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We study the problem of efficiently computing optimal strategies in asymmetric leader-follower games repeated a finite number of times, which presents a different set of technical challenges than the infinite-horizon setting. More precisely, we give efficient algorithms for finding approximate Stackelberg equilibria in finite-horizon repeated two-player games, along with rates of convergence depending on the horizon $T$. We give two algorithms, one computing strategies with an optimal $\frac{1}{T}$ rate at the expense of an exponential dependence on the number of actions, and another (randomized) approach computing strategies with no dependence on the number of actions but a worse dependence on $T$ of $\frac{1}{T^{0.25}}$. Both algorithms build upon a linear program to produce simple automata leader strategies and induce corresponding automata best-responses for the follower. We complement these results by showing that approximating the Stackelberg value in three-player finite-horizon repeated games is a computationally hard problem via a reduction from the balanced vertex cover problem.

Bayesian optimization (BO) is a widely popular approach for the hyperparameter optimization (HPO) in machine learning. At its core, BO iteratively evaluates promising configurations until a user-defined budget, such as wall-clock time or number of iterations, is exhausted. While the final performance after tuning heavily depends on the provided budget, it is hard to pre-specify an optimal value in advance. In this work, we propose an effective and intuitive termination criterion for BO that automatically stops the procedure if it is sufficiently close to the global optimum. Our key insight is that the discrepancy between the true objective (predictive performance on test data) and the computable target (validation performance) suggests stopping once the suboptimality in optimizing the target is dominated by the statistical estimation error. Across an extensive range of real-world HPO problems and baselines, we show that our termination criterion achieves a better trade-off between the test performance and optimization time. Additionally, we find that overfitting may occur in the context of HPO, which is arguably an overlooked problem in the literature, and show how our termination criterion helps to mitigate this phenomenon on both small and large datasets.

Optimal execution is a sequential decision-making problem for cost-saving in algorithmic trading. Studies have found that reinforcement learning (RL) can help decide the order-splitting sizes. However, a problem remains unsolved: how to place limit orders at appropriate limit prices? The key challenge lies in the "continuous-discrete duality" of the action space. On the one hand, the continuous action space using percentage changes in prices is preferred for generalization. On the other hand, the trader eventually needs to choose limit prices discretely due to the existence of the tick size, which requires specialization for every single stock with different characteristics (e.g., the liquidity and the price range). So we need continuous control for generalization and discrete control for specialization. To this end, we propose a hybrid RL method to combine the advantages of both of them. We first use a continuous control agent to scope an action subset, then deploy a fine-grained agent to choose a specific limit price. Extensive experiments show that our method has higher sample efficiency and better training stability than existing RL algorithms and significantly outperforms previous learning-based methods for order execution.

We consider prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. This semi-adversarial setting includes (at the extremes) the classical i.i.d. setting, when the unknown constraint set is restricted to be a singleton, and the unconstrained adversarial setting, when the constraint set is the set of all distributions. The Hedge algorithm -- long known to be minimax (rate) optimal in the adversarial regime -- was recently shown to be simultaneously minimax optimal for i.i.d. data. In this work, we propose to relax the i.i.d. assumption by seeking adaptivity at all levels of a natural ordering on constraint sets. We provide matching upper and lower bounds on the minimax regret at all levels, show that Hedge with deterministic learning rates is suboptimal outside of the extremes, and prove that one can adaptively obtain minimax regret at all levels. We achieve this optimal adaptivity using the follow-the-regularized-leader (FTRL) framework, with a novel adaptive regularization scheme that implicitly scales as the square root of the entropy of the current predictive distribution, rather than the entropy of the initial predictive distribution. Finally, we provide novel technical tools to study the statistical performance of FTRL along the semi-adversarial spectrum.

Spatial data can exhibit dependence structures more complicated than can be represented using models that rely on the traditional assumptions of stationarity and isotropy. Several statistical methods have been developed to relax these assumptions. One in particular, the "spatial deformation approach" defines a transformation from the geographic space in which data are observed, to a latent space in which stationarity and isotropy are assumed to hold. Taking inspiration from this class of models, we develop a new model for spatially dependent data observed on graphs. Our method implies an embedding of the graph into Euclidean space wherein the covariance can be modeled using traditional covariance functions such as those from the Mat\'{e}rn family. This is done via a class of graph metrics compatible with such covariance functions. By estimating the edge weights which underlie these metrics, we can recover the "intrinsic distance" between nodes of a graph. We compare our model to existing methods for spatially dependent graph data, primarily conditional autoregressive (CAR) models and their variants and illustrate the advantages our approach has over traditional methods. We fit our model and competitors to bird abundance data for several species in North Carolina. We find that our model fits the data best, and provides insight into the interaction between species-specific spatial distributions and geography.

