arXiv subjects

David Simchi-Levi

Publications and source records attributed to David Simchi-Levi.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Value Inference for Reinforcement Learning

We study offline inference for the optimal value in reinforcement learning. Two new nuisances are derived as fixed points of a self-induced Bellman equation, in which we approximate the maximum Bellman operator by its softmax correspondence. We propose a debiased estimator through the Neyman orthogonality and establish its asymptotic normality under diverging horizons even when the behavior policy changes with time, as long as the nuisances have the statistical rates that can be achieved by many machine learning methods. We provide a concrete estimating procedure for these nuisances and show they can lead to valid inference. Synthetic experiments validate the numerical performance of our inference method, and we implement it in real-life decision-making problems, including bike repositioning and AI agentic tool use.

stat.ML↗

arXiv2026

Sharp Structure-Agnostic Minimax Risk for Partial Linear Models

We characterize the sharp structure-agnostic minimax risk for coefficient estimation in the partial linear model when the outcome and treatment nuisances are learned by two distinct black-box learners, which resolves the open problem in double machine learning posed by Gu (2025). For each nuisance $q\in\{\mu,\pi\}$, we characterize the available learner by an approximation-error budget $a_q$ and a stochastic-error budget $s_q$, with the latter controlled through localized Rademacher complexity. Writing $\mathcal E_n$ for the minimax mean-squared error, we show that \[\mathcal E_n\asymp1\wedge\left\{\frac1n+\left(a_\mu a_\pi+\min\left\{a_\pi s_\mu+s_\pi^2,\,a_\mu s_\pi+s_\mu^2\right\}\right)^2\right\}.\] The main new ingredient is a novel lower bound for the general two-learner problem. Our proof constructs four finite-mixture testing experiments using orthogonal code functions. Across these experiments, the hidden perturbations are placed outside both learner classes, outside only the treatment learner class, outside only the outcome learner class, or inside both learner classes. These four configurations capture, respectively, the interaction between the two approximation errors, the two asymmetric interactions between one learner's approximation error and the other learner's learning error, and the joint estimation difficulty of learning both nuisances. Combining the four resulting lower bounds yields the displayed rate, which matches the latest upper bound in Gu (2026). Our result shows that standard double machine learning can overstate the intrinsic difficulty of target estimation and provides a target-specific principle for learner selection: approximation error and stochastic complexity must be jointly balanced across the two nuisance learners rather than optimized separately.

cs.LG↗

arXiv2026

Multi-Turn LLM Conversations under the Least-Recently-Used Policy: Mean-Field Asymptotics and Hit Ratio Approximation

The major workloads in modern large language model (LLM) serving systems have shifted from single-shot LLM calls to multi-turn conversations, where new responses are generated based on the whole conversation history across all previous turns. The hit ratio, i.e., the average fraction of KV caches accessed directly from existing caches stored in high-bandwidth memory (HBM), is hence a crucial metric that governs system performance. Estimating the hit ratio is a highly nontrivial task due to the complex system dynamics, where the KV cache prefixes grow with turns and some must be evicted due to finite memory capacity. We formulate the system as a multi-turn conversation model under the least-recently-used (LRU) policy. Through a mean-field asymptotic framework, we prove that as the conversation arrival rate and the memory capacity grow proportionally to infinity, the hit ratio converges to a closed-form limit. Based on the characterization of the limit, we further propose a practical hit ratio estimator, and validate its accuracy by real LLM serving experiments on the Qwen3-8B model implemented on Ascend NPUs. Our results provide a theoretical foundation for the analysis of multi-turn LLM serving systems and a practical guideline for memory capacity provisioning.

cs.PF↗

arXiv2026

Simultaneous Pointwise Majorization for Mixed Tail Processes with Applications in Gaussian Chaos and Ergodic Diffusions

