arXiv subjects

Jose Blanchet

Publications and source records attributed to Jose Blanchet.

At least 37 records · Page 2Linked to original sources

arXiv2026

ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

cs.LG↗

arXiv2026

There and Back Again: Bidirectional Diffusion Bridges for Multimodality Translation

Multimodality translation (e.g., text-to-image) is a core generative AI task. However, existing approaches (1) follow generative paths that do not directly represent the source modality, limiting the flexibility of some sampling algorithms; and (2) are unidirectional, preventing inversion (e.g., image-to-text). We propose BIT: Bidirectional Image-Text Diffusion Bridges. In contrast to previous approaches, BIT starts directly from text and interpolates into images, providing (1) a source-aware generative path that enables diverse and flexible sampling algorithms; and (2) an endpoint-conditioned process that can be traversed from image to text, providing a unified, bidirectional generative framework. BIT is derived through stochastic calculus, yielding SDE forms amenable to simulation and tractable loss functions that scale to high dimensions. Our experiments show that BIT is competitive with denoising-diffusion and deterministic-flow baselines, and outperforms them on several vision--language and natural-science evaluations.

cs.LG↗

arXiv2026

Testing Fairness with Utility Tradeoffs: A Wasserstein Projection Approach

Ensuring fairness in data driven decision making has become a central concern across domains such as marketing, lending, and healthcare, but fairness constraints often come at the cost of utility. We propose a statistical hypothesis testing framework that jointly evaluates approximate fairness and utility, relaxing strict fairness requirements while ensuring that overall utility remains above a specified threshold. Our framework builds on the strong demographic parity (SDP) criterion and incorporates a utility measure motivated by the potential outcomes framework. The test statistic is constructed via Wasserstein projections, enabling auditors to assess whether observed fairness-utility tradeoffs are intrinsic to the algorithm or attributable to randomness in the data. We show that the test is computationally tractable, interpretable, broadly applicable across machine learning models, and extendable to more general settings. We apply our approach to multiple real-world datasets, offering new insights into the fairness-utility tradeoff through the perspective of statistical hypothesis testing.

cs.CY↗

arXiv2026

Sobolev Regularized Score Difference Estimation in Diffusion Models

Estimating the difference of two Stein's score functions is a fundamental problem in generative modeling. In particular, score differences arise naturally in transfer learning, where the score difference provides the mechanism for adapting a pre-trained model to a new target distribution, and in diffusion model-based post-training methods such as discriminator guidance. Existing estimators for score differences in these settings either lack of statistical consistency or are difficult to scale up in high-dimensions. We propose a statistically consistent and scalable estimator for score differences based on Sobolev regularization, which plays a crucial role in ensuring consistency and stablizing the training in the small-sample regime. Mathematically, we establish a convergence rate of $O(n^{-\frac{s-1}{d+2s-2}})$ where $d$ is the dimension and $s$ denotes the smoothness of the underlying densities, and provide a minimax lower bound of $\tildeΩ(n^{-\frac{2(s-1)}{d+2s}})$ (in mean-squared error). Empirically, our estimator exhibits significantly improved stability in small-sample regimes compared to existing methods. We demonstrate its effectiveness on real-world tasks, including transfer learning for ECG signal generation, where it substantially outperforms non-regularized score difference estimators in downstream classification performance.

stat.ML↗

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.

cs.LG↗

arXiv2026

Wasserstein Projection Tests: Higher-Order Asymptotics and Connections to Empirical Likelihood

