sequential query-efficient estimation

This work addresses the inefficiency faced by data analysts who must repeatedly submit and integrate multiple related queries to explore salient data patterns. To streamline this process, the paper introduces the ANALYZE operator, which formalizes such exploratory analysis as five auxiliary cube queries, enabling comprehensive 360-degree examination of specific data subsets. Leveraging multi-query optimization (MQO), the authors devise three query merging and execution strategies—Mid-MQO, Min-MQO, and Max-MQO—that significantly improve execution efficiency while preserving result equivalence. Experimental evaluation demonstrates that Mid-MQO consistently delivers the best overall performance across most scenarios, whereas Max-MQO excels when sibling queries are numerous and exhibit high overlap.

This work addresses the sequential estimation of function values in slowly varying sequences by introducing a general adaptive framework applicable to a wide range of linear and nonlinear functions over vector spaces. The method reuses historical query information and incorporates a local adaptive budget allocation mechanism that dynamically adjusts computational resources based on real-time variation magnitudes. It achieves, for the first time, a path-length–type cost bound of \(O(\sum \alpha_i)\), improving upon prior fixed-budget approaches that rely on worst-case assumptions about individual \(\alpha_i\). In certain settings, the variation magnitude can be estimated online with negligible overhead. Applied to tasks such as matrix powers, spectral density estimation, Monte Carlo integration, and PDE boundary value problems, the framework substantially reduces computational costs, with both theoretical analysis and empirical results demonstrating its pronounced efficiency advantage when stable sequences experience occasional abrupt changes.

This work studies efficient learning of the optimal approximation to an unknown matrix $A$ within structured matrix families (e.g., low-rank, sparse, banded, or linear subspaces), under a black-box model where only matrix-vector queries $x mapsto Ax$ and $x mapsto A^ op x$ are accessible. We propose a unified framework integrating matrix sketching, covering numbers, and dual-query analysis. Our main contributions are: (i) the first characterization of query complexity lower bounds for general structured families; and (ii) near-optimal algorithms matching these bounds. Specifically, for a finite family $mathcal{F}$, only $widetilde{O}(sqrt{log|mathcal{F}|})$ queries suffice; for a $q$-dimensional linear matrix family, query complexity improves from the classical $O(q)$ to $widetilde{O}(sqrt{q})$, which is tight up to logarithmic factors. This yields near-quadratic speedups over conventional approaches, establishing a new paradigm for fast matrix approximation, preconditioner learning, and differential operator identification.

This paper addresses the challenge of estimating causal effects when the target variable cannot be directly intervened upon and the underlying mechanism is complex—nonlinear, high-dimensional, and confounded. We propose the first active experimental design framework tailored for *indirect experiments*. Methodologically, we formulate a bilevel optimization model that integrates kernel-based estimation with adaptive sequential experimental design, yielding an analytically tractable and computationally efficient estimator for upper and lower bounds on the causal effect. Our key contributions are: (1) the first systematic formalization of feasibility conditions for indirect intervention under nonlinear confounding; and (2) dynamic narrowing of the causal bound gap to precisely localize the target query value. Extensive synthetic experiments across diverse settings demonstrate that our method significantly improves causal effect identification accuracy, with faster convergence of bound width compared to state-of-the-art baselines.

This work investigates how to leverage a sublinear number of noisy pairwise probes—comparisons indicating which of two points incurs lower loss—to improve worst-case regret in online convex optimization (OCO). The authors introduce a unified probing model and establish, for the first time, that even with only \(k = o(T)\) such noisy comparisons, the regret bound of full-feedback OCO can be significantly enhanced. By integrating a continuous exponential weights algorithm with variance-reduction analysis, they characterize the second-order effect of probing and derive an almost-tight regret upper bound of \(O\big(\min\{\sqrt{dT \ln T},\, dT \ln T / (k|1 - 2\delta|)\}\big)\), where \(\delta\) denotes the noise level. This bound is theoretically optimal in the horizon \(T\), number of probes \(k\), noise parameter \(\delta\), and number of experts \(d\) (in the finite action setting).

This work addresses the problem of selectivity estimation for linear queries—such as point and range queries—in dynamic databases. It introduces, for the first time, online learning theory to this setting, proposing an online estimation method based on histogram models and standard loss functions. The approach effectively adapts to time-varying data distributions and query workloads, delivering provably low regret in both static and dynamic environments. The core contribution lies in establishing tight upper and lower bounds on regret specifically for histogram-based linear queries, thereby providing the first formal online learning framework for dynamic selectivity estimation with theoretical performance guarantees.

This work addresses the problem of efficiently constructing an approximate matrix with a prescribed binary sparsity pattern using only black-box access via matrix-vector product queries. The authors introduce the degeneracy of the sparsity pattern as a unified and tight measure of query complexity, overcoming limitations inherent in traditional graph coloring approaches. Leveraging this notion, they propose an adaptive querying strategy together with a polynomial-time algorithm that achieves a near-optimal approximation using only Õ(degen(S)) queries while avoiding computational bottlenecks. Furthermore, they establish an information-theoretic lower bound of Ω(degen(S)) on the query complexity for any sparsity pattern S, thereby proving the optimality of their approach.