A time-varying zero-inflated serially dependent Poisson process is proposed. The model assumes that the intensity of the Poisson Process evolves according to a generalized autoregressive conditional heteroscedastic (GARCH) formulation. The proposed model is a generalization of the zero-inflated Poisson Integer GARCH model proposed by Fukang Zhu in 2012, which in return is a generalization of the Integer GARCH (INGARCH) model introduced by Ferland, Latour, and Oraichi in 2006. The proposed model builds on previous work by allowing the zero-inflation parameter to vary over time, governed by a deterministic function or by an exogenous variable. Both the Expectation Maximization (EM) and the Maximum Likelihood Estimation (MLE) approaches are presented as possible estimation methods. A simulation study shows that both parameter estimation methods provide good estimates. Applications to two real-life data sets show that the proposed INGARCH model provides a better fit than the traditional zero-inflated INGARCH model in the cases considered.

Image restoration algorithms for atmospheric turbulence are known to be much more challenging to design than traditional ones such as blur or noise because the distortion caused by the turbulence is an entanglement of spatially varying blur, geometric distortion, and sensor noise. Existing CNN-based restoration methods built upon convolutional kernels with static weights are insufficient to handle the spatially dynamical atmospheric turbulence effect. To address this problem, in this paper, we propose a physics-inspired transformer model for imaging through atmospheric turbulence. The proposed network utilizes the power of transformer blocks to jointly extract a dynamical turbulence distortion map and restore a turbulence-free image. In addition, recognizing the lack of a comprehensive dataset, we collect and present two new real-world turbulence datasets that allow for evaluation with both classical objective metrics (e.g., PSNR and SSIM) and a new task-driven metric using text recognition accuracy. Both real testing sets and all related code will be made publicly available.

Scene graph generation (SGG) is designed to extract (subject, predicate, object) triplets in images. Recent works have made a steady progress on SGG, and provide useful tools for high-level vision and language understanding. However, due to the data distribution problems including long-tail distribution and semantic ambiguity, the predictions of current SGG models tend to collapse to several frequent but uninformative predicates (e.g., on, at), which limits practical application of these models in downstream tasks. To deal with the problems above, we propose a novel Internal and External Data Transfer (IETrans) method, which can be applied in a plug-and-play fashion and expanded to large SGG with 1,807 predicate classes. Our IETrans tries to relieve the data distribution problem by automatically creating an enhanced dataset that provides more sufficient and coherent annotations for all predicates. By training on the enhanced dataset, a Neural Motif model doubles the macro performance while maintaining competitive micro performance. The code and data are publicly available at //github.com/waxnkw/IETrans-SGG.pytorch.

Deep operator learning has emerged as a promising tool for reduced-order modelling and PDE model discovery. Leveraging the expressive power of deep neural networks, especially in high dimensions, such methods learn the mapping between functional state variables. While proposed methods have assumed noise only in the dependent variables, experimental and numerical data for operator learning typically exhibit noise in the independent variables as well, since both variables represent signals that are subject to measurement error. In regression on scalar data, failure to account for noisy independent variables can lead to biased parameter estimates. With noisy independent variables, linear models fitted via ordinary least squares (OLS) will show attenuation bias, wherein the slope will be underestimated. In this work, we derive an analogue of attenuation bias for linear operator regression with white noise in both the independent and dependent variables. In the nonlinear setting, we computationally demonstrate underprediction of the action of the Burgers operator in the presence of noise in the independent variable. We propose error-in-variables (EiV) models for two operator regression methods, MOR-Physics and DeepONet, and demonstrate that these new models reduce bias in the presence of noisy independent variables for a variety of operator learning problems. Considering the Burgers operator in 1D and 2D, we demonstrate that EiV operator learning robustly recovers operators in high-noise regimes that defeat OLS operator learning. We also introduce an EiV model for time-evolving PDE discovery and show that OLS and EiV perform similarly in learning the Kuramoto-Sivashinsky evolution operator from corrupted data, suggesting that the effect of bias in OLS operator learning depends on the regularity of the target operator.

Object detection is an important and challenging problem in computer vision. Although the past decade has witnessed major advances in object detection in natural scenes, such successes have been slow to aerial imagery, not only because of the huge variation in the scale, orientation and shape of the object instances on the earth's surface, but also due to the scarcity of well-annotated datasets of objects in aerial scenes. To advance object detection research in Earth Vision, also known as Earth Observation and Remote Sensing, we introduce a large-scale Dataset for Object deTection in Aerial images (DOTA). To this end, we collect $2806$ aerial images from different sensors and platforms. Each image is of the size about 4000-by-4000 pixels and contains objects exhibiting a wide variety of scales, orientations, and shapes. These DOTA images are then annotated by experts in aerial image interpretation using $15$ common object categories. The fully annotated DOTA images contains $188,282$ instances, each of which is labeled by an arbitrary (8 d.o.f.) quadrilateral To build a baseline for object detection in Earth Vision, we evaluate state-of-the-art object detection algorithms on DOTA. Experiments demonstrate that DOTA well represents real Earth Vision applications and are quite challenging.