Optimal algorithm for identifying best arm in stochastic linear bandits with fixed confidence.
problem Identifying the best arm in stochastic linear bandits with fixed confidence.
method Extending an algorithm designed for Best Arm Identification to the ε-Thresholding Bandit Problem (TBP). result Asymptotically optimal algorithm for TBP.
A/B testing refers to the task of determining the best option among two alternatives that yield random outcomes. We provide distribution-dependent lower bounds for the performance of A/B testing that improve over the results currently available both in the fixed-confidence (or delta-PAC) and fixed-budget settings. When…
EB-TCε identifies the best arm with ε confidence in stochastic bandits.
problem Identifying the best arm in stochastic bandits with a fixed level of confidence.
method EB-TCε is a novel sampling rule for ε-best arm identification in stochastic bandits.
result EB-TCε is the first anytime algorithm for fixed confidence or fixed budget identification.
New algorithm improves best arm identification in Bayesian settings.
problem Finding the arm with the highest mean in unknown distributions.
method Developed a variant of successive elimination algorithm.
result Achieved optimal performance in Bayesian setting with logarithmic gap.
A method identifies abrupt changes in functions with fixed confidence under noisy feedback.
problem Identifying abrupt changes in piecewise constant functions quickly and with certainty.
method Fixed-confidence piecewise constant bandit problem, focusing sampling efforts near change points.
result Asymptotically optimal method proven computationally efficient and effective in experiments.
We provide a pointwise confidence bound for non-linear least-squares with fixed design.
problem Confidence estimation in non-linear ℓ2-regularized least squares. method Pointwise confidence bound for local minimizers, using weighted norm involving inverse-Hessian.
result The proposed confidence bound scales with the test input's similarity to the training data.
The stochastic multi-armed bandit model is a simple abstraction that has proven useful in many different contexts in statistics and machine learning. Whereas the achievable limit in terms of regret minimization is now well known, our aim is to contribute to a better understanding of the performance in terms of identify…
Paper shows FB and FC are equally hard up to logarithmic factors.
problem Comparing fixed budget and fixed confidence approaches in best-arm identification.
method Proposes FC2FB, a meta algorithm converting FC to FB.
result FC sample complexity is an upper bound for FB sample complexity up to logarithmic factors.
This paper introduces time-uniform CLT-based confidence intervals for statistical inference.
problem Developing valid statistical inference methods for sequential data.
method Time-uniform central limit theory and strong invariance principles.
result Asymptotic confidence sequences (CSs) that are uniformly valid over time.
There are two major paradigms of white-box adversarial attacks that attempt to impose input perturbations. The first paradigm, called the fix-perturbation attack, crafts adversarial samples within a given perturbation level. The second paradigm, called the zero-confidence attack, finds the smallest perturbation needed …
New algorithms for model selection in linear bandits adapt to instance complexity.
problem Adapting to the instance-dependent complexity of the true model in linear bandits.
method Design of algorithms in fixed confidence and fixed budget settings, leveraging experimental design and selection-validation procedures.
result Near instance optimal guarantees for model selection in linear bandits.
Optimal best-arm identification with known number of optimal arms.
problem Identifying the best arm in a multi-armed bandit with multiple optimal arms under fixed confidence.
method Deriving a new information-theoretic lower bound and proposing a modified stopping rule.
result Achieving asymptotic instance-optimality with a new lower bound and new stopping rule.
The paper identifies the best treatment to maximize NDPO, a key outcome in causal mediation analysis.
problem Identifying the treatment that maximizes the expected natural direct potential outcome (NDPO) in causal mediation analysis.
method Developed a fixed-confidence best-arm identification (BAI) algorithm based on the Track-and-Stop (TaS) framework, using a cutting-set method to solve a semi-infinite optimization problem.
result The proposed algorithm achieves sample-efficient identification with a high-probability correctness guarantee and asymptotic optimality.
New method balances performance and cost in identifying best arm.
problem Identifying the best arm in multi-armed bandit models.
method Minimizes a risk functional that balances performance and cost.
result Proposes DBCARE algorithm that matches theoretical lower bounds.
Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.
problem Tackles robustness to outliers and adversarial corruptions in mean estimation.
method Designs new robust exponential supermartingales to create confidence sequences.
result Achieves optimal width and shows smaller margin of error compared to fixed-time robust methods.
New algorithms improve stopping time for best arm identification.
problem Efficiently identifying the best alternative in experiments.
method Proposed algorithms with exponential-tailed stopping time.
result Proved that some algorithms never stop, leading to new methods.
