. To address this challenge, we introduce a directional bias certificate $(M_{\mathrm{bias}},ρ)$ that measures the offline-to-online gap through an $M_{\mathrm{bias}}$-induced norm and assigns different bias budgets to different directions. Building on this certificate, we propose \emph{Ellipsoidal-MINUCB}, which augments the online learning with an offline-pooled branch that safely exploits historical data. When the certificate is known, we show that the algorithm matches the standard SupLinUCB rate in the worst case and improves when offline coverage aligns with low-bias directions. When the certificate is unknown, we estimate it adaptively from offline and accumulated online data and establish a corresponding regret guarantee. Numerical experiments support the theory and show gains in aligned regimes.

cs.LG↗

arXiv2026

Staffing under Taylor's Law: A Unifying Framework for Bridging Square-root and Linear Safety Rules

Staffing rules are an essential management tool in service industries for meeting target service levels. The square-root safety rule, based on the Poisson arrival assumption, has been commonly used. However, empirical findings suggest that arrivals often exhibit ``over-dispersion'', meaning that the variance exceeds the mean. In this paper, we develop a new doubly stochastic Poisson process model that captures two key features of over-dispersed arrivals: (i) Taylor's law, which links the variance to the mean through a power-law relationship, and (ii) temporal correlation decay, where the correlation between arrival counts in disjoint time intervals decreases as the time gap grows. Using this model, we study how over-dispersion affects staffing and derive a closed-form staffing formula to ensure a desired service level. Our formula shows that the safety level grows as a power of the nominal load. The exponent lies between 1/2 (the square-root safety rule) and 1 (the linear safety rule). It depends on the degree of over-dispersion, and it implies that Taylor's law is the dominant factor in determining staffing levels in heavy traffic. Extensive numerical experiments with both simulated and real arrival data show that our model and staffing rules significantly outperform various alternatives.

math.PR↗

arXiv2025

OR-R1: Automating Modeling and Solving of Operations Research Optimization Problem via Test-Time Reinforcement Learning

Optimization modeling and solving are fundamental to the application of Operations Research (OR) in real-world decision making, yet the process of translating natural language problem descriptions into formal models and solver code remains highly expertise intensive. While recent advances in large language models (LLMs) have opened new opportunities for automation, the generalization ability and data efficiency of existing LLM-based methods are still limited, asmost require vast amounts of annotated or synthetic data, resulting in high costs and scalability barriers. In this work, we present OR-R1, a data-efficient training framework for automated optimization modeling and solving. OR-R1 first employs supervised fine-tuning (SFT) to help the model acquire the essential reasoning patterns for problem formulation and code generation from limited labeled data. In addition, it improves the capability and consistency through Test-Time Group Relative Policy Optimization (TGRPO). This two-stage design enables OR-R1 to leverage both scarce labeled and abundant unlabeled data for effective learning. Experiments show that OR-R1 achieves state-of-the-art performance with an average solving accuracy of $67.7\%$, using only $1/10$ the synthetic data required by prior methods such as ORLM, exceeding ORLM's solving accuracy by up to $4.2\%$. Remarkably, OR-R1 outperforms ORLM by over $2.4\%$ with just $100$ synthetic samples. Furthermore, TGRPO contributes an additional $3.1\%-6.4\%$ improvement in accuracy, significantly narrowing the gap between single-attempt (Pass@1) and multi-attempt (Pass@8) performance from $13\%$ to $7\%$. Extensive evaluations across diverse real-world benchmarks demonstrate that OR-R1 provides a robust, scalable, and cost-effective solution for automated OR optimization problem modeling and solving, lowering the expertise and data barriers for industrial OR applications.