Classical chaining controls an indexed stochastic process through a single worst-case bound and can therefore obscure substantial variation across the index set. We develop the first simultaneous pointwise majorization theory for Banach-valued processes with finite-metric mixed-tail increments. Suppose that an anchored process $(Z_t)_{t\in T}$ satisfies, for some integer $m\ge1$, pseudo-metrics $d_1,\ldots,d_m$, and orders $\alpha_1,\ldots,\alpha_m>0$, \begin{align*} \mathbb{P}\{\|Z_t-Z_s\|>\sum_{j=1}^m u^{1/\alpha_j}d_j(s,t)\}\le 2e^{-u},s,t\in T. \end{align*} For ambient priors $\mu_1,\ldots,\mu_m$, let $v_j(t):=d_j(t,t_0), \Phi_j(t):=\int_0^{4v_j(t)}(\log\frac{1}{\mu_j(B_{d_j}(t,r))})^{1/\alpha_j}dr$. We prove that, $\forall \delta\in(0,1)$, with probability at least $1-\delta$, simultaneously for all $t\in T$, \begin{align*} \|Z_t\|\le C_{m,\boldsymbol\alpha}\sum_{j=1}^m\{\Phi_j(t)+v_j(t)(\log(e/\delta))^{1/\alpha_j}\}. \end{align*} Here $\boldsymbol\alpha:=(\alpha_1,\ldots,\alpha_m)$ and $C_{m,\boldsymbol\alpha}$ depend only on $m$ and these tail orders. The result subsumes single-metric sub-Weibull processes of every positive order as the case $m=1$. In the Gaussian setting, it sharpens the pointwise upper bound of \citet{xu2026} by eliminating the logarithmic terms generated by dyadic peeling. The proof retains the index-wise costs of measure-generated admissible chains and synchronizes the regimes through a nested common refinement. Finally, we apply our theorems to stationary diffusion empirical processes and decoupled Gaussian chaos to obtain simultaneous pointwise envelope bounds, which can further be applied to other statistics problems.

math.PR↗

arXiv2026

OR-Transformer: Scaling Real-Time Decision-Making to 1,000 Items

Modern supply chain operations can require coordinating replenishment across thousands of heterogeneous items under correlated stochastic demand, heterogeneous lead times, and shared fixed ordering costs, yielding observation spaces exceeding $10^4$ dimensions. At this scale, rolling-horizon stochastic mixed-integer linear programs (MILPs) become prohibitively slow, while standard reinforcement learning (RL) methods face increasingly challenging credit assignment in high-dimensional action spaces. We introduce OR-Transformer, a deep reinforcement learning framework for joint replenishment under stochastic demand, with an item-permutation-equivariant Transformer architecture and pathwise-gradient training through the inventory dynamics. Across problem sizes up to 1,024 inventory items, OR-Transformer increasingly outperforms learning-based and rolling-horizon MILP baselines as scale grows. It also reduces online decision-making time by over 4 million times relative to MILP solvers, enabling real-time, large-scale deep RL in supply chain operations.

cs.LG↗

arXiv2026

Refined Thompson Learning for Adaptive Bandits: Power-Efficient Flexibility Scheduling Across Data Centers

The rapid growth of large-scale AI workloads in data centers has placed increasing pressure on power grids in recent years. Since power systems must continuously balance supply and demand, there is growing interests in leveraging data-center workload flexibility as a grid service. We propose a contextual restless multi-armed bandit (CRMAB) framework in which a grid operator requests load reductions without observing internal job-scheduling decisions. Under index-ability guarantee, each data center or physical machine is modeled as a Markov decision process (MDP) over a cyclic virtual-machine (VM) job queue, with unknown rewards and transition dynamics learned online using Thompson sampling and Whittle-index policies. To improve learning under sparse and noisy observations, the framework augments an adaptive Thompson--Whittle (TW) policy with domain-informed transition priors and gated prior mixing. In baseline experiments, the best adaptive refined variant achieves 91.4\% of the oracle reward after 100 rounds and 96.8\% after 1,000 rounds. Across a 16-setting stress test spanning different state-space sizes and levels of contextual noise, the best refined variant consistently outperforms the original TW policy with high confidence while remaining competitive with EXP4. A graph-based prior further incorporates data-center hardware constraints, including computing-resource limits. Overall, the results demonstrate the economic potential of data-center flexibility as a grid service and highlight the importance of high-quality, open-source AI workload traces for developing and evaluating such services.

