Study best arm identification with contextual info, achieving optimal misidentification probability.
problem Identify the best treatment arm with minimal misidentification probability in a small gap scenario.
method Developed RS-AIPW strategy that matches lower bound of misidentification probability in the small-gap regime.
result RS-AIPW strategy is asymptotically optimal for best arm identification.
New strategy optimally identifies best arm in unknown variance Gaussian bandits.
problem Identifying the best arm in two-armed Gaussian bandits with unknown variances.
method Proposes a Neyman Allocation (NA)-Augmented Inverse Probability weighting (AIPW) strategy to estimate variances and draw arms adaptively.
result Demonstrates asymptotic optimality of the proposed strategy in the small-gap regime.
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.
Bayesian algorithm improves best-arm identification within fixed budget.
problem Maximizing probability of identifying optimal arm within fixed budget.
method Proposes Bayesian elimination algorithm and derives upper bound on misidentification probability.
result Upper bound on misidentification probability reflects prior quality and matches lower bound.
A novel algorithm reduces communication costs in federated best arm identification.
problem Identifying the best arm in a federated multi-armed bandit setup with minimal communication cost.
method Proposes a novel algorithm called FedElim that communicates only in exponential time steps.
result Demonstrates that communication is almost cost-free in FedElim, with a total cost at most 3 times the maximum under its variant.
Study best arm identification with limited precision sampling in bandits.
problem Limited precision sampling in multi-armed bandit problems.
method Proposed a modified tracking-based algorithm to handle non-unique optimal allocations and presented non-asymptotic bounds.
result Asymptotically optimal tracking-based algorithm for best arm identification.
Study best arm identification in restless Markov multi-armed bandits with state-dependent transitions.
problem Identify the best arm in a multi-armed bandit with time-varying states.
method Propose a sequential policy to select arms without knowing their exact TPMs.
result Upper and lower bounds on expected time to find the best arm match in a special case.
The paper develops a theory for identifying the best arm in non-parametric multi-armed bandits with a fixed budget.
problem Identifying the best arm in non-parametric multi-armed bandits with a limited number of trials.
method The paper proposes upper and lower bounds on the average log-probability of misidentification using information-theoretic quantities and a refined analysis of the successive-rejects strategy.
result The paper provides new upper and lower bounds on the average log-probability of misidentification, which generalize existing bounds.
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 \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…
Optimal strategy found for identifying best arm in bandits with small gap.
problem Best arm identification in two-armed bandits with a fixed budget and small gap.
method Neyman allocation rule augmented with inverse probability weighting.
result Proposed strategy is asymptotically optimal when gap is small.
Study optimizes identifying the best arm with fixed rounds and Gaussian outcomes.
problem Designing efficient experiments to identify the best arm with fixed rounds and Gaussian outcomes.
method Developed worst-case lower bounds and the GNA-EBA strategy for optimal identification.
result GNA-EBA strategy is asymptotically worst-case optimal.
Improved knowledge gradient (iKG) outperforms the original KG algorithm in best arm identification problems.
problem Best arm identification (BAI) problem with limitations of the original KG algorithm.
method Follows the one-step look ahead of KG but chooses the measurement that maximizes the probability of selecting the best arm.
result Improved knowledge gradient (iKG) is asymptotically optimal and easier to extend to variant BAI problems.
Opt-BBAI identifies the best arm with minimal batches and pulls, optimizing both sample and batch complexity.
problem Batched best arm identification (BBAI) problem, aiming to minimize policy switches and resource usage.
method Proposed Opt-BBAI algorithm, achieving near-optimal sample and batch complexity in non-asymptotic settings.
result First algorithm to achieve near-optimal sample and batch complexity in non-asymptotic settings.
Optimal top-2 method improves best arm identification with reduced error.
problem Identifying the arm with the highest mean in a set of arms.
method A novel top-2 algorithm that pulls the empirical best arm with probability β and the challenger arm otherwise.
result The proposed algorithm matches the information theoretic lower bound on sample complexity as δ approaches 0.
New algorithm finds best feasible arm in grouped bandits.
problem Finding the best arm with all attributes above a threshold.
method Feasibility Constrained Successive Rejects (FCSR) algorithm.
result FCSR identifies the best feasible arm with optimal dependence on problem parameters.
Improved adaptive algorithms for identifying the best arm in MABs with fixed budget.
problem Identifying the best arm in stochastic Multi-Armed Bandits with a fixed sampling budget.
method Established a connection between Large Deviation Principles and adaptive algorithms, improving error probability bounds and devising new algorithms.
result The \sred algorithm outperforms existing algorithms in identifying the best arm.
Optimizes identifying the best arm with fixed samples.
problem Finding the arm with the highest mean in a fixed number of samples.
method Characterizes minimax optimal rates and introduces algorithms to achieve them.
result Characterizes and introduces algorithms for optimal 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.
Motivated by drug design, we consider the best-arm identification problem in generalized linear bandits. More specifically, we assume each arm has a vector of covariates, there is an unknown vector of parameters that is common across the arms, and a generalized linear model captures the dependence of rewards on the cov…
A novel algorithm for best-arm identification in non-stationary linear bandits reduces error probability.
problem Non-stationary environments in A/B testing scenarios.
method Proposes a novel algorithm P1-RAGE for robust best-arm identification. result Error probability decreases as exp(−TΔ(1)2/d), demonstrating robustness to non-stationarity. Paper tackles best mixed arm identification with cost constraints in bandit models.
problem Finding the best mixed arm with cost constraints in a stochastic bandit model.
method Proposes SFSR algorithm combining successive reject and score-function-based rejection criteria.
result Upper and lower bounds on mis-identification probability show exponential decay with budget.
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. Box Thirding identifies the best arm efficiently under limited samples.
problem Efficiently identifying the best arm with limited sampling.
method Iterative ternary comparison of arms, discarding the weakest and exploring the best.
result Achieves comparable performance to Successive Halving with less predefined parameters.
New algorithm identifies best arm in non-stationary linear bandits with improved complexity.
problem Best arm identification in non-stationary linear bandits with adversarial parameters.
method Proposed Adjacent-optimal design and extsfAdjacent−BAI algorithm. result Error probability matches arm-set-dependent lower bound up to constants.
New algorithm identifies best target arm with known additive relationship between source and target MAB instances.
problem Identifying the best arm in a target MAB instance when only source arms can be pulled and there's a known additive relationship between the two.
method Proposes an LUCB-style algorithm to identify an ε-optimal target arm with high probability.
result Theoretical analysis highlights aspects of the transfer learning problem and recovers the LUCB algorithm for single domain BAI as a special case.
This paper studies active learning in the context of robust statistics. Specifically, we propose a variant of the Best Arm Identification problem for \emph{contaminated bandits}, where each arm pull has probability ε of generating a sample from an arbitrary contamination distribution instead of the true und…
New algorithm identifies best arm in rare event scenarios.
problem Identifying the best arm with tiny reward probability.
method Approximated Compound Poisson process for faster algorithms.
result Improved computational efficiency with minor sample complexity increase.
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.
A two-phase algorithm identifies the best arm in sparse linear bandits with fixed budget.
problem Best arm identification in sparse linear bandits with limited budget.
method Lasso and Optimal-Design (Lasso-OD) based linear best-arm identification.
result Lasso-OD achieves significant performance improvement for sparse and high-dimensional linear bandits.
GNA optimally identifies the best arm with small gaps.
problem Best arm identification in fixed-budget settings.
method Generalized Neyman Allocation (GNA) for asymptotically locally minimax optimal BAI.
result GNA's worst-case bounds match the lower and upper bounds in the small-gap regime.
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. Optimal algorithm identifies best arm for risk measures in heavy-tailed distributions.
problem Identifying the arm with smallest CVaR, VaR, or weighted sum of CVaR and mean from heavy-tailed distributions.
method Multi-armed bandit best-arm identification framework, solving non-convex optimization problem.
result Optimal δ-correct algorithm with matching lower bound on expected samples.
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.
A new algorithm for identifying the best arm in linear feedback with safety constraints.
problem Identifying the best arm in linear feedback with safety constraints.
method A gap-based algorithm that ensures safety while minimizing sample complexity.
result The algorithm achieves meaningful sample complexity while ensuring safety.
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.
Algorithm identifies best arm in bandit game with variance consideration.
problem Identifying the best arm in a stochastic multi-armed bandit game with varying variances.
method Adaptive algorithm using grouped median elimination to explore gaps and variances.
result Guarantees to output the best arm with probability (1-δ) using optimal number of samples.
Adaptive algorithm identifies best arm with abstention, showing phase transition from polynomial to exponential error probability.
problem Bayesian best-arm identification with abstention to reduce undetected error.
method Adaptive algorithm PGWS that optimally uses abstention budget.
result Introducing any positive abstention budget induces an exponential decay in undetected error probability.
New algorithms improve best-arm identification with varying rewards.
problem Identifying the best arm with varying reward variances in fixed budget.
method Proposed two algorithms: SHVar for known variances, SHAdaVar for unknown variances; uses non-uniform budget allocation.
result Bounding misidentification probabilities for both algorithms.
Optimal strategy identified for minimizing regret in fixed-budget best arm selection.
problem Minimizing expected simple regret in fixed-budget best arm selection.
method Two-Stage (TS)-Hirano-Imbens-Ridder (HIR) strategy using HIR estimator.
result TS-HIR strategy is asymptotically minimax optimal.
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.
While the objective in traditional multi-armed bandit problems is to find the arm with the highest mean, in many settings, finding an arm that best captures information about other arms is of interest. This objective, however, requires learning the underlying correlation structure and not just the means of the arms. Se…
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.
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.
Algorithm identifies best arm in piecewise stationary linear bandits with minimal samples.
problem Identifying the best arm in a piecewise stationary linear bandit model with unknown contexts and changepoints.
method Design of PSεBAI+ algorithm, consisting of PSεBAI and NεBAI subroutines. result PSεBAI+ achieves optimal sample complexity up to a logarithmic factor. Given a vector of probability distributions, or arms, each of which can be sampled independently, we consider the problem of identifying the partition to which this vector belongs from a finitely partitioned universe of such vector of distributions. We study this as a pure exploration problem in multi armed bandit sett…
Efficiently identifies best algorithms for game tasks.
problem Selecting optimal algorithms for game tasks efficiently.
method Best arm identification for multi-armed bandits with confidence intervals.
result Significantly improved performance in simple regret and error probability.
New research shows fixed-budget best-arm identification cannot match static oracle performance.
problem Fixed-budget best-arm identification's performance limitations.
method Analysis of various adaptive and static algorithms for best-arm identification.
result For any algorithm, there exists at least one instance where the error decay rate is at most \((1 + \frac{\log(K)}{8})^{-1}\) times that of the static oracle.