This paper studies a risk minimization problem with decision dependent data distribution. The problem pertains to the performative prediction setting in which a trained model can affect the outcome estimated by the model. Such dependency creates a feedback loop that influences the stability of optimization algorithms such as stochastic gradient descent (SGD). We present the first study on performative prediction with smooth but possibly non-convex loss. We analyze a greedy deployment scheme with SGD (SGD-GD). Note that in the literature, SGD-GD is often studied with strongly convex loss. We first propose the definition of stationary performative stable (SPS) solutions through relaxing the popular performative stable condition. We then prove that SGD-GD converges to a biased SPS solution in expectation. We consider two conditions of sensitivity on the distribution shifts: (i) the sensitivity is characterized by Wasserstein-1 distance and the loss is Lipschitz w.r.t.

They also prevent people from misusing images, especially those generated by AI models. We propose a family of regeneration attacks to remove these invisible watermarks. The proposed attack method first adds random noise to an image to destroy the watermark and then reconstructs the image. This approach is flexible and can be instantiated with many existing imagedenoising algorithms and pre-trained generative models such as diffusion models. Through formal proofs and extensive empirical evaluations, we demonstrate that pixel-level invisible watermarks are vulnerable to this regeneration attack. Our results reveal that, across four different pixel-level watermarking schemes, the proposed method consistently achieves superior performance compared to existing attack techniques, with lower detection rates and higher image quality. However, watermarks that keep the image semantically similar can be an alternative defense against our attacks. Our finding underscores the need for a shift in research/industry emphasis from invisible watermarks to semantic-preserving watermarks.

Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and estimation ability of deep learning on anisotropic Besov spaces. The anisotropic Besov space is characterized by direction-dependent smoothness and includes several function classes that have been investigated thus far. We demonstrate that the approximation error and estimation error of deep learning only depend on the average value of the smoothness parameters in all directions. Consequently, the curse of dimensionality can be avoided if the smoothness of the target function is highly anisotropic. Unlike existing studies, our analysis does not require a low-dimensional structure of the input data. We also investigate the minimax optimality of deep learning and compare its performance with that of the kernel method (more generally, linear estimators). The results show that deep learning has better dependence on the input dimensionality if the target function possesses anisotropic smoothness, and it achieves an adaptive rate for functions with spatially inhomogeneous smoothness.

Our supplementary includes the following sections: Section B: Framework details. Disclaimer for the visual CoT dataset and the related model. The authors are committed to ensuring its regular upkeep and updates. B.1 Model details We choose the pre-trained ViT-L/14 of CLIP [57] as the vision encoder and Vicuna-7/13B [13] as our LLM, which has better instruction following capabilities in language tasks compared to LLaMA [64]. Consider an input original image, we take the vision encoder to obtain the visual feature. B.2 Implementation details Following the setup described by Vicuna [13], our model undergoes a two-stage training process.

Multi-Modal Large Language Models (MLLMs) have demonstrated impressive performance in various VQA tasks. However, they often lack interpretability and struggle with complex visual inputs, especially when the resolution of the input image is high or when the interested region that could provide key information for answering the question is small. To address these challenges, we collect and introduce the large-scale Visual CoT dataset comprising 438k question-answer pairs, annotated with intermediate bounding boxes highlighting key regions essential for answering the questions. Additionally, about 98k pairs of them are annotated with detailed reasoning steps. Importantly, we propose a multi-turn processing pipeline that dynamically focuses on visual inputs and provides interpretable thoughts. We also introduce the related benchmark to evaluate the MLLMs in scenarios requiring specific local region identification. Extensive experiments demonstrate the effectiveness of our framework and shed light on better inference strategies. The Visual CoT dataset, benchmark, and pre-trained models are available on this webpage to support further research in this area.

Reinforcement Learning (RL) encompasses diverse paradigms, including modelbased RL, policy-based RL, and value-based RL, each tailored to approximate the model, optimal policy, and optimal value function, respectively. This work investigates the potential hierarchy of representation complexity among these RL paradigms. By utilizing computational complexity measures, including time complexity and circuit complexity, we theoretically unveil a potential representation complexity hierarchy within RL. We find that representing the model emerges as the easiest task, followed by the optimal policy, while representing the optimal value function presents the most intricate challenge. Additionally, we reaffirm this hierarchy from the perspective of the expressiveness of Multi-Layer Perceptrons (MLPs), which align more closely with practical deep RL and contribute to a completely new perspective in theoretical studying representation complexity in RL. Finally, we conduct deep RL experiments to validate our theoretical findings.

We address a generalization of the bandit with knapsacks problem, where a learner aims to maximize rewards while satisfying an arbitrary set of long-term constraints. Our goal is to design best-of-both-worlds algorithms that perform optimally under both stochastic and adversarial constraints. Previous works address this problem via primal-dual methods, and require some stringent assumptions, namely the Slater's condition, and in adversarial settings, they either assume knowledge of a lower bound on the Slater's parameter, or impose strong requirements on the primal and dual regret minimizers such as requiring weak adaptivity. We propose an alternative and more natural approach based on optimistic estimations of the constraints. Surprisingly, we show that estimating the constraints with an UCBlike approach guarantees optimal performances.

Follow-the-Regularized-Leader (FTRL) is a powerful framework for various online learning problems. By designing its regularizer and learning rate to be adaptive to past observations, FTRL is known to work adaptively to various properties of an underlying environment.

Estimating individualized treatment rules (ITRs) is fundamental in causal inference, particularly for precision medicine applications.

A.1 Proof of Theorem 1 Theorem 1. (MDI are Shapley values) For all feature X Notice already the similarity with the intermediate formulation in the proof of Theorem 1 from [Louppe et al., 2013] where Equation 5 reduces the inner sum to a single term, the one corresponding to the given b = x This proof directly stems from the following intuitive observation: the irrelevance property considers all x while the local irrelevance one only considers one x. If local irrelevance is satisfied for all x, then irrelevance is satisfied.