cs.CE↗

arXiv2026

When Reasoning Narrows the Move: Diversity Collapse in LLM Game Play

Supervised fine-tuning (SFT) is widely used to adapt large language models to downstream tasks, but its effect on behavioral diversity in sequential decision-making remains under-explored. We study this question in a controlled suite of deterministic board games based on tic-tac-toe variants, where optimal actions are exactly computable and diversity can be measured directly. Across state-level evaluation, arena gameplay, and training trajectories, we find that reasoning-mode generation frequently suppresses action diversity without uniformly improving action accuracy. Furthermore, standard SFT improves accuracy but often induces premature diversity collapse, which exceeds what is minimally required by the accuracy-diversity tradeoff. We then show that action augmentation, which trains on all optimal actions per state rather than a single demonstrated action, would partially mitigates this effect. Our results identify narrow-support imitation as a source of policy collapse in LLM decision-making and suggest that preserving action support during SFT is important for maintaining exploratory behavior.

cs.CL↗

arXiv2026

Optimizing the Preconditioner: A Black-box Online-to-Nonconvex Conversion with Static Regret Minimization Oracles

We study whether stochastic nonconvex optimization can be reduced to ordinary static regret minimization in online convex optimization in a black-box manner. For smooth nonconvex objectives, our reduction maintains a predictable gradient tracker, while a black-box online learner selects a preconditioner that determines how this tracker is transformed into the update direction. The learner receives linear convex losses and is evaluated against a single fixed comparator over one undiscounted online game. For a $\beta$-smooth objective with range bounded by $M$ and an unbiased stochastic-gradient oracle with variance bounded by $\sigma^2$, we establish $$\frac{1}{T}\sum_{t=1}^T \mathbb E\!\left[\|\nabla f(x_t)\|_2^2\right] \lesssim \frac{\sigma\sqrt{M\beta}}{\sqrt T} + \frac{\sqrt{M\beta}\, \mathscr R_T(\mathcal A,I_d)}{T} + \frac{M\beta}{T}.$$ Consequently, any black-box OCO algorithm with $\mathscr R_T(\mathcal A,I_d)=O(\sqrt T)$ recovers the classical $O(\frac{1}{\sqrt{T}})$ convergence rate. We further show that the same black-box framework extends beyond the smooth setting to Lipschitz nonconvex objectives without Lipschitz continuous gradients. Importantly, this extension continues to rely only on an ordinary static-regret guarantee and requires no stronger notion of online regret. When the OCO oracle admits square-root static regret, the resulting conversion achieves the optimal $O(T^{-2/7})$ convergence rate for the corresponding Goldstein stationary point. These results resolve the open problem posed by Chen and Hazan (2024). More broadly, our framework separates optimizer design into gradient prediction and online preconditioner selection, providing a principled perspective on how adaptive optimization methods may be understood through static regret and applied in nonconvex optimization.

cs.LG↗

arXiv2026

Strategic Bargaining in Multi-Buyer Markets: Reinforcement Learning from Verifiable Rewards for LLM Negotiations

Negotiation is a fundamental strategic interaction in management science, characterized by agents attempting to reach agreements while protecting private information, such as reservation costs and hidden valuations. A prevalent yet complex scenario involves a single seller negotiating concurrently with multiple buyers, each possessing heterogeneous, private budgets. In such settings, constrained by a limited number of communication turns, the seller must balance exploring the broader market to discover the highest valuation with concentrating sufficient turns on a single target buyer to secure the best possible outcome. Our analysis reveals a significant gap in standard Large Language Models (LLMs): while these models are linguistically proficient, they fail to act as effective economic decision-makers. Specifically, they exhibit a failure to explore the buyer pool, often fixating on the current highest bid rather than strategically investigating the market to discover latent high valuations. In this paper, we propose a specialized training recipe using Reinforcement Learning from Verifiable Rewards (RLVR). By anchoring the reward function to objective economic outcomes, the strategic balance between market discovery and surplus extraction emerges natively through the learning process. Our results demonstrate that the trained seller undergoes a multi-stage strategic evolution, learning to leverage price anchoring and strategic probing to identify more profitable counterparties. The agent extracts a substantially higher surplus than frontier models by both improving its persuasive bargaining skills and consistently closing deals with high-value buyers. Finally, we show that our seller strategies generalize robustly to unseen buyer negotiation styles and budget distributions.

