Predicting the effect of interventions with many possible variations, e.g., therapeutic content that affects mental health outcomes or an earnings call transcript that drives movement in share price, is useful across several domains. However, classical causal estimators tend to assume that all possible interventions are observed, which is infeasible when interventions vary widely, for instance, in the space of all text strings. We adapt a well-known approach of recasting causal inference as a learning problem, to address high-dimensional treatment spaces. Specifically, under standard assumptions like no unobserved confounding, we show that causal error decomposes into a series of moment-balancing errors of increasing order, and design objectives that directly improve causal estimation. We also show how to project the effect of a high-dimensional treatment onto lower-dimensional treatment attributes, which allows a single model to answer several causal questions without additional attribute-specific training. We empirically evaluate our estimators in settings with high-dimensional continuous, discrete, and text treatments, the last of which used a semi-synthetic dataset of Amazon Reviews. Our experiments demonstrate the benefit of higher-order balance error optimization and competitive performance of projected causal estimates with attribute-specific estimators.

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We propose a framework for online meta-optimization of parameters that govern optimization, called Amortized Proximal Optimization (APO). We first interpret various existing neural network optimizers as approximate stochastic proximal point methods which trade off the current-batch loss with proximity terms in both function space and weight space. The idea behind APO is to amortize the minimization of the proximal point objective by meta-learning the parameters of an update rule. We show how APO can be used to adapt a learning rate or a structured preconditioning matrix. Under appropriate assumptions, APO can recover existing optimizers such as natural gradient descent and KFAC. It enjoys low computational overhead and avoids expensive and numerically sensitive operations required by some second-order optimizers, such as matrix inverses.

Establishing a reliable and iteratively refined robotic system is essential for deploying real-world applications. While Vision-Language-Action (VLA) models are widely recognized as the foundation model for such robotic deployment, their reliance on offline expert demonstrations critically limits their capacity for post-deployment refinement. To mitigate this limitation, we introduce Action Preference Optimization (APO), a method designed to refine VLA models by human-assisted preference alignment gathered through interaction with environments. This method begins with a human-robot collaboration framework for reliable failure correction and interaction trajectory collection through human intervention. However, directly leveraging these interaction trajectories for preference optimization is non-trivial due to the challenges of irreversible robotic actions and token distribution mismatch. To solve this, APO proposes an adaptive reweighting algorithm with binary desirability signals derived from interaction, empowering VLA models effectively suppress failure-prone actions while enhancing corrective action adaptation. Ultimately, APO equips VLA models with the crucial capability to learn from failure, paving the way for their iterative refinement and reliable deployment in dynamic environments. The experiments conducted in simulation and real-world scenarios prove superior generalization and robustness of our human-assisted framework across a variety of manipulation tasks. We believe this work could bring insights for efficient and stable optimization of VLA models through human-robot collaboration. The code and dataset are released at https://github.com/GeWu-Lab/Action-Preference-Optimization

Realizing low-cost communication in robotic mixed reality (RoboMR) systems presents a challenge, due to the necessity of uploading high-resolution images through wireless channels. This paper proposes Gaussian splatting (GS) RoboMR (GSMR), which enables the simulator to opportunistically render a photo-realistic view from the robot's pose by calling ``memory'' from a GS model, thus reducing the need for excessive image uploads. However, the GS model may involve discrepancies compared to the actual environments. To this end, a GS cross-layer optimization (GSCLO) framework is further proposed, which jointly optimizes content switching (i.e., deciding whether to upload image or not) and power allocation (i.e., adjusting to content profiles) across different frames by minimizing a newly derived GSMR loss function. The GSCLO problem is addressed by an accelerated penalty optimization (APO) algorithm that reduces computational complexity by over $10$x compared to traditional branch-and-bound and search algorithms. Moreover, variants of GSCLO are presented to achieve robust, low-power, and multi-robot GSMR. Extensive experiments demonstrate that the proposed GSMR paradigm and GSCLO method achieve significant improvements over existing benchmarks on both wheeled and legged robots in terms of diverse metrics in various scenarios. For the first time, it is found that RoboMR can be achieved with ultra-low communication costs, and mixture of data is useful for enhancing GS performance in dynamic scenarios.

Small language models (SLMs) offer promising and efficient alternatives to large language models (LLMs). However, SLMs' limited capacity restricts their reasoning capabilities and makes them sensitive to prompt variations. To address these challenges, we propose a novel framework that enhances SLM reasoning capabilities through LLM generated blueprints. The blueprints provide structured, high-level reasoning guides that help SLMs systematically tackle related problems. Furthermore, our framework integrates a prompt template search mechanism to mitigate the SLMs' sensitivity to prompt variations. Our framework demonstrates improved SLM performance across various tasks, including math (GSM8K), coding (MBPP), and logic reasoning (BBH). Our approach improves the reasoning capabilities of SLMs without increasing model size or requiring additional training, offering a lightweight and deployment-friendly solution for on-device or resource-constrained environments.

We propose a framework for online meta-optimization of parameters that govern optimization, called Amortized Proximal Optimization (APO). We first interpret various existing neural network optimizers as approximate stochastic proximal point methods which trade off the current-batch loss with proximity terms in both function space and weight space. The idea behind APO is to amortize the minimization of the proximal point objective by meta-learning the parameters of an update rule. We show how APO can be used to adapt a learning rate or a structured preconditioning matrix. Under appropriate assumptions, APO can recover existing optimizers such as natural gradient descent and KFAC. It enjoys low computational overhead and avoids expensive and numerically sensitive operations required by some second-order optimizers, such as matrix inverses.

Achieving generalization in neural approaches across different scales and distributions remains a significant challenge for the Traveling Salesman Problem~(TSP). A key obstacle is that neural networks often fail to learn robust principles for identifying universal patterns and deriving optimal solutions from diverse instances. In this paper, we first uncover Purity Law (PuLa), a fundamental structural principle for optimal TSP solutions, defining that edge prevalence grows exponentially with the sparsity of surrounding vertices. Statistically validated across diverse instances, PuLa reveals a consistent bias toward local sparsity in global optima. Building on this insight, we propose Purity Policy Optimization~(PUPO), a novel training paradigm that explicitly aligns characteristics of neural solutions with PuLa during the solution construction process to enhance generalization. Extensive experiments demonstrate that PUPO can be seamlessly integrated with popular neural solvers, significantly enhancing their generalization performance without incurring additional computational overhead during inference.

Chenxuan Liu, He Li, Zongze Li, Shuai Wang, Wei Xu, Kejiang Y e, Derrick Wing Kwan Ng, Fellow, IEEE, and Chengzhong Xu, Fellow, IEEE Abstract --Realizing green communication in robotic mixed reality (RoboMR) systems presents a challenge, due to the necessity of uploading high-resolution images at high frequencies through wireless channels. This paper proposes Gaussian splatting (GS) RoboMR (GSRMR), which achieves a lower energy consumption and makes a concrete step towards green RoboMR. The crux to GSRMR is to build a GS model which enables the simulator to opportunistically render a photo-realistic view from the robot's pose, thereby reducing the need for excessive image uploads. Since the GS model may involve discrepancies compared to the actual environments, a GS cross-layer optimization (GSCLO) framework is further proposed, which jointly optimizes content switching (i.e., deciding whether to upload image or not) and power allocation across different frames. The GSCLO problem is solved by an accelerated penalty optimization (APO) algorithm. Experiments demonstrate that the proposed GSRMR reduces the communication energy by over 10 x compared with RoboMR. Furthermore, the proposed GSRMR with APO outperforms extensive baseline schemes, in terms of peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM).