#01Sep 1, 2026
math.PR
Pointwise Majorization for sub-Weibull and Mixed Tail Processes with Applications in Quadratic Chaos and Ergodic Diffusions
Haichen Hu, David Simchi-Levi
Classical chaining controls an indexed stochastic process through a single worst-case bound, which can obscure substantial variation across the index set. We establish the first simultaneous pointwise majorization theory for Banach-valued processes with sub-Weibull or two-metric mixed-tail increments. For an anchored sub-Weibull process on a separable index space, write $v(t):=d(t,t_0)$. Given a reference measure $μ$, the envelope at $t$ is governed by the pointwise Fernique-Talagrand functional of order $α$, $Φ_{μ,d}^{(α)}(t):=\int_0^{4v(t)}(\log\frac{1}{μ(B_d(t,r))})^{1/α}dr$. $\forall δ\in(0,1)$, we obtain that $$ \mathbb{P}(\|Z_t\|\lesssim\{Φ_{μ,d}^{(α)}(t)+v(t)(\log(e/δ))^{1/α}\},\forall t)\ge 1-δ. $$ Our bound is determined by the pointwise complexity $Φ_{μ,d}^{(α)}$ rather than a global quantity. The result holds for every $α>0$ and does not involve dyadic logarithmic terms from peeling. For mixed tail processes, with fixed measures $μ_1,μ_2$ and $v_j(t):=d_j(t,t_0)$, $Φ_j(t):=\int_0^{4v_j(t)}(\log\frac{1}{μ_j(B_{d_j}(t,r))})^{1/α_j}dr, j=1,2$, for any $δ\in(0,1)$, we show that $$\mathbb{P}(\|Z_t\|\lesssim\sum_{j=1}^2\{Φ_j(t)+v_j(t)(\log\frac{e}δ)^{1/α_j}\},\forall t)\ge 1-δ.$$ Although the two regimes are coupled in the mixed tail condition, each retains its own pseudo-metric, reference measure, pointwise Fernique-Talagrand functional, and tail exponent. The proof tracks the index-wise costs of measure-generated admissible chains and synchronizes them through a nested common refinement. For applications, we derive matrix-specific bounds for centered quadratic chaos under pseudo-metrics induced by the operator and Frobenius norms, and observable-specific finite-time bounds for diffusion empirical processes.
#02Sep 1, 2026
cs.LG
NashDreamer: Model-Based Reinforcement Learning for Zero-Sum Imperfect-Information Games
Tomáš Holeček, Viliam Lisý
Model-based reinforcement learning (MBRL) has achieved remarkable results in single-agent domains, yet its extension to competitive imperfect information games (IIGs) remains underexplored. In multi-agent settings, opponent-induced non-stationarity complicates the learning process, and decentralized model learning faces severe identifiability barriers, which we argue make centralized model learning a mathematical necessity. Building on this analysis, we propose NashDreamer, a principled MBRL framework for two-player zero-sum IIGs. It introduces a centralized Multi-Agent Recurrent State-Space Model (MARSSM) that decouples environment dynamics from the effect of players' strategies on their individual observations. NashDreamer is designed to use arbitrary policy gradient algorithms and inherits their convergence guarantees towards Nash equilibria under an idealized model. Empirical evaluations across four benchmark games demonstrate that NashDreamer substantially improves sample efficiency over model-free baselines early in the training. Finally, we theoretically analyze the architecture's optimization landscape, identifying the vulnerability of the Dreamer family of algorithms to posterior collapse in stochastic environments. We leave it as an open challenge.
#03Sep 1, 2026
cs.LG
Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks
Jing Xiao, Xinhai Chen, Qinglin Wang and 5 more
Training Physics-Informed Neural Networks (PINNs) requires jointly optimizing physics residual and initial/boundary condition loss terms, which often induce conflicting gradients. Gradient surgery methods mitigate this issue by constructing directions from loss-specific gradients to reduce conflict before optimizer transformation. However, even when the constructed direction is conflict-free, this property may not be preserved after optimizer transformation. Let $a_t$ denote the direction constructed by gradient surgery, $u_t$ the optimizer proposal, and $\mathcal{C}_t$ the conflict-free cone induced by the loss-specific gradients. We show that modern optimizers can transform $a_t$ through mechanisms such as historical state, adaptive scaling, preconditioning, or decoupled weight decay, so $a_t \in \mathcal{C}_t$ does not generally imply $u_t \in \mathcal{C}_t$. We refer to this optimizer-induced discrepancy in conflict-freeness between $a_t$ and $u_t$ as Gradient-Update Mismatch (GUM). Accordingly, we propose Gradient-Update Alignment (GUA), which projects $u_t$ onto $\mathcal{C}_t$ to obtain the aligned update $p_t$ and applies $p_t$ to the parameters. When the optimizer maintains internal state, GUA further adjusts this state toward targets reconstructed from the applied update. We conduct extensive experiments and find that GUM is widespread across momentum, adaptive, and curvature-based optimizers, with conflict rates reaching up to 86.3%. Across all PINN settings, GUA achieves conflict-free applied updates and consistently improves various gradient surgery methods, reducing the relative $L_2$ error by up to 98.2% in individual settings. Data and code are available at https://github.com/JingXiao10/GUA.
#04Sep 1, 2026
stat.ML
Variable Selection for Feature-Based Newsvendor
Zhaoliang Yuan, Jie Wang
Feature-based newsvendor models use observable covariates to tailor inventory decisions, aiming to balance holding and shortage costs under demand uncertainty. However, high-dimensional feature sets often hinder interpretability and inflate data collection and implementation costs. This paper studies variable selection for the feature-based newsvendor problem under a hard cardinality constraint on the number of selected features. We formulate the resulting $\ell_0$-constrained empirical newsvendor problem with $\ell_2$-regularization, establish its computational hardness, and develop a mixed-integer second-order cone programming reformulation that strengthens the standard Big-$M$ formulation. To enable scalability beyond exact optimization, we develop a randomized-rounding algorithm with a bi-criteria guarantee and a greedy heuristic. Statistically, we provide theoretical analysis of the resulting sparse policy estimator, including finite-sample estimation error, out-of-sample risk bounds, and support recovery guarantees. Extensive experiments on both synthetic and real data illustrate the computational and statistical trade-offs among various baselines. Our results demonstrate that the proposed variable selection framework achieves competitive out-of-sample operational costs while using substantially fewer covariates.
#05Sep 1, 2026
cs.CV
H3-World: Turning Language Understanding into World Control
Danze Chen, Zeqing Wang, Ziyue Lin and 2 more
We present H3-World, an efficient framework that turns the 33B MiniMax-H3 video generator into an interactive world model. Our key finding is that, as large video generators become more capable, language is emerging as a natural interface for control. MiniMax-H3, for example, already supports zero-shot control of character behavior and camera motion through natural-language instructions. Building on this, H3-World turns this coarse language interface into precise, temporally grounded world control, without introducing dedicated action modules. Specifically, we represent each action as a structured combination of character and camera instructions, and align them with the corresponding temporal video latents. To make the control temporally precise, we further introduce temporal attention routing, which restricts each instruction to its intended time interval and reduces control leakage across actions. Importantly, H3-World directly reuses the semantic representations learned during large-scale video pretraining and requires only lightweight adaptation. With only 8,000 gameplay samples, 10,000 LoRA optimization steps, and 0.199% trainable parameters, H3-World achieves effective character and camera control while preserving strong generation quality. It also generalizes to unseen scenarios. These results show that the control capabilities emerging in large video generators can be efficiently transformed into interactive world control.