cs.LG↗

arXiv2026

Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation

Adaptive experiments for average treatment effects (ATE) require randomized allocations balancing valid inference with statistical efficiency. The oracle design is a covariate-dependent Neyman rule governed by unknown arm-conditional outcome variances. We investigate whether this sequential variance-estimation and allocation process can be amortized via in-context learning. We introduce Bayesian in-context experimenters: transformer policies trained to imitate a Bayesian posterior Neyman teacher. The teacher updates nonparametric beliefs over potential outcomes using experimental history to assign posterior Neyman treatment probabilities. This design converges to the oracle rule, supporting efficient ATE inference. Transformers constructively implement this mapping through attention-based sufficient statistics and projected gradient descent, imitating Bayesian updating for Gaussian-series priors. To address unknown outcome smoothness, we combine smoothness-indexed experimenters using a mixture-of-experts transformer. The gate acts as a hierarchical posterior over smoothness classes, concentrating on near-oracle experts. By bounding the complexity of the transformer class, we prove this amortized policy can be learned via empirical risk minimization using supervised pretraining. Experiments confirm accurate teacher imitation, adaptive allocation, and improved ATE precision over baselines.

cs.LG↗

arXiv2026

Semiparametric Efficiency in Sequential Experiments: Characterization and Design via Average Propensity

Modern experiments, including evaluations of AI-enabled services and platform interventions, often depart from independent and identically distributed (i.i.d.) sampling because assignments may be adaptive, balanced across covariates, or subject to rollout constraints such as exposure, fairness, and budget limits. This paper studies the efficiency benchmark for estimating causal targets in such sequential experiments. We show that every non-anticipating design induces an average propensity score, and we establish a semiparametric lower bound: for regular locally unbiased estimators, attainable precision is bounded by the i.i.d. efficiency benchmark evaluated at this induced score. The average propensity score thereby serves as a common benchmark and design target, allowing sequential experimental design to be viewed as choosing or learning an efficient allocation rule, with operational constraints entering through the admissible set when present. We then develop implementable batched adaptive designs that approach this benchmark through two complementary mechanisms. The first uses regression adjustment based on efficient influence functions; for general smooth estimands it attains the benchmark under standard nuisance-rate conditions, while for linear functionals of outcome means it achieves a sharp second-order rate. The second uses adaptive covariate balancing to attain the same benchmark through the assignment mechanism, enabling simple moment-based estimation. Both routes require only a small number of policy updates, making them compatible with delayed feedback and easier to monitor in operational deployments. Numerical experiments and an empirical study of AI medical-assistant evaluation demonstrate the practical efficiency gains, including in multi-treatment settings. Overall, the paper provides a unified framework for characterizing and designing efficient sequential experiments.

stat.ME↗

arXiv2026

Service-Induced Congestion in Memory-Constrained LLM Serving

In large language model (LLM) serving, each request accumulates persistent graphics processing unit (GPU) memory during service as its key-value cache grows with every generated token. Under high concurrency, aggregate memory usage therefore increases endogenously over time: the service process itself creates future capacity pressure. When memory capacity is exceeded, systems evict active requests, discarding cached state and restarting them later, which wastes computation and reduces throughput. We develop a discrete-time dynamical model of memory-constrained LLM inference that captures admission, memory growth, and eviction under continuous batching. In the saturated-input regime, the system admits both eviction-free fixed points and limit cycles with evictions. For homogeneous workloads, we show that the eviction-free equilibrium is unstable and that, except for a Lebesgue-measure-zero exact-capture set, the system converges to a unique worst-case limit cycle that is asymptotically stable outside this exceptional set, with throughput losses as large as 50%. For heterogeneous workloads, we prove a stability criterion in the two-class common-input setting and explain how the survival-polynomial mechanism generalizes to multiple classes and heterogeneous-input lengths. Under an input-dominated scaling regime, coprime decoding lengths stabilize the eviction-free equilibrium, while non-coprime lengths create synchronized modes that drive instability. These results characterize when workload heterogeneity desynchronizes completions and helps stabilize memory-constrained serving. More broadly, we identify service-induced congestion as a structural instability mechanism and derive scheduling design principles for sustaining high throughput.

