arXiv subjects

Zhengyuan Zhou

Publications and source records attributed to Zhengyuan Zhou.

At least 19 recordsLinked to original sources

arXiv2026

Allocation Stability and Wald Inference under Variance-Aware UCB

Allocation stability is often used to justify Gaussian inference from bandit data, but when is it necessary? In this paper, we address this question for a two-armed, fixed-horizon variance-aware UCB policy with bounded reward distributions that may vary with the horizon. We find a sharp criterion in terms of the reward gap and variances that determines whether the optimal-arm count admits a deterministic approximation with vanishing relative error, while the suboptimal-arm count is always stable. Despite the possible instability of the optimal-arm count, we show that the ordinary Wald statistic for a linear combination of the arm means has a standard normal limit for every fixed nonzero coefficient vector, provided the product of the pull count and reward variance diverges in probability for each arm. Under the same condition, however, this Gaussian approximation holds uniformly over deterministic nonzero coefficient vectors if and only if the optimal-arm count is stable. The analysis relies on two main ingredients: (i) a pathwise comparison with an auxiliary policy whose final optimal-arm count is asymptotically equivalent to the original count and independent of the optimal-arm reward sequence; and (ii) joint limits for the rescaled optimal-arm count and the two studentized sample-mean errors under the original policy, which yield nonstandard Wald limits for certain linear combinations of the arm means with coefficients that vary with the horizon.

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arXiv2026

Adaptive Self-Consistency: From Black-Box Sampling to Distribution-Valued Feedback

Self-consistency samples many reasoning trajectories and aggregates their final answers, treating the LLM as a black box that returns one answer per trajectory. Yet the final answer of each trajectory is sampled from a softmax vector that is available from the model's log-probabilities. We refer to this as the grey-box setting in which each trajectory reveals this answer distribution rather than a single draw from it. We formulate efficient inference in this setting as sequential mode identification with distribution-valued observations: sample trajectories one at a time and stop as soon as the LLM's modal answer is identified at a prescribed confidence level. We characterize the asymptotic stopping rate of mode identification with distribution-valued observations exactly and show that it is never worse than the black-box rate. We then propose the ASC-D algorithm, a betting stopping rule that attains this asymptotic stopping rate. On MMLU-Redux, ASC-D uses $46.4$--$95.6\%$ fewer trajectories than answer-only adaptive self-consistency baselines and achieves the highest fixed-budget correct-certification rate across three open-source models.

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arXiv2026

Towards Optimal Inventory Control under Censored Demand: A Biased Sample-Average Approximation Approach

We study data-driven multi-period lost-sales inventory control under censored demand, where a stockout reveals only that demand exceeded the stocking level. We develop a unified, model-based framework for policy learning from censored data, built on a new cost decomposition for base-stock policies and a biased sample-average approximation (SAA) approach. The cost decomposition allows us to propose a new coverage condition under which censored observations are informative enough for sample-efficient policy learning. Guided by this coverage condition, we design two biased SAA algorithms: an upper-biased one that achieves near-optimal sample complexity under the offline coverage condition, and a lower-biased one that actively generates the required coverage and achieves near-optimal regret online. More broadly, this biased SAA approach provides a general principle for implementing pessimism and optimism under censored feedback, which may be of independent interest.

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arXiv2026

Robust Assortment Optimization from Observational Data

Assortment optimization is a fundamental challenge in modern retail and recommendation systems, where the goal is to select a subset of products that maximizes expected revenue under complex customer choice behaviors. While recent advances in data-driven methods have leveraged historical data to learn and optimize assortments, these approaches typically rely on strong assumptions -- namely, the stability of customer preferences and the correctness of the underlying choice models. However, such assumptions frequently break in real-world scenarios due to preference shifts and model misspecification, leading to poor generalization and revenue loss. Motivated by this limitation, we propose a robust framework for data-driven assortment optimization that accounts for potential distributional shifts in customer choice behavior. Our approach models potential preference shift from a nominal choice model that generates data and seeks to maximize worst-case expected revenue. We first establish the computational tractability of robust assortment planning when the nominal model is known, then advance to the data-driven setting, where we design statistically optimal algorithms that minimize the data requirements while maintaining robustness. Our theoretical analysis provides both upper bounds and matching lower bounds on the sample complexity, offering theoretical guarantees for robust generalization. Notably, we uncover and identify the notion of ``robust item-wise coverage'' as the minimal data requirement to enable sample-efficient robust assortment learning. Our work bridges the gap between robustness and statistical efficiency in assortment learning, contributing new insights and tools for reliable assortment optimization under uncertainty.

