arXiv research

Study on adaptivity to kernel regularity in bandit problems.

New algorithms avoid a dominant lower-order term in heavy-tailed loss settings.

Given a mixture between two populations of coins, "positive" coins that each have -- unknown and potentially different -- bias $\geq\frac{1}{2}+Δ$ and "negative" coins with bias $\leq\frac{1}{2}-Δ$, we consider the task of estimating the fraction $ρ$ of positive coins to within additive error $ε$. We achieve an upper a…

The study sets limits on how well systems can be controlled adaptively.

New bounds on adaptivity cost in stochastic optimization.

In adaptive data analysis, the user makes a sequence of queries on the data, where at each step the choice of query may depend on the results in previous steps. The releases are often randomized in order to reduce overfitting for such adaptively chosen queries. In this paper, we propose a minimax framework for adaptive…

This work sets lower bounds on the number of score queries needed for diffusion sampling.

Paper proposes a 1-bit mean estimation method with near-optimal sample complexity.

The paper studies privacy-protected BAI with fixed confidence, deriving lower bounds and proposing an adaptive algorithm.

We study distributed estimation methods under communication constraints in a distributed version of the nonparametric random design regression model. We derive minimax lower bounds and exhibit methods that attain those bounds. Moreover, we show that adaptive estimation is possible in this setting.

In this paper we study the limitations of parallelization in convex optimization. A convenient approach to study parallelization is through the prism of \emph{adaptivity} which is an information theoretic measure of the parallel runtime of an algorithm [BS18]. Informally, adaptivity is the number of sequential rounds a…

Proposes online debiasing estimators for adaptive linear regression.

Algorithm identifies best policy in MDPs with adaptive sampling.

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of the data distribution, and show distribution-specific upper and lower bounds on…

New algorithms improve online prediction from experts with privacy constraints.

Paper develops an efficient mean estimator for 1-bit communication constraints.

This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one population corresponding to distribution P1 with as few samples as possible. The main…

Optimal adaptive experiment for choosing best treatment with binary outcomes.

The paper addresses privacy-preserving BAI in clinical trials and user studies.

This paper explores the adaptive (active) PAC (probably approximately correct) top-$k$ ranking (i.e., top-$k$ item selection) and total ranking problems from $l$-wise ($l\geq 2$) comparisons under the multinomial logit (MNL) model. By adaptively choosing sets to query and observing the noisy output of the most favored …

New algorithms improve model selection in linear bandits with optimal regret.

An algorithm learns from multiple models to match an oracle's risk.

Sharp bounds on ERM's minimal error in regression.

In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an information-theoretic setting, it is known that Fano's inequality typically doe…

We present Rotated Adaptive Tetra-iterated Quantizer (RATQ), a fixed-length quantizer for gradients in first order stochastic optimization. RATQ is easy to implement and involves only a Hadamard transform computation and adaptive uniform quantization with appropriately chosen dynamic ranges. For noisy gradients with al…

We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of experiments to discover the causal directions of all the edges in a causal graph. Previou…

This work creates a CS for non-negative heavy-tailed data with bounded mean.

Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is commonly performed in practice, as an iterative process of interacting repeatedly wi…

Optimal rank-adaptive matrix estimation from linear measurements.

Adaptive discretization improves model-based RL in large spaces.

Paper analyzes nonconvex bandit problems with improved adaptive methods.

The paper sets bounds on how much regret is unavoidable in adaptive LQR with unknown B-matrix.

New algorithm reduces interventional strategy complexity for causal graph discovery.

We present a simple noise-robust margin-based active learning algorithm to find homogeneous (passing the origin) linear separators and analyze its error convergence when labels are corrupted by noise. We show that when the imposed noise satisfies the Tsybakov low noise condition (Mammen, Tsybakov, and others 1999; Tsyb…

Algorithm aggregates rewards from multiple players to learn related tasks in online bandit learning.

Improved regret bounds for contextual bandits considering variance sequences.

Fairly allocate items with noisy queries, reducing envy.

We show that for the problem of testing if a matrix $A \in F^{n \times n}$ has rank at most $d$, or requires changing an $ε$-fraction of entries to have rank at most $d$, there is a non-adaptive query algorithm making $\widetilde{O}(d^2/ε)$ queries. Our algorithm works for any field $F$. This improves upon the previous…

Study optimizes experimental design for best treatment arm identification.

New bounds show empirical EOT adapts to simpler measure.

The paper tackles adaptive questioning to classify candidate ability.

We derive upper and lower bounds for the policy regret of $T$-round online learning problems with graph-structured feedback, where the adversary is nonoblivious but assumed to have a bounded memory. We obtain upper bounds of $\widetilde O(T^{2/3})$ and $\widetilde O(T^{3/4})$ for strongly-observable and weakly-observab…

The study examines conditions for achieving a simple lower bound in estimating mean from samples.

Dictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured/collected signals or data. This paper finds fundamental limits on the sample complexity of estimating dictionaries for tensor data by proving a lower bound on the minimax risk. This lower …

Estimates time-series drifts from i.i.d. data using a direct Nadaraya-Watson plug-in method.

Detecting a planted submatrix in random matrices with non-asymptotic methods.

New algorithm reduces control error in systems with changing dynamics.

Local differential privacy (LDP) is a model where users send privatized data to an untrusted central server whose goal it to solve some data analysis task. In the non-interactive version of this model the protocol consists of a single round in which a server sends requests to all users then receives their responses. Th…