math.OC↗

arXiv2026

Adaptive Inference for Resource-Constrained Dynamic Pricing

We study dynamic pricing over a finite selling horizon when limited resource capacity determines revenue and the observations available for inference at a prespecified price. Resource depletion can remove the target neighborhood from the feasible price set, changing the experiment generated by the pricing policy. We develop inference-aware re-solving controllers that check target-band feasibility before current covariates arrive and log the pricing mixture. Target-reserved and smooth controllers take population mean-pair geometry as a predeployment input; learned barycentric re-solving instead estimates stationary mean-consumption vectors of predeclared component kernels. On an affine binding-capacity family, an exact-input target-reserved controller assigning mass $t^{-\gamma}$ obtains an information clock of order $T^{1-\gamma}$ in probability, radius $O_p\{T^{-(1-\gamma)/2}\}$, and, under an exposed-face reward identity, a signed fluid-benchmark gap bounded above by $O(\log T+T^{1-\gamma})$. Under the exogenous affine-face condition, predeclared target support, and polynomial error spending with exponent greater than one, learned barycentric re-solving has a linear information clock in probability and an $O(\log T)$ signed-gap upper bound; centered local pricing has the same orders under slack capacity and global target optimality. An exact-input, target-compatible smooth alternative without reservation gives a linear clock in probability, an $O_p(T^{-1/2})$ deterministic-envelope radius with unconditional coverage and reporting probability tending to one, and an $O(\log^2 T)$ signed-gap upper bound. Boundary results show when physical support is lost and why a $1/t$ target branch yields only $O_p(1)$ information if it is the sole target-local source. The policy reports an interval when its prespecified support and information conditions hold and otherwise abstains.

stat.ML↗

arXiv2026

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons

Pairwise human-preference platforms such as Chatbot Arena have become central to large language model (LLM) evaluation, yet reliable task-specific ranking remains challenging. Global leaderboards mask task heterogeneity, while ranking each fine-grained task independently is unstable under sparse, imbalanced comparisons. We propose a low-rank framework for task-specific LLM ranking from sparse pairwise comparisons, modeling the task-by-model ability matrix $\Theta^\star \in \mathbb{R}^{d_t \times d_m}$ as low rank so that information is shared across related tasks while task-specific differences are preserved. We first develop a max-norm ($\ell_\infty$) accurate estimator for the latent scores, combining a convex initializer with alternating-minimization refinement, and prove task-wise top-$K$ recovery guarantees under sparse sampling. Our main contribution is an uncertainty quantification framework for task-specific ranking. We construct cross-fitted one-step debiased estimators for fixed score contrasts -- such as the task-specific ability gap between two models -- yielding asymptotically valid confidence intervals that attain the semiparametric efficiency bound. We then extend the inference to the high-dimensional ranking regime, where per-task ranks and top-$K$ membership are determined by many dependent score-gap hypotheses. Using Gaussian and multiplier-bootstrap calibration, we obtain simultaneous confidence sets for per-task ranks and valid top-$K$ membership tests across many tasks and models. Experiments on synthetic data and Chatbot Arena show that low-rank sharing improves sample efficiency over independent task-wise Bradley-Terry estimation and produces tighter, better-calibrated ranking certificates, with the largest gains in the sparse regime typical of real LLM benchmarks.

stat.ME↗

arXiv2026

Reliability and Effectiveness of Autonomous AI Agents in Supply Chain Management

This paper studies autonomous generative AI agents in multi-echelon supply chains using the MIT Beer Game. We identify four inference-time levers that shape performance: model selection, policies and guardrails, centralized data sharing, and prompt engineering. Model capability is the dominant factor: an out-of-the-box reasoning model exceeds human-level performance, and optimized reasoning models reduce costs by up to 67% relative to human teams. However, strong average performance masks substantial reliability risks. We introduce agent bullwhip: the amplification of run-to-run decision instability in autonomous multi-echelon systems. A central component is decision bullwhip, the portion of order variability generated by stochastic agent decisions rather than by changes in customer demand. We show that decision instability can amplify both across facilities at a fixed point in time and within the same facility over time, even when the demand path is held fixed. Repeated sampling, a natural test-time remedy, fails to meaningfully reduce this instability, suggesting that reliability requires changing the underlying decision policy rather than merely averaging over model outputs. To address this limitation, we propose a Group Relative Policy Optimization (GRPO)-based reinforcement-learning post-training framework that trains a shared base LLM using system-level supply-chain rewards. Post-training substantially reduces tail events, curtails agent bullwhip, and improves the reliability of autonomous supply-chain agents.