UCB exploration improves best arm identification in fixed-budget settings.
problem Best arm identification in fixed-budget scenarios.
method Adaptive allocations based on upper confidence bounds (UCBs) with prior information learning.
result Empirically and theoretically efficient for Bayesian BAI problem with improved performance.
APGAI identifies good arms anytime with fixed budget.
problem Identifying a good arm with a fixed sampling budget.
method An anytime algorithm for good arm identification in stochastic bandits.
result APGAI achieves efficient detection of good arms with upper bounds on probability of error and sampling complexity.
Generative models need per-sample confidence scores to improve quality and stability.
problem Generative models produce unreliable outputs and lack confidence measures.
method Flow Matching with Confidence (FMwC) injects noise and integrates it through the network, providing per-sample confidence scores.
result The confidence score correlates with the velocity field's divergence, offering insights into generative processes.
We investigate and provide new insights on the sampling rule called Top-Two Thompson Sampling (TTTS). In particular, we justify its use for fixed-confidence best-arm identification. We further propose a variant of TTTS called Top-Two Transportation Cost (T3C), which disposes of the computational burden of TTTS. As our …
Private statistical inference methods improve confidence interval lengths.
problem Constructing private confidence intervals with differential privacy.
method Proposed two private variants of non-parametric bootstrap.
result Achieve similar coverage accuracy to non-private methods with shorter intervals.
Open problem: fixed-budget best arm identification complexity.
problem Understanding the complexity of identifying the best arm in a fixed budget setting.
method Analyzing existing results and conjectures in the fixed-confidence setting.
result Open questions remain about the fixed-budget setting.
Confidence bands for tuning curves improve hyperparameter comparison in NLP.
problem Ambiguity in comparing hyperparameter tuning methods.
method Constructs exact, simultaneous, and distribution-free confidence bands for tuning curves.
result Confidence bands provide a robust basis for comparing methods rigorously.
The paper introduces methods to quantify uncertainty in sampling without replacement.
problem Accurately estimating parameters from finite populations sampled without replacement.
method Develops confidence sequences using Bayesian and empirical methods.
result Improved confidence intervals and sequences for sampling without replacement.
Improved confidence bounds for linear logistic model with applications to bandits.
problem Improving confidence bounds for linear logistic model.
method Self-concordant analysis of the logistic loss to avoid dependence on worst-case variance.
result Significant improvement in confidence bounds, avoiding dependence on 1/κ. We design new algorithms for the combinatorial pure exploration problem in the multi-arm bandit framework. In this problem, we are given K distributions and a collection of subsets V⊂2[K] of these distributions, and we would like to find the subset v∈V that has largest mean, whi…
Optimal best arm identification for multi-objective bandits with fixed error probability.
problem Identifying the best arm for each of multiple objectives with fixed confidence.
method Surrogate proportions to sample arms at each time step, eliminating max-min optimisation.
result Asymptotically optimal algorithm for multi-objective best arm identification.
We consider the problem of near-optimal arm identification in the fixed confidence setting of the infinitely armed bandit problem when nothing is known about the arm reservoir distribution. We (1) introduce a PAC-like framework within which to derive and cast results; (2) derive a sample complexity lower bound for near…
Optimal ability estimation in adaptive testing with binary responses.
problem Estimating a continuous ability parameter from sequential binary responses.
method Adaptive selection of questions to maximize Fisher information, updating estimate using method-of-moments, and deciding accuracy with a test statistic.
result Fisher-tracking strategy achieves optimal performance in fixed-confidence and fixed-budget regimes.
The paper offers efficient algorithms for combinatorial and linear bandits using empirical process theory.
problem Optimal algorithms for combinatorial and linear bandits with practical sample complexity.
method Empirical process theory, Gaussian-width, minimizing experimental design objective.
result Sample complexity matches lower bounds, especially for combinatorial classes.
New algorithm identifies best arm in semiparametric bandits with near optimal efficiency.
problem Fixed-confidence Best Arm Identification in semiparametric bandits with unknown baseline shift.
method Phase-elimination algorithm based on orthogonalized regression design.
result Nearly optimal high-probability sample-complexity upper bound established.
Optimizes identifying top-k items from comparisons with minimal comparisons.
problem Finding the top-k items from pairwise comparisons with a fixed error rate.
method Developed an asymptotically optimal algorithm using primal-dual procedure and adaptive comparison allocation.
result Proves the algorithm is asymptotically optimal for top-k identification.
Study three types of uncertainty quantification for binary classification without distributional assumptions.
problem Uncertainty quantification for binary classification in a distribution-free setting.
method Established theorems connecting calibration, confidence intervals, and prediction sets for score-based classifiers.
result Distribution-free calibration is only possible using scoring functions that partition feature space into countably many sets.
