arXiv research

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

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

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…

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

Algorithm identifies best policy in MDPs with adaptive sampling.

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…

Sharp bounds on ERM's minimal error in regression.

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L_2 regularization: We introduce the γ-adapted-dimension, which is a simple function of the spectrum of a distribution's covariance matrix, and show distribution-specific upper and lower bounds on the s…

New bounds show empirical EOT adapts to simpler measure.

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…

New algorithm reduces interventional strategy complexity for causal graph discovery.

Private optimization faster on interpolation problems with quadratic growth.

Optimizes sample and round complexity in adaptive sampling from multiple distributions.

Optimal rank-adaptive matrix estimation from linear measurements.

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

New complexity measure for interactive learning reduces regret to near-optimal levels.

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 model-based methods adapt pre-trained policies to unseen environments efficiently.

Improved variance reduction for Riemannian non-convex optimization with adaptive batch size.

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 …

Adaptive exploration scheme for evaluating multiple policies with different rewards.

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…

MACI improves LLM factuality inference with higher retention and lower time cost.

Sampling from distributions to find the one with the largest mean arises in a broad range of applications, and it can be mathematically modeled as a multi-armed bandit problem in which each distribution is associated with an arm. This paper studies the sample complexity of identifying the best arm (largest mean) in a m…

Study on adaptivity to kernel regularity in bandit problems.

A mixture of factor analyzers is a semi-parametric density estimator that generalizes the well-known mixtures of Gaussians model by allowing each Gaussian in the mixture to be represented in a different lower-dimensional manifold. This paper presents a robust and parsimonious model selection algorithm for training a mi…

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…

Proposes a new tensor decomposition method for functional temporal data with adaptive complexity.

We propose the first fully-adaptive algorithm for pure exploration in linear bandits---the task to find the arm with the largest expected reward, which depends on an unknown parameter linearly. While existing methods partially or entirely fix sequences of arm selections before observing rewards, our method adaptively c…

This paper introduces an inner product on chain complexes of finite simplicial complexes that is well-adapted to the harmonic study of subdivisions. Its definition utilizes a decomposition of the chain spaces that suggests a sequence of subdivision invariants which we show do not all vanish for non-trivial subdivisions…

In this paper, we present an online adaptive PCA algorithm that is able to compute the full dimensional eigenspace per new time-step of sequential data. The algorithm is based on a one-step update rule that considers all second order correlations between previous samples and the new time-step. Our algorithm has O(n) co…

New findings on complexity limits in fixed budget bandit identification.

The paper tackles efficient change point detection with limited samples.

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

AdaRL improves robust RL by adaptively adjusting policy complexity.

Proposes a new framework for investing that adapts to market regimes.

Study robust best-arm identification in linear bandits with lower bounds and algorithms.

New algorithm adapts to unknown demand smoothness for dynamic pricing.

We study the problem of multi-agent reinforcement learning (MARL) with adaptivity constraints -- a new problem motivated by real-world applications where deployments of new policies are costly and the number of policy updates must be minimized. For two-player zero-sum Markov Games, we design a (policy) elimination base…

Improved sample complexity for identifying best policies in risk-sensitive reinforcement learning.

This paper proposes a method to compress and adapt CNNs for real-world applications.

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…

New algorithms estimate function levels with near-optimal efficiency.

We study active learning where the labeler can not only return incorrect labels but also abstain from labeling. We consider different noise and abstention conditions of the labeler. We propose an algorithm which utilizes abstention responses, and analyze its statistical consistency and query complexity under fairly nat…

New algorithm reduces regret for kernelized bandits by adapting to specific problem instances.

We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$ \emph{exact} queries of the form $w^{(i)} = Mv^{(i)}$ for $i \in \{1,\dots,T\}$, where $v^{(i)}$…

We propose a novel technique for analyzing adaptive sampling called the {\em Simulator}. Our approach differs from the existing methods by considering not how much information could be gathered by any fixed sampling strategy, but how difficult it is to distinguish a good sampling strategy from a bad one given the limit…

We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an exact update of the optimal $\ell_{1,\infty}$-penalized recursive least squares (R…