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arXiv2026

Sequential Batch Learning in Finite-Action Linear Contextual Bandits

We study the sequential batch learning problem in linear contextual bandits with finite action sets, where the decision maker is constrained to split incoming individuals into (at most) a fixed number of batches and can only observe outcomes for the individuals within a batch at the batch's end. Compared with both standard online contextual-bandit learning and offline policy learning in contextual bandits, this sequential batch learning problem provides a finer-grained formulation of many personalized sequential decision making problems in practical applications, including medical treatment in clinical trials, product recommendation in e-commerce and adaptive experiment design in crowdsourcing. We study two settings of the problem: one where the contexts are arbitrarily generated and the other where the context vectors are mutually independent across actions and time and follow a common Gaussian distribution. In each setting, we establish a regret lower bound and provide an algorithm, whose regret upper bound nearly matches the lower bound. As an important insight revealed therefrom, in the former setting, we show that the number of batches required to achieve the fully online performance is polynomial in the time horizon, while for the latter setting, a pure-exploitation algorithm with a judicious batch partition scheme achieves the fully online performance even when the number of batches is less than logarithmic in the time horizon. In the stochastic context setting, we additionally provide tight margin-based (i.e. instance-dependent) upper and lower regret bounds that delineate performance in terms of how difficult the problem instance is. Together, our results provide a near-complete characterization of sequential decision making in linear contextual bandits when batch constraints are present.

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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.

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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.

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arXiv2026

Optimal Bayesian Stopping for Efficient Inference of Consistent LLM Answers

A simple strategy for improving LLM accuracy, especially in math and reasoning problems, is to sample multiple responses and submit the answer most consistently reached. In this paper we leverage Bayesian prior information to save on sampling costs, stopping once sufficient consistency is reached. Although the exact posterior is computationally intractable, we further introduce an efficient "L-aggregated" stopping policy that tracks only the L-1 most frequent answer counts. Theoretically, we prove that L=3 is all you need: this coarse approximation is sufficient to achieve asymptotic optimality, and strictly dominates prior-free baselines, while having a fast posterior computation. Empirically, this identifies the most consistent (i.e., mode) LLM answer using fewer samples, and can achieve similar answer accuracy while cutting the number of LLM calls (i.e., saving on LLM inference costs) by up to 50%.

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arXiv2026

Harnessing Unimodality in Semiparametric Contextual Pricing via Oracle Price Map Learning

We study contextual dynamic pricing in a semiparametric scalar-index valuation model where the latent value is $v_t=μ_\ast(\mathsf c_t)+ξ_t$, with an unknown utility map $μ_\ast$ and an unknown additive noise distribution. The key decision object is the one-dimensional oracle price map $u\mapsto p^\ast(u)$ induced by the scalar index $u=μ_\ast(\mathsf c)$ and the noise tail. Under the $β$-Hölder smoothness of the tail function for $β\geq 2$ and a revenue-geometry condition that gives a unique, stable, interior maximizer, this oracle map is itself $(β-1)$-smooth. We exploit such structure through $\mathsf{ORBIT}$, a modular coarse-to-fine policy that takes a scalar pilot index as input, localizes a benchmark price in each active bin, and learns a local polynomial approximation of the oracle map inside a trust region via bandit convex optimization. For the baseline linear utility model $μ_\ast(\mathsf c)=\mathsf c^\topθ_\ast$, an adaptive elliptical exploration scheme constructs the required scalar pilot online without distributional assumptions on the contexts. The resulting policy achieves regret $\widetilde{O}\big(T^{\frac{2β-1}{4β-3}}+\sqrt{dT}\big)$. For fixed $d$, we establish a matching lower bound in the horizon dependence, unveiling that the nonparametric oracle-map learning term is minimax sharp. The same scalar-pilot interface also yields extensions to sparse high-dimensional linear utility and nonparametric Hölder utility.

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arXiv2026

The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions

Existing auto-bidding algorithms in digital advertising often treat the value of an ad opportunity as the revenue obtained when an ad is shown and/or clicked, and bid accordingly. This can lead to wasteful spending because the true value is the marginal gain from paid exposure: even without winning a sponsored slot, an advertiser may still earn revenue via an organic search result (e.g., on Google or Amazon). Motivated by recent work, we model ad value as a treatment effect--the outcome difference between winning and losing the auction--and study online learning for bidding in second-price (Vickrey) auctions under this causal perspective. We develop algorithms that attain rate-optimal regret under several feedback models. A key ingredient exploits the information revealed by the second-price payment rule, which strictly improves regret relative to analogous learning problems in first-price auctions.

