Separating Oblivious and Adaptive Models of Variable Selection

Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics. In this work, we investigate the statistical and computational landscapes of sparse recovery with $\ell_\infty$ error guarantees. This variant of the problem is motivated by \emph{variable selection} tasks, where the goal is to estimate the support of a $k$-sparse signal in $\mathbb{R}^d$. Our main contribution is a provable separation between the \emph{oblivious} (``for each'') and \emph{adaptive} (``for all'') models of $\ell_\infty$ sparse recovery. We show that under an oblivious model, the optimal $\ell_\infty$ error is attainable in near-linear time with $\approx k\log d$ samples, whereas in an adaptive model, $\gtrsim k^2$ samples are necessary for any algorithm to achieve this bound. This establishes a surprising contrast with the standard $\ell_2$ setting, where $\approx k \log d$ samples suffice even for adaptive sparse recovery. We conclude with a preliminary examination of a \emph{partially-adaptive} model, where we show nontrivial variable selection guarantees are possible with $\approx k\log d$ measurements.

Improved Regret and Contextual Linear Extension for Pandora's Box and Prophet Inequality

We study the Pandora's Box problem in an online learning setting with semi-bandit feedback. In each round, the learner sequentially pays to open up to $n$ boxes with unknown reward distributions, observes rewards upon opening, and decides when to stop. The utility of the learner is the maximum observed reward minus the cumulative cost of opened boxes, and the goal is to minimize regret defined as the gap between the cumulative expected utility and that of the optimal policy. We propose a new algorithm that achieves $\widetilde{O}(\sqrt{nT})$ regret after $T$ rounds, which improves the $\widetilde{O}(n\sqrt{T})$ bound of Agarwal et al. [2024] and matches the known lower bound up to logarithmic factors. To better capture real-life applications, we then extend our results to a natural but challenging contextual linear setting, where each box's expected reward is linear in some known but time-varying $d$-dimensional context and the noise distribution is fixed over time. We design an algorithm that learns both the linear function and the noise distributions, achieving $\widetilde{O}(nd\sqrt{T})$ regret. Finally, we show that our techniques also apply to the online Prophet Inequality problem, where the learner must decide immediately whether or not to accept a revealed reward. In both non-contextual and contextual settings, our approach achieves similar improvements and regret bounds.

RemoteSAM: Towards Segment Anything for Earth Observation

We aim to develop a robust yet flexible visual foundation model for Earth observation. It should possess strong capabilities in recognizing and localizing diverse visual targets while providing compatibility with various input-output interfaces required across different task scenarios. Current systems cannot meet these requirements, as they typically utilize task-specific architecture trained on narrow data domains with limited semantic coverage. Our study addresses these limitations from two aspects: data and modeling. We first introduce an automatic data engine that enjoys significantly better scalability compared to previous human annotation or rule-based approaches. It has enabled us to create the largest dataset of its kind to date, comprising 270K image-text-mask triplets covering an unprecedented range of diverse semantic categories and attribute specifications. Based on this data foundation, we further propose a task unification paradigm that centers around referring expression segmentation. It effectively handles a wide range of vision-centric perception tasks, including classification, detection, segmentation, grounding, etc, using a single model without any task-specific heads. Combining these innovations on data and modeling, we present RemoteSAM, a foundation model that establishes new SoTA on several earth observation perception benchmarks, outperforming other foundation models such as Falcon, GeoChat, and LHRS-Bot with significantly higher efficiency. Models and data are publicly available at https://github.com/1e12Leon/RemoteSAM.