Tests of moment restrictions can be constructed by projecting the empirical distribution onto the set of laws satisfying the null. Wasserstein projection (WP) performs this projection by transporting mass in the sample space, rather than only reweighting observed atoms as in empirical likelihood (EL), and therefore incorporates both the ground geometry and the local variation of the moment function. Existing WP theory provides a first-order null limit but does not quantify finite-sample calibration or distinguish tests with the same limiting local power. We derive stochastic expansions of the rescaled WP statistic under the null and under Pitman-type local alternatives, identifying its order-$n^{-1/2}$ correction with a uniform remainder of order $\widetilde{O}_p(n^{-1})$. The resulting Edgeworth theory gives an order-$\widetilde{O}(n^{-1})$ size error for the plug-in WP test and an explicit order-$n^{-1/2}$ correction to local power. For scalar moments under local location shifts, WP, EL, and Hotelling's $T^2$ have the same first-order power, whereas their second-order ranking is determined by derivative-based curvature for WP and value-based skewness for EL. Extending the expansion by one further order, we construct two Bartlett-type corrections that improve coverage accuracy to $\widetilde{O}(n^{-3/2})$. Finally, we develop a certified localized dual algorithm that controls numerical error in the test decision. A theory-guided smooth fairness experiment using a common asymptotic chi-square reference quantile finds WP power gains over the corresponding EL and $T^2$ tests in the derivative-curvature regime predicted by the comparison theory.

math.ST↗

arXiv2026

Bayesian Distributionally Robust Merton Problem with Nonlinear Wasserstein Projections

We revisit Merton's continuous-time portfolio selection through a data-driven, distributionally robust lens. Our aim is to tap the benefits of frequent trading over short horizons while acknowledging that drift is hard to pin down, whereas volatility can be screened using realized or implied measures for appropriately selected assets. Rather than time-rectangular distributional robust control -- which replenishes adversarial power at every instant and induces over-pessimism -- we place a single ambiguity set on the drift prior within a Bayesian Merton model. This prior-level ambiguity preserves learning and tractability: a minimax swap reduces the robust control to optimizing a nonlinear functional of the prior, enabling Karatzas and Zhao \cite{KZ98}-type's closed-form evaluation for each candidate prior. We then characterize small-radius worst-case priors under Wasserstein uncertainty via an explicit asymptotically optimal pushforward of the nominal prior, and we calibrate the ambiguity radius through a nonlinear Wasserstein projection tailored to the Merton functional. Synthetic and real-data studies demonstrate reduced pessimism relative to DRC and improved performance over myopic DRO-Markowitz under frequent rebalancing.

math.OC↗

arXiv2026

Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control

We study diffusion control problems under parameter uncertainty. Controllers based on plug-in estimation can be brittle due to potential distribution shifts. Bayesian control with a prior on the parameters offers a formulation with beliefs about such shifts. However, as with any Bayesian model, the prior may be misspecified. To mitigate misspecification and reduce over-pessimism compared to classical robust control approaches (e.g. \citet{hansen2008robustness}), we propose a distributionally robust Bayesian control (DRBC) formulation in which an adversary perturbs the prior within a divergence neighborhood of a baseline prior. We develop a strong duality result that reduces the distributionally robust prior evaluation to a low-dimensional optimization and yields a practical simulation-based policy evaluation and learning procedure with structured policy parameterizations. We validate the efficiency of the algorithm on a synthetic linear-quadratic control example and real-data portfolio selection.

math.OC↗

arXiv2026

Bounding adapted Wasserstein metrics

The Wasserstein distance $\mathcal{W}_p$ is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well studied in recent years. The adapted Wasserstein distance $\mathcal{A}\mathcal{W}_p$ extends this theory to laws of discrete time stochastic processes in their natural filtrations, making it particularly well suited for analyzing time-dependent stochastic optimization problems. While the topological differences between $\mathcal{A}\mathcal{W}_p$ and $\mathcal{W}_p$ are well understood, their differences as metrics remain largely unexplored beyond the trivial bound $\mathcal{W}_p\lesssim \mathcal{A}\mathcal{W}_p$. This paper closes this gap by providing upper bounds of $\mathcal{A}\mathcal{W}_p$ in terms of $\mathcal{W}_p$ through investigation of the smooth adapted Wasserstein distance. Our upper bounds are explicit and are given by a sum of $\mathcal{W}_p$, Eder's modulus of continuity and a term characterizing the tail behavior of measures. As a consequence, upper bounds on $\mathcal{W}_p$ automatically hold for $\mathcal{AW}_p$ under mild regularity assumptions on the measures considered. A particular instance of our findings is the inequality $\mathcal{A}\mathcal{W}_1\le C\sqrt{\mathcal{W}_1}$ on the set of measures that have Lipschitz kernels. Our work also reveals how smoothing of measures affects the adapted weak topology. In fact, we find that the topology induced by the smooth adapted Wasserstein distance exhibits a non-trivial interpolation property, which we characterize explicitly: it lies in between the adapted weak topology and the weak topology, and the inclusion is governed by the decay of the smoothing parameter.