cs.AI↗

arXiv2025

Learning to Bid in Non-Stationary Repeated First-Price Auctions

First-price auctions have recently gained significant traction in digital advertising markets, exemplified by Google's transition from second-price to first-price auctions. Unlike in second-price auctions, where bidding one's private valuation is a dominant strategy, determining an optimal bidding strategy in first-price auctions is more complex. From a learning perspective, the learner (a specific bidder) can interact with the environment (other bidders, i.e., opponents) sequentially to infer their behaviors. Existing research often assumes specific environmental conditions and benchmarks performance against the best fixed policy (static benchmark). While this approach ensures strong learning guarantees, the static benchmark can deviate significantly from the optimal strategy in environments with even mild non-stationarity. To address such scenarios, a dynamic benchmark--representing the sum of the highest achievable rewards at each time step--offers a more suitable objective. However, achieving no-regret learning with respect to the dynamic benchmark requires additional constraints. By inspecting reward functions in online first-price auctions, we introduce two metrics to quantify the regularity of the sequence of opponents' highest bids, which serve as measures of non-stationarity. We provide a minimax-optimal characterization of the dynamic regret for the class of sequences of opponents' highest bids that satisfy either of these regularity constraints. Our main technical tool is the Optimistic Mirror Descent (OMD) framework with a novel optimism configuration, which is well-suited for achieving minimax-optimal dynamic regret rates in this context. We then use synthetic datasets to validate our theoretical guarantees and demonstrate that our methods outperform existing ones.

cs.LG↗

arXiv2025

Minimax Optimality in Contextual Dynamic Pricing with General Valuation Models

We study contextual dynamic pricing, where a decision maker posts personalized prices based on observable contexts and receives binary purchase feedback indicating whether the customer's valuation exceeds the price. Each valuation is modeled as an unknown latent function of the context, corrupted by independent and identically distributed market noise from an unknown distribution. Relying only on Lipschitz continuity of the noise distribution and bounded valuations, we propose a minimax-optimal algorithm. To accommodate the unknown distribution, our method discretizes the relevant noise range to form a finite set of candidate prices, then applies layered data partitioning to obtain confidence bounds substantially tighter than those derived via the elliptical-potential lemma. A key advantage is that estimation bias in the valuation function cancels when comparing upper confidence bounds, eliminating the need to know the Lipschitz constant. The framework extends beyond linear models to general function classes through offline regression oracles. Our regret analysis depends solely on the oracle's estimation error, typically governed by the statistical complexity of the class. These techniques yield a regret upper bound matching the minimax lower bound up to logarithmic factors. Furthermore, we refine these guarantees under additional structures -- e.g., linear valuation models, second-order smoothness, sparsity, and known noise distribution or observable valuations -- and compare our bounds and assumptions with prior dynamic-pricing methods. Finally, numerical experiments corroborate the theory and show clear improvements over benchmark methods.

cs.LG↗

arXiv2025

Efficient Transfer Learning via Causal Bounds

Transfer learning seeks to accelerate sequential decision-making by leveraging offline data from related agents. However, data from heterogeneous sources that differ in observed features, distributions, or unobserved confounders often render causal effects non-identifiable and bias naive estimators. We address this by forming ambiguity sets of structural causal models defined via integral constraints on their joint densities. Optimizing any causal effect over these sets leads to generally non-convex programs whose solutions tightly bound the range of possible effects under heterogeneity or confounding. To solve these programs efficiently, we develop a hit-and-run sampler that explores the entire ambiguity set and, when paired with a local optimization oracle, produces causal bound estimates that converge almost surely to the true limits. We further accommodate estimation error by relaxing the ambiguity set and exploit the Lipschitz continuity of causal effects to establish precise error propagation guarantees. These causal bounds are then embedded into bandit algorithms via arm elimination and truncated UCB indices, yielding optimal gap-dependent and minimax regret bounds. To handle estimation error, we also develop a safe algorithm for incorporating noisy causal bounds. In the contextual-bandit setting with function approximation, our method uses causal bounds to prune both the function class and the per-context action set, achieving matching upper and lower regret bounds with only logarithmic dependence on function-class complexity. Our analysis precisely characterizes when and how causal side-information accelerates online learning, and experiments on synthetic benchmarks confirm substantial regret reductions in data-scarce or confounded regimes.

cs.LG↗

arXiv2025

Adaptive Inertial Method

In this paper, we introduce the Adaptive Inertial Method (AIM), a novel framework for accelerated first-order methods through a customizable inertial term. We provide a rigorous convergence analysis establishing a global convergence rate of O(1/k) under mild conditions, requiring only convexity and local Lipschitz differentiability of the objective function. Our method enables adaptive parameter selection for the inertial term without manual tuning. Furthermore, we derive the particular form of the inertial term that transforms AIM into a new Quasi-Newton method. Notably, under specific circumstances, AIM coincides with the regularized Newton method, achieving an accelerated rate of O(1/k^2) without Hessian inversions. Through extensive numerical experiments, we demonstrate that AIM exhibits superior performance across diverse optimization problems, highlighting its practical effectiveness.

math.OC↗