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.
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.
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.
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 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.
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.
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.
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.
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.
Study best arm identification in restless bandits with unknown TPMs.
problem Identify the best arm with fixed confidence in restless bandits with unknown TPMs.
method Proposed a policy for best arm identification and proved its expected stopping time matches the lower bound.
result The state-action visitation proportions match the optimal proportions under any asymptotically optimal policy.
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.
Optimal best-arm identification in linear bandits reduces sampling budget.
problem Identifying the best arm with fixed confidence in stochastic linear bandits.
method A simple algorithm that tracks an optimal proportion of arm draws, updated as rarely as desired.
result The algorithm's sampling complexity matches known lower bounds, asymptotically almost surely and in expectation.
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 …
CascadeBAI identifies best arms in cascading bandits with fixed confidence.
problem Finding the best set of items in cascading bandits with limited feedback.
method Developed CascadeBAI algorithm, derived upper and lower bounds on time complexity, introduced left-sided sub-Gaussian random variables.
result CascadeBAI is optimal in some practical regimes and performs well with limited feedback.
We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop' strategy, which we prove to be asymptotically optimal. It consists in a new sampling rule (which tracks the optim…
Improved theoretical guarantees for Top Two algorithms.
problem Theoretical support for best arm identification with bounded distributions.
method General analysis of Top Two methods, identifying desirable properties and replacing sampling step.
result Theoretical support for Top Two algorithms with bounded distributions.
Contextual information helps identify the best arm more efficiently.
problem Best arm identification with contextual covariate information.
method Proposed a context-aware version of the 'Track-and-Stop' strategy.
result Expected number of arm draws matches lower bound asymptotically.
PROBE optimizes best-arm identification with cheap proxies, improving sample complexity.
problem Fixed-confidence best-arm identification with costly rewards and correlated cheap proxies.
method PROBE uses control-variate adjustment and phase elimination to learn residual variance online.
result PROBE achieves oracle sample complexity up to a constant factor and additive calibration cost.
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 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.
VA-LUCB identifies best arm with variance constraint, achieving optimal sample complexity.
problem Identifying the best arm with variance constraint under fixed confidence.
method Parameter-free algorithm VA-LUCB, analyzing sample complexity and proving lower bounds.
result Optimal sample complexity up to a logarithmic factor in HVA, demonstrated by experiments. We consider the problem of \textit{best arm identification} with a \textit{fixed budget T}, in the K-armed stochastic bandit setting, with arms distribution defined on [0,1]. We prove that any bandit strategy, for at least one bandit problem characterized by a complexity H, will misidentify the best arm with pr…
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 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…
New algorithms identify best arm with less pulls, adapting to arm covariances.
problem Best arm identification under dependent and correlated arm distributions.
method Adaptive algorithms estimating arm covariances to minimize pulls.
result Substantial improvement in best arm identification over standard setting.
Paper tackles efficient BAI in graph-smooth bandits.
problem Best arm identification with graph smoothness constraint.
method Gradient ascent algorithm for sample complexity.
result Asymptotically optimal strategy for BAI.
New strategies for identifying the best arm in bandits with decreasing variances.
problem Best arm identification in bandits with time-varying variances.
method Two policies: initial wait followed by continuous sampling, and periodic sampling with weighted average.
result Analytical guarantees and simulations show improved performance over existing methods.
The paper tackles best arm identification in contaminated bandits with optimal error guarantees and sample complexity.
problem Best arm identification in stochastic bandits with adversarial reward contamination.
method Proposes two algorithms: a gap-based algorithm and a successive elimination-based algorithm for sub-Gaussian bandits.
result Asymptotically optimal sample complexity for both algorithms.
Optimizes pure exploration in linear bandits with a new algorithm.
problem Best-arm identification in linear stochastic bandits.
method Developed the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits.
result Avoids the pitfall of a simple but difficult instance and bypasses the need to solve an optimal design problem.