math.PR↗

arXiv2026

Wasserstein Distributionally Robust Regret Optimization

Distributionally robust optimization (DRO) is widely used for decision-making under uncertainty, but its adversarial focus on worst-case loss can lead to overly conservative policies. To mitigate this, we study ex-ante Distributionally Robust Regret Optimization (DRRO) with Wasserstein ambiguity sets, designed to balance robustness with upside potential. We develop a theory of Wasserstein DRRO (WDRRO) paralleling Wasserstein DRO. Under smoothness and regularity, WDRRO selects among ERM optima by a first-order gradient-discrepancy rule. If the ERM optimizer is unique, first-order sensitivity vanishes and a second-order expansion governs deviations. For convex quadratics ERM and DRRO coincide for any radius. We then study regimes where these assumptions fail: nondifferentiable max-affine losses, discrete references, and larger radii, where WDRRO can differ from ERM and WDRO. We show that computing WDRRO regret is NP-hard even without bilinear terms. Nevertheless, we develop exact algorithms, a tractable convex relaxation with guarantees, and experiments showing tightness and loss-dependent behavior.

math.OC↗

arXiv2026

Wasserstein Distributionally Robust Regret Optimization for Reinforcement Learning from Human Feedback

Reinforcement learning from human feedback (RLHF) is a central post-training tool for aligning large language models, but its training reward is only a learned proxy for true human utility. This creates a decision problem under objective misspecification: the policy is optimized against an estimated reward, while deployment performance is governed by an unobserved population preference. The resulting gap leads to reward over-optimization, where proxy reward keeps improving after true quality deteriorates. We propose distributionally robust regret optimization (DRRO) for RLHF with a Wasserstein ambiguity set over reward laws, using promptwise $\ell_p$ distances between reward vectors as transport costs. Unlike standard distributionally robust optimization, which pessimizes worst-case value, DRRO pessimizes worst-case regret relative to the best policy under the same plausible reward perturbation. We show that the expressive-policy problem decomposes into promptwise regret problems. For each prompt, the inner adversary has a dual-norm closed form; under the $\ell_1$ transport cost used by our algorithm, the optimizer has a water-filling structure. These results lead to a practical policy-gradient algorithm that adds a simple sampled bonus to GRPO-style training. Theory and experiments both show that DRRO is less over-pessimistic than standard DRO and mitigates over-optimization more effectively than existing baselines.

cs.LG↗

arXiv2026

Rates of Convergence to Stationarity for Reflected Brownian Motion

We provide the first rate of convergence to stationarity analysis for reflected Brownian motion (RBM) as the dimension grows under some uniformity conditions. In particular, if the underlying routing matrix is uniformly contractive, uniform stability of the drift vector holds, and the variances of the underlying Brownian motion (BM) are bounded, then we show that the RBM converges exponentially fast to stationarity with a relaxation time of order $O(d^4\log(d)^3)$ as the dimension $d\to\infty$. Our bound for the relaxation time follows as a corollary of the nonasymptotic bound we obtain for the initial transient effect, which is explicit in terms of the RBM parameters.