cs.AI↗

arXiv2026

Model-Based Reinforcement Learning with Double Oracle Efficiency in Policy Optimization and Offline Estimation

Reinforcement learning (RL) in large environments often suffers from severe computational bottlenecks, as conventional regret minimization algorithms require repeated, costly calls to planning and statistical estimation oracles. While recent advances have explored offline oracle-efficient algorithms, their computational complexity typically scales with the cardinality of the state and action spaces, rendering them intractable for large-scale or continuous environments. In this paper, we address this fundamental limitation by studying offline oracle-efficient episodic RL through the lens of log-barrier and log-determinant regularization. Specifically, for tabular Markov Decision Processes (MDPs), we propose a novel algorithm that achieves the optimal $\tilde{O}(\sqrt{T})$ regret bound while requiring only $O(H\log\log T)$ calls to both the offline statistical estimation and planning oracles when $T$ is known and $O(H\log T)$ calls when $T$ is unknown. Crucially, this oracle complexity is entirely independent of the size of the state and action spaces. This strict independence drastically reduces the planning oracle complexity, representing a substantial improvement over existing offline oracle-efficient algorithms (Qian et al., 2024). Furthermore, we demonstrate the versatility of our framework by generalizing the algorithm to linear MDPs featuring infinite state spaces and arbitrary action spaces. We prove that this generalized approach successfully attains meaningful sub-linear regret. Consequently, our work yields the first doubly oracle-efficient (i.e., efficient with respect to both statistical estimation and policy optimization) regret minimization algorithm capable of solving MDPs with infinite state and action spaces, significantly expanding the boundaries of computationally tractable RL.

cs.LG↗

arXiv2026

Instructing LLMs to Negotiate using Reinforcement Learning with Verifiable Rewards

The recent advancement of Large Language Models (LLMs) has established their potential as autonomous interactive agents. However, they often struggle in strategic games of incomplete information, such as bilateral price negotiation. In this paper, we investigate if Reinforcement Learning from Verifiable Rewards (RLVR) can effectively teach LLMs to negotiate. Specifically, we explore the strategic behaviors that emerge during the learning process. We introduce a framework that trains a mid-sized buyer agent against a regulated LLM seller across a wide distribution of real-world products. By grounding reward signals directly in the maximization of economic surplus and strict adherence to private budget constraints, we reveal a novel four-phase strategic evolution. The agent progresses from naive bargaining to using aggressive starting prices, moves through a phase of deadlock, and ultimately develops sophisticated persuasive skills. Our results demonstrate that this verifiable training allows a 30B agent to significantly outperform frontier models over ten times its size in extracting surplus. Furthermore, the trained agent generalizes robustly to stronger counterparties unseen during training and remains effective even when facing hostile, adversarial seller personas.

cs.AI↗

arXiv2026

LLM Evaluation as Tensor Completion: Low Rank Structure and Semiparametric Efficiency

Large language model (LLM) evaluation platforms increasingly rely on pairwise human judgments. These data are noisy, sparse, and non-uniform, yet leaderboards are reported with limited uncertainty quantification. We study this as semiparametric inference for a low-rank latent score tensor observed through pairwise comparisons under Bradley-Terry-Luce-type models. This places LLM evaluation in a new tensor completion setting with structured observations, non-uniform sampling, and pairwise contrasts. Our target is a smooth functional $\psi(T^\star)$, including linear estimands such as ability gaps and nonlinear ones such as win probabilities. We derive the information operator on the low-rank tangent space, the efficient influence function, and the semiparametric efficiency bound, then construct a one-step debiased estimator with asymptotic normality. A central challenge is that the information operator is anisotropic and does not commute with the tangent-space projection, creating a bottleneck absent from isotropic models. We introduce a score-whitening method that equalizes local Fisher information and restores stable inference at the optimal sample-complexity scale. Our results provide a principled framework for uncertainty quantification in LLM evaluation and more broadly for inference on low-rank structures from pairwise data.

stat.ME↗