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arXiv2026

Optimal Online and Offline Algorithms for Contextual MNL with Applications to Assortment and Pricing

Selecting which products to display and at what prices is a central decision in retail and e-commerce operations. In many applications, these two choices must be made jointly under limited display capacity and uncertain customer demand. In this paper, we study the joint assortment and pricing problem under a price-based contextual multinomial logit model, where customer preferences depend on both product features and selling prices. Our analysis begins with the construction of a new confidence region for demand estimation under price-dependent features. Building on this result, we develop a pessimistic offline algorithm and SupCB-type online algorithms for joint assortment and pricing optimization. In the offline setting, we establish a suboptimality guarantee governed by local information around the optimal assortment-price pair, rather than by exact coverage of the optimal action. In the online setting, our SupCB-type algorithm improves the best previously known regret bound to $\widetilde{O}(W\sqrt{dT\log N}/L_0)$, and we also provide a computationally simpler Thompson-sampling alternative. When specialized to the assortment-only or pricing-only setting, our bounds recover the near-minimax-optimal rates established in those respective domains, thereby bridging the gap between the mature study on assortment optimization or dynamic pricing and the limited literature on their joint optimization.

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arXiv2026

DR-SAC: Distributionally Robust Soft Actor-Critic for Reinforcement Learning under Uncertainty

Deep reinforcement learning (RL) has achieved remarkable success, yet its deployment in real-world scenarios is often limited by vulnerability to environmental uncertainties. Distributionally robust RL (DR-RL) algorithms have been proposed to resolve this challenge, but existing approaches are largely restricted to value-based methods in tabular settings. In this work, we introduce Distributionally Robust Soft Actor-Critic (DR-SAC), the first actor-critic based DR-RL algorithm for offline learning in continuous action spaces. DR-SAC maximizes the entropy-regularized rewards against the worst possible transition models within an KL-divergence constrained uncertainty set. We derive the distributionally robust version of the soft policy iteration with a convergence guarantee and incorporate a generative modeling approach to estimate the unknown nominal transition models. Experiment results on five continuous RL tasks demonstrate our algorithm achieves up to 9.8 times higher average reward than the SAC baseline under common perturbations. Additionally, DR-SAC significantly improves computing efficiency and applicability to large-scale problems compared with existing DR-RL algorithms. Code is publicly available at github.com/Lemutisme/DR-SAC.

cs.LG↗

arXiv2026

Revisiting the Last-Iterate Convergence of Stochastic Gradient Methods

In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex functions, different works have established the optimal $O(\log(1/δ)\log T/\sqrt{T})$ or $O(\sqrt{\log(1/δ)/T})$ high-probability convergence rates for the final iterate, where T is the time horizon and δis the failure probability. However, to prove these bounds, all the existing works are either limited to compact domains or require almost surely bounded noise. It is natural to ask whether the last iterate of SGD can still guarantee the optimal convergence rate but without these two restrictive assumptions. Besides this important question, there are still lots of theoretical problems lacking an answer. For example, compared with the last-iterate convergence of SGD for non-smooth problems, only few results for smooth optimization have yet been developed. Additionally, the existing results are all limited to a non-composite objective and the standard Euclidean norm. It still remains unclear whether the last-iterate convergence can be provably extended to wider composite optimization and non-Euclidean norms. In this work, to address the issues mentioned above, we revisit the last-iterate convergence of stochastic gradient methods and provide the first unified way to prove the convergence rates both in expectation and in high probability to accommodate general domains, composite objectives, non-Euclidean norms, Lipschitz conditions, smoothness, and (strong) convexity simultaneously. Additionally, we extend our analysis to obtain the last-iterate convergence under heavy-tailed and sub-Weibull noise.

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arXiv2026

Joint Value Estimation and Bidding in Repeated First-Price Auctions

We study regret minimization in repeated first-price auctions (FPAs), where a bidder observes only the realized outcome after each auction -- win or loss. This setup reflects practical scenarios in online display advertising where the actual value of an impression depends on the difference between two potential outcomes, such as clicks or conversion rates, when the auction is won versus lost. We incorporate causal inference into this framework and analyze the challenging case where only the treatment effect admits a simple dependence on observable features. Under this framework, we propose algorithms that jointly estimate private values and optimize bidding strategies under two different feedback types on the highest other bid (HOB): the full-information feedback where the HOB is always revealed, and the binary feedback where the bidder only observes the win-loss indicator. Under both cases, our algorithms are shown to achieve near-optimal regret bounds. Notably, our framework enjoys a unique feature that the treatments are actively chosen, and hence eliminates the need for the overlap condition commonly required in causal inference.