math.PR↗

arXiv2026

Statistical Inference for Stochastic Gradient Descent: Beyond Finite Variance

Stochastic gradient descent (SGD) is foundational to large-scale statistical learning and stochastic optimization. However, in some modern statistical learning problems, stochastic gradients can exhibit infinite-variance behavior. Consequently, classical inference methods for SGD that rely on a finite-variance assumption break down. We develop a model-agnostic methodology for constructing confidence regions from SGD iterates in both the finite- and infinite-variance regimes. We first show that Polyak--Ruppert averaging has an asymptotic directional scale no larger than that of the fastest-rate final iterate, analogous to its lower asymptotic variance in the finite-variance setting. Accordingly, we focus our inference methodology on the Polyak--Ruppert averaged estimator. Specifically, we establish a joint central limit theorem for this estimator and an empirical second-moment normalizer from the same iterates. This joint limit yields a self-normalized statistic in which the leading tail-dependent scaling terms cancel. We then use subsampling to estimate the relevant quantiles, avoiding explicit estimation of nuisance parameters including tail indices, slowly varying functions, or stable-law parameters. The resulting confidence regions are straightforward to implement and asymptotically valid in both the finite- and infinite-variance regimes. Empirical studies show reliable coverage in various settings, supporting the proposed method as a practical tool for uncertainty quantification in stochastic optimization.

stat.ML↗

arXiv2026

Distributionally Robust Reinforcement Learning with Interactive Data Collection: Fundamental Hardness and Near-Optimal Algorithms

The sim-to-real gap, which represents the disparity between training and testing environments, poses a significant challenge in reinforcement learning (RL). A promising approach to addressing this challenge is distributionally robust RL, often framed as a robust Markov decision process (RMDP). In this framework, the objective is to find a robust policy that achieves good performance under the worst-case scenario among all environments within a pre-specified uncertainty set centered around the training environment. Unlike previous work, which relies on a generative model or a pre-collected offline dataset enjoying good coverage of the deployment environment, we tackle robust RL via interactive data collection, where the learner interacts with the training environment only and refines the policy through trial and error. In this robust RL paradigm, two main challenges emerge: managing distributional robustness while striking a balance between exploration and exploitation during data collection. Initially, we establish that sample-efficient learning without additional assumptions is unattainable owing to the curse of support shift; i.e., the potential disjointedness of the distributional supports between the training and testing environments. To circumvent such a hardness result, we introduce the vanishing minimal value assumption to RMDPs with a total-variation (TV) distance robust set, postulating that the minimal value of the optimal robust value function is zero. We prove that such an assumption effectively eliminates support shift pathologies for RMDPs with a TV distance robust set, and present an algorithm with near-optimal sample complexity. To demonstrate the breadth of our framework, we extend our algorithm and theory to new robust set formulations and robust Markov games. To illustrate the operational relevance, we apply our algorithm to data-driven robust inventory control.

cs.LG↗

arXiv2026

Lipschitz Regularity in Wasserstein Robust Stochastic Optimal Control

Robust Markov decision processes provide a principled framework for protecting sequential decision-making against transition-law misspecification and have attracted substantial recent research interest. As in non-robust stochastic optimal control, an important question is whether the robust value function is sufficiently regular for approximation and learning. This paper studies Lipschitz regularity of optimal value functions for Wasserstein robust stochastic optimal control on possibly unbounded Polish state spaces under an infinite-horizon discounted reward criterion. We consider two robustness formulations: a kernel-robust model, in which the adversary perturbs the next-state distribution within a Wasserstein ball around a nominal transition kernel, and a noise-robust model, in which the adversary perturbs the driving noise of the state transition dynamics. In the non-robust setting, Lipschitz rewards and Lipschitz transition dynamics do not, in general, imply a Lipschitz value function. In contrast, we show that in these Wasserstein robust formulations, Lipschitz assumptions on the model primitives yield Lipschitz robust value functions. Thus, Wasserstein robustness not only protects against misspecification but also regularizes the Bellman fixed point, providing stability relevant to discretization, value-function approximation, estimation, and learning.