Algorithm identifies best arm with biased proxy and selective ground truth audits.
problem Fixed-confidence best-arm identification with biased proxy and selective ground truth.
method Propensity-weighted estimator and adaptive auditing algorithm.
result Plug-in Neyman rule achieves near-oracle audit efficiency.
We present a new algorithm based on an gradient ascent for a general Active Exploration bandit problem in the fixed confidence setting. This problem encompasses several well studied problems such that the Best Arm Identification or Thresholding Bandits. It consists of a new sampling rule based on an online lazy mirror …
New algorithm for efficiently identifying the best arm in stochastic bandits.
problem Best arm identification in stochastic multi-armed bandits with fixed confidence.
method Sequential probability ratio tests for arm selection.
result Asymptotically optimal sample complexity and guaranteed δ−PAC performance. 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…
Improved best-arm identification in correlated multi-armed bandits.
problem Best-arm identification in multi-armed bandits with correlated rewards.
method Proposed C-LUCB algorithm that exploits upper bounds on conditional rewards.
result Significant reduction in sample complexity for best-arm identification.
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.
New policy combines Thompson sampling with best challenger rule for best arm identification.
problem Best arm identification in bandit framework with fixed confidence.
method Combines Thompson sampling with best challenger rule.
result Asymptotically optimal for any two-armed bandit problems, near optimal for general K-armed bandit problems.
New algorithm identifies best arm efficiently in stochastic bandits.
problem Efficiently identifying the best arm in stochastic bandits with optimal performance.
method Develops a computationally efficient algorithm for optimal best arm identification.
result Achieves optimal performance with minimal computational complexity.
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.
Algorithm identifies best arm in combinatorial bandits with semi-bandit feedback.
problem Identifying the best arm in combinatorial bandits with semi-bandit feedback.
method Interpreted as a sequential zero-sum game, developed a CombGame meta-algorithm with finite time guarantees.
result First computationally efficient algorithm that is asymptotically optimal and has competitive empirical performance.
Algorithm identifies the best arm in linear bandits with high probability.
problem Best arm identification in linear multi-armed bandits with noisy measurements.
method Phased Elimination Linear Exploration Game (PELEG) using no-regret learners.
result PELEG achieves sample complexity matching lower bounds.
New algorithm reduces sample complexity for multi-task bandits.
problem Optimizing representation and predictor pairs for multi-task bandits.
method OSRL-SC algorithm with sample complexity H(Glog(1/δG)+Xlog(1/δH)). result OSRL-SC algorithm approaches sample complexity lower bounds.
The paper addresses privacy-preserving BAI in clinical trials and user studies.
problem Privacy-preserving Best Arm Identification in adaptive clinical trials and user studies.
method The paper derives lower bounds on sample complexity for BAI algorithms with differential privacy constraints and proposes private variants of Top Two algorithms.
result Private variants of Top Two algorithms achieve asymptotic optimality in terms of sample complexity for BAI problems under differential privacy constraints.
New policy minimizes error in finding best arm with privacy constraints.
problem Best arm identification with differential privacy constraints.
method Maximum absolute determinants principle for ε-DP policy. result Error probability decays exponentially in T with matching exponents. Improved elimination strategies for adaptive bandit identification reduce sample complexity and computational burden.
problem Inefficient elimination strategies in bandit identification.
method Adaptive elimination methods that update sampling rules frequently and reduce problem size.
result Adaptive elimination methods achieve better sample complexity and computational efficiency.
Improved BAI under DP reduces gap to constant.
problem Fixed-confidence BAI under global DP for Bernoulli distributions.
method New lower bound, stopping rule, and Top Two sampling rule.
result Reduces gap to a small multiplicative constant.
New algorithm reduces sample complexity for Top Two method.
problem Fixed-confidence best arm identification for Top Two methods.
method UCB-based Top Two algorithm for non-asymptotic analysis.
result First non-asymptotic upper bound on expected sample complexity.
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.