New methods for private statistical inference under local differential privacy.
problem Private statistical inference for population means with bounded observations.
method Nonparametric, nonasymptotic statistical inference using a generalized randomized response mechanism.
result Private confidence intervals and sequences for population means under LDP constraints.
The paper tackles multi-armed bandits with vector losses, focusing on minimizing the ℓ∞-norm of relative losses.
problem Minimizing the ℓ∞-norm of relative losses in multi-armed bandits with multiple losses. method Defines relative loss vector, derives lower bounds, and provides matching algorithms for both fixed-confidence best-arm identification and regret minimization.
result Derives problem-dependent sample complexity lower bound and matching algorithms for fixed-confidence best-arm identification.
The paper studies privacy-protected BAI with fixed confidence, deriving lower bounds and proposing an adaptive algorithm.
problem Privacy-protected Best Arm Identification (BAI) in data-sensitive applications.
method Derives lower bounds on sample complexity, proposes AdaP-TT algorithm with Laplace noise, and validates with experiments.
result AdaP-TT matches the sample complexity lower bound up to constants in the high-privacy regime.
A new strategy for identifying the best arm in Gaussian bandits with improved exploration.
problem Best-arm identification for Gaussian bandits with bounded means and unit variance.
method Exploration-Biased Sampling, a non-asymptotic approach with improved exploration behavior.
result Improved exploration behavior makes the strategy more stable and interpretable.
Fuzzy prediction sets generalize binary predictions to include elements at varying confidence levels.
problem Binary prediction sets are limited; fuzzy prediction sets offer richer guarantees.
method Generalize prediction sets to fuzzy sets, showing they are e-values with merging properties.
result Optimal e-values lead to optimal fuzzy prediction sets, including optimal conformal prediction.
We study an original problem of pure exploration in a strategic bandit model motivated by Monte Carlo Tree Search. It consists in identifying the best action in a game, when the player may sample random outcomes of sequentially chosen pairs of actions. We propose two strategies for the fixed-confidence setting: Maximin…
We give a new algorithm for best arm identification in linearly parameterised bandits in the fixed confidence setting. The algorithm generalises the well-known LUCB algorithm of Kalyanakrishnan et al. (2012) by playing an arm which minimises a suitable notion of geometric overlap of the statistical confidence set for t…
Optimal algorithm for selecting high-quality arms from infinite bandit arms.
problem Efficiently choosing the best arm from an infinite set of options.
method Developed algorithms for both fixed confidence and fixed budget settings, achieving optimal or near-optimal sample complexities.
result Optimal sample complexity results for both fixed confidence and fixed budget settings, resolving open questions in the field.
Parameter estimation, statistical tests and confidence sets are the cornerstones of classical statistics that allow scientists to make inferences about the underlying process that generated the observed data. A key question is whether one can still construct hypothesis tests and confidence sets with proper coverage and…
Efficient inference method for adaptive experiments with tighter confidence sequences.
problem Efficient inference of Average Treatment Effect in a changing policy sequential experiment.
method Semiparametric efficient inference using Adaptive Augmented Inverse-Probability Weighted estimator and asymptotic confidence sequences.
result Derives tighter confidence sequences for adaptive experiments under data-dependent stopping times.
BCI system improves word selection efficiency using sequential best-arm identification.
problem Conventional non-adaptive BCI paradigms lead to a lengthy learning process.
method Casted as sequence of best-arm identification tasks in multi-armed bandits, using pre-trained LLMs and STTS algorithm.
result Substantial empirical improvement in word selection efficiency demonstrated.
The paper proposes a novel upper confidence bound (UCB) procedure for identifying the arm with the largest mean in a multi-armed bandit game in the fixed confidence setting using a small number of total samples. The procedure cannot be improved in the sense that the number of samples required to identify the best arm i…
Develops new e-processes and confidence sequences for Gaussian means with unknown variance.
problem Constructing valid t-tests and confidence sequences for Gaussian means with unknown variance.
method Explores generalized nonintegrable martingales and extended Ville's inequality, developing two new e-processes and confidence sequences.
result Analyzes the width of resulting confidence sequences with a polynomial dependence on error probability, proving it to be unavoidable and even better than classical fixed-sample t-tests.
The paper tackles best arm identification with minimal regret in experiments.
problem Identifying the best arm with minimal regret in experiments.
method Information-theoretic techniques and Double KL-UCB algorithm.
result Achieves asymptotic optimality in identifying the best arm with minimal regret.
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…