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arXiv2026

Functional Critics Are Essential for Actor-Critic: From Off-Policy Stability to Efficient Exploration

The actor-critic (AC) framework has achieved strong empirical success in off-policy reinforcement learning but suffers from the "moving target" problem, where the evaluated policy changes continually. Functional critics, or policy-conditioned value functions, address this by explicitly including a representation of the policy as input. While conceptually appealing, previous efforts have struggled to remain competitive against standard AC. In this work, we revisit functional critics within the actor-critic framework and identify two critical aspects that render them a necessity rather than a luxury. First, we demonstrate their power in stabilizing the complex interplay between the "deadly triad" and the "moving target". We provide a convergent off-policy AC algorithm under linear functional approximation that dismantles several longstanding barriers between theory and practice: it utilizes target-based TD learning, accommodates dynamic behavior policies, and operates without the restrictive "full coverage" assumptions. By formalizing a dual trust-coverage mechanism, our framework provides principled guidelines for pursuing sample efficiency-rigorously governing behavior policy updates and critic re-evaluations to maximize off-policy data utility. Second, we uncover a foundational link between functional critics and efficient exploration. We demonstrate that existing model-free approximations of posterior sampling are limited in capturing policy-dependent uncertainty, a gap the functional critic formalism bridges. These results represent, to our knowledge, first-of-their-kind contributions to the RL literature. Practically, we propose a tailored neural network architecture and a minimalist AC algorithm. In preliminary experiments on the DeepMind Control Suite, this implementation achieves performance competitive with state-of-the-art methods without standard implementation heuristics.

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arXiv2026

Surface-based Molecular Design with Multi-modal Flow Matching

Therapeutic peptides show promise in targeting previously undruggable binding sites, with recent advancements in deep generative models enabling full-atom peptide co-design for specific protein receptors. However, the critical role of molecular surfaces in protein-protein interactions (PPIs) has been underexplored. To bridge this gap, we propose an omni-design peptides generation paradigm, called SurfFlow, a novel surface-based generative algorithm that enables comprehensive co-design of sequence, structure, and surface for peptides. SurfFlow employs a multi-modality conditional flow matching (CFM) architecture to learn distributions of surface geometries and biochemical properties, enhancing peptide binding accuracy. Evaluated on the comprehensive PepMerge benchmark, SurfFlow consistently outperforms full-atom baselines across all metrics. These results highlight the advantages of considering molecular surfaces in de novo peptide discovery and demonstrate the potential of integrating multiple protein modalities for more effective therapeutic peptide discovery.

cs.LG↗

arXiv2025

Learning Optimal Distributionally Robust Stochastic Control in Continuous State Spaces

We study data-driven learning of robust stochastic control for infinite-horizon systems with potentially continuous state and action spaces. In many managerial settings--supply chains, finance, manufacturing, services, and dynamic games--the state-transition mechanism is determined by system design, while available data capture the distributional properties of the stochastic inputs from the environment. For modeling and computational tractability, a decision maker often adopts a Markov control model with i.i.d. environment inputs, which can render learned policies fragile to internal dependence or external perturbations. We introduce a distributionally robust stochastic control paradigm that promotes policy reliability by introducing adaptive adversarial perturbations to the environment input, while preserving the modeling, statistical, and computational tractability of the Markovian formulation. From a modeling perspective, we examine two adversary models--current-action-aware and current-action-unaware--leading to distinct dynamic behaviors and robust optimal policies. From a statistical learning perspective, we characterize optimal finite-sample minimax rates for uniform learning of the robust value function across a continuum of states under ambiguity sets defined by the $f_k$-divergence and Wasserstein distance. To efficiently compute the optimal robust policies, we further propose algorithms inspired by deep reinforcement learning methodologies. Finally, we demonstrate the applicability of the framework to real managerial problems.

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arXiv2025

Optimal Arm Elimination Algorithms for Combinatorial Bandits

Combinatorial bandits extend the classical bandit framework to settings where the learner selects multiple arms in each round, motivated by applications such as online recommendation and assortment optimization. While extensions of upper confidence bound (UCB) algorithms arise naturally in this context, adapting arm elimination methods has proved more challenging. We introduce a novel elimination scheme that partitions arms into three categories (confirmed, active, and eliminated), and incorporates explicit exploration to update these sets. We demonstrate the efficacy of our algorithm in two settings: the combinatorial multi-armed bandit with general graph feedback, and the combinatorial linear contextual bandit. In both cases, our approach achieves near-optimal regret, whereas UCB-based methods can provably fail due to insufficient explicit exploration. Matching lower bounds are also provided.

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