math.OC↗

arXiv2026

TERMS-Bench: Diagnosing LLM Negotiation Agents Beyond Deal Rate

Negotiation is a central mechanism of economic exchange, shaping markets, procurement, labor agreements, and resource allocation. It is also a canonical testbed for agentic language models, requiring multi-turn interaction under hidden preferences, strategic communication, and binding constraints. These properties make negotiation hard to evaluate: unlike math or code, it has no intrinsic verifier. Existing LLM negotiation evaluations rely on LLM-vs.-LLM interaction or aggregate outcomes such as deal rate, leaving failures opaque. We introduce Terms-Bench, short for Testbed for Economic Reasoning in Multi-turn Strategy, a Bayesian-game framework that makes the environment itself the verifier by specifying the counterpart's latent type, policy, and payoff structure. We instantiate it in bilateral price negotiation, where the counterpart's private state and simulator policy are hidden from the agent but observable to the evaluator. This turns the counterpart from a black-box opponent into a diagnostic instrument, enabling agent-attributable failure analysis and oracle-reference optimality gaps. Evaluating 13 LLM agents spanning frontier systems from major providers, Terms-Bench turns negotiation evaluation from aggregate ranking into actionable diagnosis: where agents fail, why they fail, and what to strengthen. Empirically, frontier models saturate deal rate yet diverge in surplus extraction, cue use, belief calibration, and compliance, revealing agent-specific bargaining bottlenecks masked by prior benchmarks.

cs.GT↗

arXiv2026

Fast Convergence of Policy Regret in Learning Stochastic Optimal Control

Policy learning in modern operations environments faces a fundamental tension between limited operational data and the large, often continuous, state and action spaces over which good decisions must be identified and deployed. We study value-based policy learning in stochastic optimal control: a greedy policy induced by an estimate of the optimal action-value function $Q^*$ is deployed, and its performance is measured by regret. The empirical success of this approach calls for statistical insight into the structures that enable fast regret convergence. We show that, in continuous action spaces, fast policy learning is induced by three geometric structures: a growth exponent $p$, which quantifies how quickly $Q^*$ separates suboptimal actions from its maximizers; a margin-mass exponent $m$, which controls how much deployment mass lies on states with weak growth; and an action-wise regularity exponent $q$, which measures the smoothness of the $Q^*$-estimation error across actions. Given a $n^{-1/2}$-accurate estimator of $Q^*$, we show that the minimax-optimal policy regret convergence rate is \[ \widetildeΘ\left( n^{-\min\left\{\frac{p}{2(p-q)},\frac{m+1}{2m}\right\}} \right), \] up to a logarithmic factor at the boundary between the two regimes. The exponent $q$ is crucial: $q>0$ yields faster-than-$n^{-1/2}$ regret. This regime is natural in operations applications. In particular, we verify $q>0$ under mild regularity conditions in dynamic inventory control and service allocation examples, while the mechanism underlying this fast rate regime extends beyond these settings.

math.OC↗

arXiv2026

Why is the strength of an elastomeric polymer network so low?

Experiments have long shown that a polymer network of covalent bonds commonly ruptures at a stress that is orders of magnitude lower than the strength of the covalent bonds. Here we investigate this large reduction in strength by coarse-grained molecular dynamics simulations. We show that the network ruptures by sequentially breaking a small fraction of bonds, and that each broken bond lies on the minimum "shortest path". The shortest path is the path of the fewest bonds that connect two monomers at the opposite ends of the network. As the network is stretched, the minimum shortest path straightens and bears high tension set by covalent bonds, while most strands off the path deform by entropic elasticity. After a bond on the minimum shortest path breaks, the process repeats for the next minimum shortest path. As the network is stretched and bonds are broken, the scatter in lengths of the shortest paths first narrows, causing stress to rise, and then broadens, causing stress to decline. This sequential breaking of a small fraction of bonds causes the network to rupture at a stress that is orders of magnitude below the strength of the covalent bonds.

cond-mat.soft↗